High Energy Physics in Underground Labs

Advances in High Energy Physics

Guest Editors: Bogdan Mitrica, Maury Goodman, and Jacek Szabelski High Energy Physics in Underground Labs Advances in High Energy Physics

This is a special issue published in “Advances in High Energy Physics.” All articles are open access articles distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Editorial Board

Botio Betev, Switzerland J. Gracey, UK Ira Rothstein, USA P. J. Bussey, UK Hong-Jian He, China Kate Scholberg, USA Duncan L. Carlsmith, USA Ian Jack, UK Frederik Scholtz, South Africa Kingman Cheung, Taiwan Ashutosh V. Kotwal, USA George Siopsis, USA S. H. Dong, Mexico Pietro Musumeci, USA Terry Sloan, UK Edmond Craig Dukes, USA Piero Nicolini, Germany Neil Spooner, UK Paula Eerola, Sweden Seog H. Oh, USA Luca Stanco, Italy Amir H. Fatollahi, Iran Dugan O’Neil, Canada Elias C. Vagenas, Greece Frank Filthaut, The Netherlands Sandip Pakvasa, USA Nikos Varelas, USA Joseph Formaggio, USA Manfred Paulini, USA Kadayam Viswanathan, Canada Chao-Qiang Geng, Taiwan Anastasios Petkou, Greece YauW.Wah,USA Cecilia Gerber, USA Alexey A. Petrov, USA Contents

High Energy Physics in Underground Labs, Bogdan Mitrica, Maury Goodman, and Jacek Szabelski Volume 2013, Article ID 180610, 2 pages

Cosmic Muon Detection for Geophysical Applications,Laszl´ oOl´ ah,´ Gergely Gabor´ Barnafoldi,¨ Gergo˝ Hamar, Hunor Gergely Melegh, Gergely Suranyi,´ and DezsoVarga˝ Volume 2013, Article ID 560192, 7 pages

A Mobile Detector for Muon Measurements Based on Two Diﬀerent Techniques,B.Mitrica,D.Stanca, M. Petcu, I. M. Brancus, R. Margineanu, A. Apostu, C. Gomoiu, A. Saftoiu, G. Toma, H. Rebel, A. Haungs, O. Sima, A. Gherghel-Lascu, and M. Niculescu-Oglinzanu Volume 2013, Article ID 256230, 7 pages

Charge Coupled Devices as Particle Detectors, Dan A. Iordache, Paul E. Sterian, and Ionel Tunaru Volume 2013, Article ID 425746, 12 pages

Precise 3D Track Reconstruction Algorithm for the ICARUS T600 Liquid Argon Time Projection Chamber Detector, M. Antonello, B. Baibussinov, P. Benetti, E. Calligarich, N. Canci, S. Centro, A. Cesana, K. Cieslik, D. B. Cline, A. G. Cocco, A. Dabrowska, D. Dequal, A. Dermenev, R. Dolﬁni, C. Farnese, A. Fava, A. Ferrari, G. Fiorillo, D. Gibin, S. Gninenko, A. Guglielmi, M. Haranczyk, J. Holeczek, A. Ivashkin, J. Kisiel, I. Kochanek, J. Lagoda, S. Mania, A. Menegolli, G. Meng, C. Montanari, S. Otwinowski, A. Piazzoli, P. Picchi, F. Pietropaolo, P. Plonski, A. Rappoldi, G. L. Raselli, M. Rossella, C. Rubbia, P. Sala, A. Scaramelli, E. Segreto, F. Sergiampietri, D. Stefan, J. Stepaniak, R. Sulej, M. Szarska, M. Terrani, F. Varanini, S. Ventura, C. Vignoli, H. Wang, X. Yang, A. Zalewska, and K. Zaremba Volume 2013, Article ID 260820, 16 pages

The Structure of an Automatic Decision System for a Large Number of Independent Particle Detectors, Andreea Rodica Sterian Volume 2013, Article ID 839570, 6 pages

Site Assessment for Astroparticle Detector Location in Evaporites of the Polkowice-Sieroszowice Copper Ore Mine, Poland, Jaroslaw Slizowski, Zenon Pilecki, Kazimierz Urbanczyk, Elzbieta Pilecka, Leszek Lankof, and Rafal Czarny Volume 2013, Article ID 461764, 12 pages

Classic (Nonquantic) Algorithm for Observations and Measurements Based on Statistical Strategies of Particles Fields, D. Savastru, Simona Dontu, Roxana Savastru, and Andreea Rodica Sterian Volume 2013, Article ID 876870, 11 pages

Realistic Approach of the Relations of Uncertainty of Heisenberg, Paul E. Sterian Volume 2013, Article ID 872507, 7 pages

Simulations of Muon Flux in Slanic Salt Mine, Mehmet Bektasoglu, Halil Arslan, and Denis Stanca Volume 2012, Article ID 751762, 8 pages

Status and New Data of the Geochemical Determination of the pp-Neutrino Flux by LOREX, M. K. Pavicevi´ c,´ F. Bosch, G. Amthauer, I. Anicin,ˇ B. Boev, W. Bruchle,¨ V. Cvetkovic,´ Z. Djurciˇ c,´ W. F. Henning, R. Jelenkovic,´ V. Pejovic,´ and A. Weiss Volume 2012, Article ID 274614, 15 pages Exclusive Reconstruction of B-Decays with Missing Neutrals,M.Dima Volume 2012, Article ID 123083, 8 pages

Perspectives on Entangled Nuclear Particle Pairs Generation and Manipulation in Quantum Communication and Cryptography Systems,OctavianDanil˘ a,˘ Paul E. Sterian, and Andreea Rodica Sterian Volume 2012, Article ID 801982, 10 pages Hindawi Publishing Corporation Advances in High Energy Physics Volume 2013, Article ID 180610, 2 pages http://dx.doi.org/10.1155/2013/180610

Editorial High Energy Physics in Underground Labs

Bogdan Mitrica,1 Maury Goodman,2 and Jacek Szabelski3

1 Horia Hulubei National Institute for Physics and Nuclear Engineering, 077125 Magurele, Romania 2 Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439-4803, USA 3 National Centre for Nuclear Research, Ulica Uniwersytecka 5, 90-137 Lodz, Poland

Correspondence should be addressed to Bogdan Mitrica; [email protected]

Received 9 May 2013; Accepted 9 May 2013

Copyright © 2013 Bogdan Mitrica et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The field of high energy physics covers a large area of The paper entitled “The structure of an automatic decision modern research, such as astrophysics, cosmic rays, neutrino system for a large number of independent particle detectors” by oscillations, dark matter, and cosmology. In order to sup- A.R.Sterianpresentsastatisticalmodelforsignalprocessing press backgrounds, many modern experiments are located and sampling in the case of a large number of independent in underground sites around the world: Fermilab (USA), particle detectors (LNIPDs). An automatic decision system Kamioka (Japan), Gran Sasso (Italy), and others. Some mod- hasbeenanalysed,anditisestimatedthatitcouldbeusedfor ern experiments are now running: Super-Kamiokande, T2 K a large number of modern experiments. (Japan), MINOS (USA), and so forth. Others are in devel- In the paper “Site assessment for astroparticle detector opment: LBNE, LAGUNA, Hyper-Kamiokande, INO, and so location in evaporites of the Polkowice-Sieroszowice copper ore forth. mine, Poland,” J. Slizowski et al. present an evaluation of This special issue brings together information and new the possibility to excavate a large underground camera for data from the modern underground experiments all over the the GLACIER detector as part of the LAGUNA study. The world and covers a large number of related subjects such as authors show that the Polkowice-Sieroszowice copper ore dark energy, neutrino oscillations, underground research fa- mine, Poland, is a realistic location for a GLACIER type de- cilities, very large underground detectors, and modern tech- tector. niques in particle detection. This special issue covers issues In the article “Classic (nonquantic) algorithm for obser- related to both theoretical and experimental aspects of these vations and measurements based on statistical strategies of problems. particles fields” by D. Savastru et al., some algorithms for In the paper “Charge coupled devices as particle detectors,” selection and estimation based on statistical hypothesis have D. A. Iordache et al. present a theoretical contribution about been investigated. A new algorithm is presented in detail and charge coupled devices which can be used as particle detec- can be used for astroparticle detection. tors. A new and improved dark current spectroscopy (DCS) The paper “Realistic approach of the relations of uncer- method brings us new information regarding the semicon- tainty of heisenberg,” by P. E. Sterian treats an important ductor particle detectors. theoretical problem regarding the Heisenberg’s uncertainty in In the paper “Precise 3D track reconstruction algorithm the view of modern experiments. The article brings an origi- for the ICARUS T600 liquid argon time projection chamber nal and new idea about the quantum problem of simultaneous detector,” M. Antonello et al. present the status and quality of measurements of position and momentum. the Lar TPC detectors during the ICARUS T600 operation. In the research article “Simulations of muon flux in Proposed by C. Rubbia, the Lar TPC detector idea brings Slanic salt mine” by M. Bektasoglu et al., new Monte Carlo a new method for spatial and calorimetric measurement of simulation results regarding the directional muon flux in charged particle interactions. the underground Slanic Prahova salt mine are presented. 2 Advances in High Energy Physics

The simulations are based on GEANT 4 code and take into consideration a realistic topography of the mine. The resulting code is an important tool for anyone interested in the area of underground muon flux research. The article entitled “Status and new data of the geochemical determination of the pp-neutrino flux by LOREX” by M. K. Pavicevi´ c´ et al. shows the state of the art for LORandite EXperiment (LOREX). The paper presents the latest results and the future plans for this experiment. The paper “Exclusive reconstruction of 𝛽-decays with missing neutrals” by M. Dima treats a modern and important problem of 𝛽-decays based on a new way to investigate momentum conservation. The method can be used also for other particle physics experimens. The article “Perspectives on entangled nuclear particle pairs generation and manipulation in quantum communication and cryptography systems” by O. Danil˘ aetal.isfocusedonthe˘ problem of the two quantum elements phenomenon which canbeusedforquantumcryptographyandphysicalcharac- terization of the universe. In the research article “A mobile detector for muon measurements based on two different techniques” by B. Mitrica et al., measurements of the underground muon flux performed with a mobile detector are presented. Two possible configurations using wavelength shifters and PMTs and optical fibers which are then read out by a single PMT are presented. Results obtained with both configurations were compared. The paper “Cosmic muon detection for geophysical applications” by L. Olah´ et al. presents a possible direct application of muon flux measurements focused issues related to the geophysical investigation of mountains. The papers included in this special issue cover a small number of the diverse issues faced by underground experiments. The theoretical and experimental issues covered here will impact the future of particle physics and lead to further studies that help us understand the constituents of the universe. Bogdan Mitrica Maury Goodman Jacek Szabelski Hindawi Publishing Corporation Advances in High Energy Physics Volume 2013, Article ID 560192, 7 pages http://dx.doi.org/10.1155/2013/560192

Research Article Cosmic Muon Detection for Geophysical Applications

László Oláh,1,2 Gergely Gábor Barnaföldi,2 Gergy Hamar,2 Hunor Gergely Melegh,3 Gergely Surányi,4 and Dezsy Varga1

1 Department of Physics of Complex Systems, Eotv¨ os¨ University, 1/A Pazm´ any´ P. set´ any,´ 1117 Budapest, Hungary 2 Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, 29-33 Konkoly-Thege Miklos´ Street, 1121 Budapest, Hungary 3 Budapest University of Technology and Economics, 3-9 Muegyetem˝ rkp., 1111 Budapest, Hungary 4 Geological, Geophysical and Space Science Research Group of the HAS, Eotv¨ os¨ University, 1/C Pazm´ any´ P. set´ any,´ 1117 Budapest, Hungary

Correspondence should be addressed to Laszl´ oOl´ ah;´ laszlo.olah@cern.ch

Received 5 January 2013; Accepted 31 March 2013

Academic Editor: Jacek Szabelski

Copyright © 2013 Laszl´ oOl´ ah´ et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

A portable cosmic muon detector has been developed for environmental, geophysical, or industrial applications. The device is a tracking detector based on the Close Cathode Chamber, an MWPC-like technology, allowing operation in natural underground caves or artificial tunnels, far from laboratory conditions. The compact, low power consumption system with sensitive surface of 2 0.1 m measures the angular distribution of cosmic muons with a resolution of 10 mrad, allowing for a detailed mapping of the rock thickness above the muon detector. Demonstration of applicability of the muon telescope (REGARD Muontomograph) for civil engineering and measurements in artificial underground tunnels or caverns are presented.

1. Introduction Muon tomography and radiography detectors are usually trackers, which record the direction of the incoming muons Cosmic accelerators provide the highest energy particles with sufficient precision. Our portable Muontomograph isa which continually hit our Earth. These primary particles are trackingdetectoraswell,similartothatusedinhigh-energy mostly protons and He nuclei which strongly interact with physics laboratories. However, the design was especially nuclei (N, O, He, etc.) of the upper atmosphere and generate developed and built for geophysical applications with the secondary particle showers at an altitude of typically 20– main emphasis on power efficiency, durability, and portability 30 km. Secondary particles at the end of the decay chains are [5, 6]. These features are providing the possibility of tomo- mostly muons, highly penetrating charged particles, which graphic mapping of rock thickness by measuring the angular can reach the surface of the Earth and enter to underground. distribution of cosmic muons from an observation point well Since the middle of 𝑋𝑋th century, cosmic muons have below the structures to be investigated. been measured extensively and applied for geophysical The present paper introduces the basic structure of the [1], archaeological [2], geological [3], and speleological [4] REGARD (Eotv¨ os¨ Lorand´ University and Wigner RCP col- researches. All these kinds of measurements are based on laboration for R&D of gaesous detectors) Muontomograph, the energy loss of high-energy particles—mainly muons with a portable and durable tracking-detector based on Close cosmic origin—in matter. Since the muon flux is steeply Cathode Chamber (CCC) technology [7, 8]. An industrial decreasing as a function of the energy, therefore passed (civil engineering) application is described: surveying an matter above the detector modifies the threshold energy for unmapped artificial cavern system inKob˝ anya,´ Budapest, the detectable particles and correspondingly the flux. Due to Hungary. The angular distribution of high-energy cosmic this fact, the measured muon flux correlates with the density muons was measured, analysed, and compared to the rock length of traversed material, which is the key issue in the thickness above the detector measured by high-precision aforementioned various applications. GPS. 2 Advances in High Energy Physics

Front-end electronics Aluminium frame 51 cm Chambers: MT4 Gas reductor MT5 Gas in 15 cm

32 cm MT6 MT7 17.5 cm 80 cm Battery 12 V/50 Ah Gas out DAQ: 17.5 cm Gas ﬂow regulator LV and HV modules 46 cm 20.7 cm trigger unit HMI: Bottle: Ar + CO2: 10 L (150 bar) 2 buttons control the detector SD card storages the data (a) (b)

Figure 1: The layout and structure of the REGARD Muontomograph, including the power supply (a) and the gas system (b) based on[5, 6].

2. Structure of the Muontomograph proportional chamber, where the lower cathode plane (on ground potential) is much closer to the wire plane than the During the design of the detector, our aim was to optimize upper cathode plane as plotted on Figure 2(b).Thereare the sometimes contradicting aspects of effective sensitive two types of wires forming the proper electric field in the surface, angular resolution, detection efficiency, portability chamber: 21 𝜇m sense (anode) wires and 100 𝜇mfieldshaping (weight, resistance to mechanical shocks), resistance to high wires with 2 mm distance between them. The lower cathode humidity, low power consumption, and cost efficiency. The is segmented into 4 mm wide strips (pads) perpendicular to final design of the REGARD Muontomograph turned outto thewires.Thedistancebetweenthewireplaneandthecloser be well adapted for the experimental purposes mentioned pad plane is 1.5 mm, the total thickness of the sensitive gas 2 before. volume is 10 mm, and the area is 320 × 320 mm . The electric field within the chamber was obtained from 2.1. The Basic Detector Outline. The most substantial param- simulations, shown in Figure 2(a). The individual field wires eter of a cosmic muontomograph is the sensitive surface of as well as the pads are simultaneously read out by high- the detector. gain front-end electronics, which provides two-dimensional In order to acquire the best statistics during the shortest position information about the muon hits in each layer—as possible measurement period, the surface of the cosmic ray clusters. detectors needs to be maximized. On the other hand, overly In contrast to traditional Multiwire Proportional Cham- largesizeisprohibitiveifactuallysomeonewouldliketo bers (MWPCs), the CCC structure does not require weighty measure the interior of unexplored underground places, such outer support frames (see Figure 3), which is the key advan- as natural caves or artificial channels which may be diffi- tage in sense of portability. The chosen detector technology cult to access. These places require human handling of the therefore optimizes weight, position resolution, and effi- equipments, which limits size and weight of a detector. In ciency aspects. This specific version of MWPC-like layout has our case, the size of the detector was designed to fit into advantage in high tolerance against the mechanical inaccura- the caverns of the Ajand´ ek´ Cave, Pilis, Hungary, described cies (100–200 𝜇m)andotherinfluencessuchasvibrationsand in [5, 6]. The detector can be safely handled manually by a 3 shocks during transfer to deployment position. single person: size of the final system is 51×46×32 cm ,with The detector system, similarly to most gaseous tracking totalweightofabout13kg.Themuontelescopeishousedin detectors, requires continuous gas flow during data taking. a plexiglass box, which, besides giving mechanical support, Inourcase,thegasisanonflammablemixtureofArand provides environmental isolation as well. CO2 in 82 : 18 proportion. As presented on Figure 1(b),the gas after pressure reduction goes into the flow regulator and 2.2. The CCC Detector Layers. The Muontomograph consists flow meter first and then enters the CCC chamber volumes of four parallel sensitive detector layers of Close Cathode sequentially from top to bottom. Before the exhausting, Chambers (CCC), denoted by “MT4,” “MT5,” “MT6,” and the gas is redirected into the plexiglass housing box in “MT7” as in Figure 1 from top to bottom. The detector lay- order to reduce the inner humidity by 30–50%. During the ers have been instrumented with segmented cathode and measurements in the Kob˝ anya´ tunnel system, a standard 10- sensitive field-shaping wire structure as shown in Figure 2. liter bottle (with 150 bar filling pressure) was sufficient for 20 The Close Cathode Chamber is an asymmetric multiwire days of continuous operation at ∼3l/hflow. Advances in High Energy Physics 3

7 complete Muontomograph system, including all subunits, 6 does not exceed 380 mA, which is maximal while writing the SDcard.Weusedastandard50Ahbatterywhichallowedthe 5 detectortorunforuninterruptedperiodsofmorethan5days. 4 The interconnected anode wire signals from the CCC layers were exploited to form the DAQ trigger. This means that (mm) 3 no additional subdetectors were needed (e.g., a pair of scin- 2 tillator planes) which would add weight and power consumption. A coincidence circuit has been implemented into 1 the trigger module of the DAQ, which provides the trigger 0 condition: the coincidence of one of the upper two and one 012345678910 of the lower two chambers [5]. (mm) The individual field wire and pad signals (carrying the (a) position information) were amplified and discriminated by Cathode CMOS-based front-end electronics (FEEs). The FEEs receive the trigger signal from the DAQ and store the bits in shift reg- 𝑠 (4 mm)

mm isters. FEEs are connected in series, which allows the multi- 10

mm) plexed data readout through a single data line. One event 2

– contains 640 bits. 1.5

( The processor also monitors the analogue environmental 𝑑 Field wires Sense wires parameters (humidity, temperature, and pressure) event-by- PCB baseplate (on ground) event, allowing the reconstruction of the whole timeline of each measurement. The recorded data are written to a stan- (b) dard SD (Secure Digital) card. For example, a single portable Figure 2: (a) The electric field in a Close Cathode Chamber, based memory card of 2 GB capacity enables approximately a full on simulation. (b) The inner structure of a CCC chamber in a cross year of measurement time in 50-meter rock-equivalent depth. section [7, 8]. 2.4. Offline Data Analysis. Standard high-energy physics procedures have been used in the offline data analysis. The analysis initiates with the alignment of the CCC layers. Event- by-event (track-by-track) analysis procedures have been performed independently for the two (pad and field wire) directions.Theparticlehitsarefoundbyaclusterfinding algorithm. Typical cluster sizes (the number of adjacent fired pads or field wires) are 2–4, which are corresponding 8– 16 mm cluster widths. The noisy pads and field wires (less than Figure 3: Photo of the inner pad and wire structure of a Close 1% in fraction) have been excluded from further analysis. Cathode Chamber. Straight line particle trajectories are found by a combina- torial tracking algorithm. Multiple tracks were rare (<2%) in the underground sample and have been neglected for further 2.3. Data Acquisition System. APIC32microcontroller-based analysis. The slope of the tracks with the necessary acceptance data acquisition (DAQ) system was applied in the Muonto- and efficiency corrections have been applied for cosmic muon 3 mograph, which is a small size (12×8×8cm ) unit between flux calculation (see more in5 [ ]). the middle CCC layers, as drawn in Figure 1.Themainfunc- A Monte Carlo simulation has been designed to study tions are integrated into a common system plan (see Figure specific capabilities and limitations of the detector system, 4). Three main modules are distinguished: a processor board such as efficiency loss (local or overall), position resolution, (motherboard) controls the data acquisition, including the or noise effects (clusters or individual noisy channels). The low-voltage power system (LV), a high-voltage module (HV) simulation confirms that the noise has little (<1%) systematic to operate the chambers, and the Human-Machine Interface effect on tracking performance, and it also provides a reliable block (HMI) for maintenance and data storage access. angular resolution estimation of 11 mrad, which is close to The high-voltage parts are housed in a separated board the value extracted from data directly [5]. Such angular res- with appropriate protection against electric shocks. Two olution corresponds to a well-resolved cavity of 1 m diameter HV lines are supplying the chambers with typical values of seen from 50-meter distance. +1100 Vand−600 V. The low-voltage power supply of the auxiliary electronics, the trigger subsystem, and the environ- 3. Geophysical and Industrial Applications mental sensors were placed on the processor board near the PIC32 type microcontroller. The detector is supplied In this section, we present how the REGARD Muonto- through a single line, nominally at 12 V DC. Based on mograph can be used in geophysical, civil engineering, or direct measurements, the total current consumption of the industrial applications. These cases all require to place the 4 Advances in High Energy Physics

SD card LCD display Button bit 4 RS EN R/W CD WP D5V D3V3 DGND DGND SPI BUS SPI Data

PW Trigger 4 bit 12 V

Trigger Power AN system system A3V3 SE load register AGND

Data 2 CLK I C D3V3 DGND Threshold

UART Detector Processor H5V Sensors HGND JTAG ICSP

u-Dat v1.0

High-voltage High-voltage 12 V on/off monitor HV+ HGND High-voltage HV−

Figure 4: The schematic plan of the electronics system of the Muontomograph, including data acquisition, low- and high-voltage power system, and Human-Machine Interface block (LCD display, control buttons, and SD card access) [5, 6]. detector under the would-be-observed area, which imme- test the applicability of the muon telescope for civil engineer- diately turns our attention to underground objects such as ing. Here we investigated a poorly mapped, Swiss-cheese-like −3 channel networks, caves and caverns, artificial tunnels, or underground structure of an urban area with 1.8 ± 0.1 g cm large-scale buildings. Here we present test measurements in averagerockdensity,whichmightbedangerousinsenseof the artificial tunnel system in Kob˝ anya,´ Budapest, Hungary, urban planning and recultivation as well as for developments. with the aim to demonstrate the evidence for a clear corre- In this section, we will show evidence that in finding hidden lation between underground tunnel and vent structures and caverns the muon tomography is a complementary method local cosmic muon flux. relative to standard geophysical measurements in disturbed, noisy, urban areas. 3.1. Measurement of Cosmic Muon Angular Distribution. The The in-use artificial tunnels at some places are equipped with air-flow systems, which are vertical (zenith) tunnels with cosmic muon flux has been measured at different depths asa 1 function of the zenith angles. The boxlike detector geometry mdiameterand10–20mlengthandopentoskyatthe implies a “natural” coordinate system along the detector axis, zenith direction. Here, as a known tunnel, the large-scale which has been translated to the usual angular variables, tak- soil inhomogeneities can be tested by such holes. However, ing into account a correction for the angle-dependent detec- we note that, under the local area of the blowholes, there tor effective surface (acceptance). may be further, unknown, nonhomogeneous rock structures. The measured muon yield at a given rock thickness Three measurements have been done approximately at the (assuming homogeneous soil) can be correlated with the same depth relative to the ground level (15–20 m, whereas the geometrical data measured by a high precision GPS device. rock thickness was reduced by the considerable height of the Inhomogeneities such as underground cavities will appear as tunnels), at different detector positions. These measurements excessfluxinthegivendirection. had the main purpose to test the surface reconstruction and/or estimate soil inhomogeneity.

3.2. Measurements in the Kob˝ anya´ Tunnel System. The main 3.2.1. Mapping a Narrow Blowhole. The first batch of mea- aim of our measurements in Kob˝ anya´ tunnel system was to surements was done with duration of about 1 week in the Advances in High Energy Physics 5

50 50 N N W E 16 40 W E 18 600 40 200 S 14 S 20 18 20 1000 1000 30 400 30 16 200 16 600 14 1400 400 400 20 14 16 12 20 20 600 600 18 18 14 800 12 14

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Figure 5: Measurements taken at Kob˝ anya´ at different places of the artificial tunnel. Upper row: Detector was exactly under the axis of the ∘ blow hole (a), 15 tilted detector at the same position (b), next to the wall of the tunnel (c), and the shifted detector position (d). Solid red lines are for the rock’s length to the given direction in angles; shading is for the muon distribution after geometrical correction.

3rd tunnel of the Kob˝ anya´ system. The detector was placed homogeneous rock structure with an average rock den- precisely under the axis of a vertical 1 m diameter tunnel open sity. to the sky, giving a large excess yield from the direction of The result of the measurement is shown in Figure 5(a). the zenith. During this measurement, 330 k muon tracks have The horizontal axis shows the West-East zenith angle, and the been detected by the Muontomograph. vertical axis shows the North-South zenith angle in degree Disregarding the hole, the shortest rock length was at units. Solid red lines indicate the calculated thickness of the the zenith direction with about 12 m length. Based on the soil/rock at given zenith/azimuth directions based on our knowledge on the local geological situation, we can assume local GPS measurements on the surface and the polygon 6 Advances in High Energy Physics method used under the ground. Solid topographical lines Table 1: The summary of the test measurements with the detector connect the points with the same thickness (disregarding the positions, depths, measurement times, and detected tracks. hole). The measured muon distribution is drawn at given Depth Time Detected tracks directions by topographical shading on the same plot. Both Detector position 3 meter day ×10 were generated by SURFER 9.0 [9]whichisastandard3D Exactly under a contouring and surface plotting program and both include 12 7 330 blowhole geometrical corrections. The calculated thickness of the rock ∘ Tilted with 15 under and the measured muon yield correlates well, and the open 12 7 225 ablowhole skyisseenasabrightspotattheorigin.(Notethattheinform- ation is contained in the appearance of the sharp maximum Next to a wall 12 6 220 2 meters far from a but not its peak flux, since not only the muon but also the 17 6 130 electron component is measured for the very small effective blowhole material at the zenith for this case.)

3.2.2. Tilted Measurement. Ameasurementwasperformedat ∼10–20 meter-rock-equivalent depths with relatively short the same detector position as the one presented in Section time duration, ∼1week(seeTable 1). 3.2.1. The duration of the data taking was about 1 week. ∼ 5∘ We note, however, that the results can be made more Here the Muontomograph was tilted with 1 from the conclusive and uncertainties of the estimated thickness zenith towards the South. The calculated rock thickness and reduced exploiting a real tomographic measurement—that measuredmuonfluxareshowninFigure 5(b) with the same is measurements from multiple points of view—for definite notations as before. localization of the small scale inhomogeneities. The tilt can be clearly seen in the upper panel of Figure 5(b) as the muon flux maximum, originating by the open sky ∘ from the hole, is shifted to the South with the expected ∼15 4. Summary and Conclusions in the coordinate system fixed to the detector. The paper presented the capabilities of the REGARD Muon- tomograph on measuring and determining rock inhomo- 3.2.3. Measurement Next to the Wall. The detector has been geneities. Several test measurements have been performed at placed as close as possible next to the sidewall of the approx- ∘ the tunnels of Kob˝ anya´ in an urban area under about 10–20- imately 6 m high tunnel, which is directed 205 compared meter rock equivalent. Muon tomography measurements can to North. Here we took data for about 1-week duration. In also be performed at larger depths, at the cost of increased Figure 5(c), GPS-data-based rock thickness is compared to measurement time due to the limited acceptance. As an the muon angular distribution (shaded). The correlation is example, about 7 weeks of measurement time provides 5% 2 strong between the GPS-based rock thickness and the muon precisionofthemuonfluxin70by70mrad angular bins, at flux. The direction of the tunnel is well visible. ∼60-meter rock equivalent depth; that is, a cavity of 3-meter size in all directions can be safely observed. One must also 3.2.4. Imaging a Shifted Blowhole. The measurement pre- note that the detection area of the present setup is typically sented in Figure 5(d) was taken in another cavern, (5th) of by an order of magnitude smaller than that of other recent the Kob˝ anya´ tunnel system with the blowhole horizontally realizations with scintillator technology [9], and furthermore, shifted about 2 mawayfromtheverticalaxisoftheMuon- the choice of MWPCs requires a gas supply. However, the tomograph. This data recording took 6 days. The Muonto- reliable tracking performance, low power consumption, and mograph was placed at the same depth as earlier measure- the fair angular resolution, which may be a challenge for ments (see Figures 5(a)–5(c) at about −20 m),buttheceil- scintillators, make the presented setup highly competitive ing of this 5th tunnel was lower with ∼15–18 rock-equi- with any other outline. The results clearly demonstrate that valent meter above. The detector was directed to North–East underground structures are well visible, and therefore this andfacedtothezenithsimilarasinSection 3.2.1. kind of tomographic approach is promising in environmen- The measured muon flux is correlating to first order with tal, geophysical, or industrial applications. the calculated thickness of the rock, and the vertical tunnel is shifted to South-West direction as contours drawn in upper Acknowledgments panel of Figure 5(d). The authors acknowledge the REGARD group. They would 3.3. Summary of the Test Results. In all of the previous also like to thank Vincze Ernoforhishelpanddirectcon-¨ cases, the effect of the vertical tunnel and the wall can be tribution to the project and to the Hungarian Speleology seen clearly with the Muontomograph. Correlation between Institute and Ariadne Speleology Association. This work soil thickness and muon flux is strong as exhibited on was supported by the Hungarian OTKA Grants NK62044, the panels of Figure 5. One can conclude that the detector NK77816, NK106119, and H07-C 74164, the OTKA-KTIA with the given parameters, especially the limited size to Grants 77719 and 77815, NIH TET 10-1 2011-0061 and ZA- ensure portability, is applicable for search of underground 15/2009, and Eotv¨ osUniversity.G.G.Barnaf¨ oldi¨ and D. Varga rock inhomogeneities, such as hidden caverns at shallow, also thank the Janos´ Bolyai Research Scholarship of the HAS. Advances in High Energy Physics 7

References

[1] E. P. George, “Cosmic rays measure overburden of tunnel,” Commonwealth Engineer, pp. 455–457, 1955. [2] L. W.Alvarez, A. J. Anderson, F.El Bedwei et al., “Search for hidden chambers in the pyramids,” Science,vol.167,no.3919,pp. 832–839, 1970. [3] K. Nagamine, M. Iwasaki, K. Shimomura, and K. Ishida, “Method of probing inner-structure of geophysical substance with the horizontal cosmic-ray muons and possible application to volcanic eruption prediction,” Nuclear Instruments and Meth- ods in Physics Research A,vol.356,no.2-3,pp.585–595,1995. [4] E. Caffau, F. Coren, and G. Giannini, “Underground cosmic-ray measurement for morphological reconstruction of the “Grotta Gigante” natural cave,” Nuclear Instruments and Methods in Physics Research A,vol.385,no.3,pp.480–488,1997. [5] G. G. Barnafoldi,¨ G. Hamar, H. G. Melegh, L. Olah,´ G. Suranyi,´ and D. Varga, “Portable cosmic muon telescope for environmental applications,” Nuclear Instruments and Methods in Phy- sics Research A,vol.689,pp.60–69,2012. [6] L. Olah,G.Barnaf´ oldi,¨ G. Hamar, H. G. Melegh, G. Suranyi,´ and D. Varga, “CCC-based muon telescope for examination of natural caves,” Geoscientific Instrumentation, Methods and Data Systems,vol.1,pp.229–234,2012. [7]D.Varga,G.Hamar,andG.Kiss,“Asymmetricmulti-wirepro- portional chamber with reduced requirements to mechanical precision,” Nuclear Instruments and Methods in Physics Research A,vol.8,no.1,pp.163–167,2011. [8]D.Varga,G.Kiss,G.Hamar,andG.Bencedi,´ “Close cathode chamber: low material budget MWPC,” Nuclear Instruments and Methods in Physics Research A,vol.698,pp.11–18,2013. [9] “SURFER 9.0,” 2013, http://www.ssg-surfer.com/. Hindawi Publishing Corporation Advances in High Energy Physics Volume 2013, Article ID 256230, 7 pages http://dx.doi.org/10.1155/2013/256230

Research Article A Mobile Detector for Muon Measurements Based on Two Different Techniques

B. Mitrica,1 D. Stanca,1 M. Petcu,1 I. M. Brancus,1 R. Margineanu,1 A. Apostu,1 C. Gomoiu,1 A. Saftoiu,1 G. Toma,1 H. Rebel,2 A. Haungs,2 O. Sima,3 A. Gherghel-Lascu,1 and M. Niculescu-Oglinzanu1

1 Horia Hulubei National Institute for Physics and Nuclear Engineering, 077125 Magurele, Romania 2 Institute of Experimental Nuclear Physics, Karlsruhe Institute of Technology-Campus North, 76021 Karlsruhe, Germany 3 Department of Physics, University of Bucharest, 077125 Magurele, Romania

Correspondence should be addressed to B. Mitrica; [email protected]

Received 25 October 2012; Accepted 17 February 2013

Academic Editor: Maury Goodman

Copyright © 2013 B. Mitrica et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Precise measurements of the muon flux are important for different practical applications, both in environmental studies and forthe estimation of the water equivalent depths of underground sites. A mobile detector for cosmic muon flux measurements has been set up at IFIN-HH, Romania. The device is used to measure the muon flux on different locations at the surface and underground. Its 2 first configuration, not used in the present, has been composed of two 1m scintillator plates, each viewed by wave length shifters 2 and read out by two Photomultiplier Tubes (PMTs). A more recent configuration, consists of two 1m detection layers, each one 2 including four 1 ⋅ 0,25 m large scintillator plates. The light output in each plate is collected by twelve optical fibers and then read out by one PMT. Comparative results were obtained with both configurations.

1. Introduction interprets the coincidence events between two overlaid active layers as passing muons. A new configuration of the active The knowledge of cosmic ray muon flux is important in layers, using optical fiber readout of the plastic scintillator many applications, from low background measurements and sheet, was implemented and tested, and its performances the estimation of water equivalent depth for different under- were compared with the previous one, which used waveg- ground locations to the characterization of the background uides for the light collection. Using this new developed in the vicinity of mega detectors for neutrino physics, like configuration, the possibility of directional measurements of Super-Kamiokande or the future LAGUNA project [1], also muon flux was observed. for numerous environmental experiments like the solar activity characterization or the weather and climate change surveillance [2]. 2. The Apparatus Also, it has successfully been used as muon tomography technique in the search for hidden rooms in pyramids [3]or The detection principle of the muon mobile detector is to in volcanology [4]. It has a long list of possible applications, identify the traversing muons as coincidence events between 2 like the detection of unknown caverns, to increase the safety two overlaid 1 m active layers of scintillator material. Used procedures in mining excavations, in the oil industry as an for the current detector, two different concepts for the active easy way to search for oil bags or at the customs checkpoints, layer are presented in Figure 1. One important property of this to scan the passing vehicles. device is its mobility, the device being conceived to measure A mobile detector for measuring the muon flux is in use themuonfluxatdifferentlocationsatthesurfaceofthe at IFIN-HH Bucharest [5]. Placed in a van for mobility, it ground or in underground. 2 Advances in High Energy Physics

1011 mm 1011

50 50

Detector box 250 1000

Scintillator 1403 100

125 cm 1403 mm

250 Wavelength shifter 250 250 250

󳰀󳰀 PM 15 50 50

98 cm 50 50 (a) (b)

Figure 1: The detection module of (a) the first detector setup. Design of KASCADE [3]; (b) the new detector setup [5].

For the former configuration of the mobile detector, two probable energy deposit of 2.4 MeV, a signal threshold of detection modules were used, each module being a scintil- 1.8 MeV is set. 2 lator plate (NE114 type) of 0.9025 m and 3 cm thickness. Considering the fact that not all muons that interact with 2 Divided into four parts (0.475 ⋅ 0.475 m )[6, 7], it is readout the first layer manage to pass to the second one, due to through a wavelength shifter (NE174A type) by two photo- scattering loses in between, the acceptance of the detector multiplier tubes (EMI 9902 type), as we can see in Figure 1(a). was also investigated, using GEANT4 code (see Figure 4). The The present configuration consists of two detection mod- muon flux at the surface of the ground was estimated using ules, each composed of 4 plastic scintillator sheets (Polystyrol CORSIKA code [8], using the primary cosmic ray spectrum 3 80%, Methylmethacrylate 20%) having 100⋅25⋅1cm .Every of proton and helium, obtained from AMS results during a sheet is crossed by 13 longitudinal strips, 12 of them being space shuttle mission [9]. 𝑎∗ = 1.56 filled with an optical fiberFigure ( 1(b)). The light signal of A correction factor has to be applied on the each sheet is readout by a PMT. The modules are arranged observed muon rate at ground level. The distance between ontopofeachother(at30cmdistance).Thesignalsfromthe the centers of the two active layers of the detector is 30 cm. eight photomultiplier tubes are OR-ed four by four (1 + 2 + For a distance of 8 cm, obtained if the two active layers are 𝑎󸀠 = 1.11 3+4)and(5+6+7+8)andthenmeasuredincoincidence overlapping, a correction factor is obtained. No using a gate of 50 ns, so no correction due to the dead time correction factor due to the geometry of the detector’s surface of the detector is necessary. A counter module registers the is required. The corrected muon flux is given by ∗ coincidence events (see Figure 2). Φ𝜇 =𝑎 ⋅𝑅, (1) The calibration has been made by comparing the measured energy deposit spectrum of the minimum ionizing par- where 𝑅 isthecountingrateofthedetectorandΦ𝜇 is the real ticles with GEANT simulated responses. The comparison of flux. themeasuredandsimulatedspectra,ofbothconfigurations, is shown in Figure 3. The difference in the most probable 3. Measurements and Results energy deposit between the two configurations comes from the different thicknesses of the plates (3 cm versus 1 cm). Using the mobility of the detector, measurements of cosmic For the first configuration, having the most probable muon flux have been performed for both configurations of energy deposit at 6.3 MeV, the signal threshold was set the active layers at different locations on the surface with to 2.1 MeV [5]. For the new configuration, with the most differentelevations.Theresults,presentedinTable 1,are Advances in High Energy Physics 3

Plate 1 HV 1 PM 1

HV 2 PM 2 Or HV 3 PM 3

HV 4 PM 4

And Counter module

Plate 2

HV 5 PM 5 Coincidence module

HV 6 PM 6 Or HV 7 PM 7 High voltageHigh voltage High

HV 8 PM 8

Figure 2: The schematic view of the electronic detection system.

1 𝐸 =2.4 peak MeV 0.8

1 0.6 𝐸 =6.3 0.8 peak MeV

0.6 0.4 Rel. number of events of number Rel. 0.4 0.2

Rel. number of events of number Rel. 0.2

0 0 0 2468101214161820 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Energy deposit (MeV) Energy deposit (MeV)

MCMC MC DataData Data (a) (b)

Figure 3: (a) The energy calibration for one scintillator plate of the previous configuration, made by comparing the measured energy deposit spectrum of the minimum ionizing particles with GEANT 3.21 [28] simulated one. (b) The energy calibration for one scintillator sheet of the recent detector setup, made by comparison of the measured energy deposit spectrum of the minimum ionizing particles with GEANT 4.94 [29]simulatedone.

comparedwiththosepreviouslyreportedin[5]anddisplayed in Figure 5. The acquisition time for each data set was 1 h, all runs being performed at approximately the same time of the day (noon) in order to reduce the eventual influence of the solar Figure 4: The schematically view of the muons interacting with the new detection system, observed with GEANT 4.94 code (magenta activity and of atmospheric conditions. lines represent muons). We can see that not all muons that cross the Measurements of the cosmic muon flux have been per- first scintillator layer will pass through the second one. formed also underground in the Unirea mine from Slanic 4 Advances in High Energy Physics

Table 1: Cosmic muon flux measured at different geographic loca- 103 tions with different elevations, using both configurations of the 102 active layers. The altitude and the coordinates were measured with a

) 10

GPS system. −1 s 1 −2 −1 Latitude Longitude Altitude Muon flux 10 ∘ ∘ −2 −1 ( ) ( ) (m a.s.l.) (m s ) 10−2 −3 44.36 28.05 7±5 119.1 ± 3.6 10 10−4 44.40 26.10 64 ± 5 122.3 ± 3.7 (m ﬂux Muon 10−5 Former 44.32 28.19 70 ± 5 128.1 ± 3.8 configuration 10−6 45.24 25.94 408 ± 5 143.2 ± 4.3 0 1000 2000 3000 4000 5000 6000 45.28 25.97 588 ± 5 145.3 ± 4.4 Depth (m.w.e.) 655 ± 5 ± 45.29 25.94 146.7 4.4 CUPP/Finland Soudan/USA 44.97 26.02 219 ± 5 129.1 ± 4.5 Belgrade/Serbia Kamioka/Japan 45.07 26.03 266 ± 5 136.7 ± 4.7 Slanic/Romania Boulby/UK Gran Sasso/Italy 438 ± 5 ± LSC/Spain 45.24 25.94 142.7 4.9 Ogoya/Japan BNO/Russia Recent 45.26 25.96 603 ± 5 143.4 ± 4.9 Solotwina/Poland Frejus/France configuration Oto-Cosmo/Japan Sudbury/USA 45.26 25.97 693 ± 5 144.6 ± 4.9 𝑛 Φ𝜇(𝑋) = 𝐴∗(𝑋0/𝑋) ∗ exp(−𝑋/𝑋0) 1145 ± 5 ± Carlsbad/USA 45.48 25.91 146.8 5.0 Y2L/Korea 45.48 25.90 1204 ± 5 150.3 ± 5.1 Figure 6: The variation of flux as function of mwe depth for the 45.36 25.52 1338 ± 5 155.9 ± 5.3 results presented in Table 2.

The estimation of the water equivalent depth from muon 160 flux data is made by the formula 𝑛 ) 150 𝑋0 −𝑋

−1 Φ (𝑋) =𝐴∗( ) ∗ ( ), s 𝜇 𝑋 exp 𝑋 (2)

−2 0 140 −2 −1 with 𝐴 = 0.03 m s being an overall normalization con- 130 stant, 𝑋0 = 1470 mwe representing an effective attenuation length for high-energy muons, and 𝑛 = 2.5 being a free Muon ﬂux (m ﬂux Muon 120 parameter [9]. The variation of the muon flux with the water equivalent depth is still an open problem and one of our 110 detector’s goals. The formula has been obtained by Monte 0 200 400 600 800 1000 1200 1400 Carlo simulation using the MUSIC code [10]. Altitude (m) Avalueof610 ± 11 mwe was obtained using the flux measured with the first configuration; from the second one, a New configuration data 597 ± 10 Former configuration data mweisbeingcalculated.Wecanseetheevolutionof Results from reference [30] the muon flux as a function of mwe depth (see Figure 6). The data are compared with others over the world (see Table 2). Figure 5: Measured results of the muon flux variation with altitude, In order to check if there are any preferential arrival obtained with both detector configurations of the active layers of directions of the muons, coincidence measurements have the detector. The circles represent the data obtained with the former been performed in the underground between the scintillator configuration. The data obtained with the new configuration is sheets of the detector setup. The measurements have been presented with triangles. The cross point represents the results from [30]. performed in Unirea mine from Slanic Prahova salt ore, close to one of the mine’s wall (see Figure 7). The “Unirea” mine ∘ ischaracterisedbytemperature:12.0–13.0C, humidity: 65– 6 3 4 2 70%, excavated volume: 2.9 ⋅ 10 m ,floorarea:7⋅10 m , 3 Prahova (−208 m depth from surface), where a low-radiation average high: 52–57 m, aerosols <10 mm: 2108 part/m ,dis- level laboratory of IFIN-HH is set up, using both configura- tance between walls: 32–36 m, and existing infrastructures: tions. The detection modules were removed from the car and electricity, roads, railway, elevator, phone, Internet, and GSM transported by an elevator to the observation level. networks (also inside the galleries). More details regarding −2 −1 The responses are similar, 0.18 ± 0.01 m s for the theradioactivebackgroundintheminearepresentedin[11]. −2 −1 first configuration and 0.19 ± 0.002 m s for the second The order of the scintillator sheets of the detector is shown one. The acquisition time was 1 hour for the first set of in Figure 8.TheresultsarepresentedinTable 3.Thesystem measurements and 10 hours for the second one. was positioned in the cavern, so the sheets 1 and 5 are to be Advances in High Energy Physics 5

Table 2: A compilation of different muon flux measurements over the world.

∘ ∘ −2 −1 Location (laboratory)/country Latitude ( ) Longitude ( ) Depth (mwe) Muon flux (m s ) 2 CUPP/Finland [13] 63.39 N 26.02 E 0 (1.8 ± 0.2) ⋅10 2 Belgrade/Serbia [14] 44.51 N 20.23 E 0 (1.37 ± 0.06) ⋅ 10 2 Slanic/Romania [5] 45.24 N 25.94 E 0 (1.43 ± 4.9) ⋅ 10 Belgrade/Serbia 44.51 N 20.23 E 25 45 Belgrade/Serbia 44.51 N 20.23 E 75 11.9 Belgrade/Serbia 44.51 N 20.23 E 100 7.24 −1 Ogoya/Japan [15] 36.20 N 136.5 E 270 5⋅10 −1 Belgrade/Serbia 44.51 N 20.23 E 300 7.9 ⋅ 10 −1 Slanic/Romania 45.24 N 25.94 E 601 (1.9 ± 0.2) ⋅ 10 −1 Slanic/Romania 45.24 N 25.94 E 610 (1.8 ± 0.1) ⋅ 10 −2 Slanic/Romania 45.24 N 25.94 E 790 (9 ± 1.0) ⋅ 10 −2 CUPP/Finland 63.39 N 26.02 E 980 (2.1 ± 0.2) ⋅ 10 −2 Solotwina/Ukraine [16] 50.11 N 23.16 E 1000 1.7 ⋅ 10 −3 LSC/Spain [17] 42.43 N 00.31 E 1200 4⋅10 −3 Oto-Cosmo/Japan [18] 34.41 N 135.5 E 1400 4⋅10 −3 Carlsbad/USA [19]33.09N117.2W15264.73 ⋅ 10 −3 CUPP/Finland 63.39 N 26.02 E 1900 (3.2 ± 0.3) ⋅ 10 −3 Y2L/Korea [20] 38.04 N 128.4 E 2000 2.7 ⋅ 10 −3 Soudan/USA [21] 47.49 N 92.14 W 2000 2⋅10 −3 LSC/Spain 42.43 N 00.31 E 2400 2⋅10 −3 Kamioka/Japan [22] 39.29 N 140.3 E 2700 3⋅10 −4 Boulby/UK [23] 54.34 N 00.58 W 2800 4.05 ⋅ 10 −4 CUPP/Finland 63.39 N 26.02 E 2810 (6.2 ± 0.6) ⋅ 10 −4 Gran Sasso/Italy [24] 42.48 N 13.33 E 3200 (3.41 ± 0.01) ⋅ 10 −4 CUPP/Finland 63.39 N 26.02 E 3960 (1.1 ± 0.1) ⋅ 10 −5 BNO/Russia [25] 43.40 N 43.32 E 4700 3⋅10 −5 Frejus/France [26] 45.08 N 06.41 E 4800 4.7 ⋅ 10 −6 Sudbury/USA [27] 46.28 N 81.10 W 6010 3⋅10 Scara 1:2000 Unirea mine Unirea D 41 D 40 D 39 E 42 E 41 E 40 E 39 F 43 F 42 F 41 F 40 F 39 G 44 G 43 G 42 G 41 G 40 G 39 H 46 H 45 H 44 H 43 H 42 H 41 H 40 H 39 I 46 I 45 I 44 I 43 I 42 I 41 I 40 I 39 J 46 J 45 J 44 J 43 J 42 J 41 J 40 J 39 K 47 K 46 K 45 K 44

Figure 7: Map of Unirea mine, with the mBq laboratory of IFIN-HH. 6 Advances in High Energy Physics

Table 3: Rate of coincidences between sheets. Measurements were the light is transferred from the scintillator plate to a PMT performed in the Unirea mine (−208 m depth from surface). The through a light guide, in the determination of the cosmic acquisition time for each measurement was set to 10 hours. The muon flux in underground locations (Unirea mine from ∩ coincidence is represented by “ ” sign. Slanic Prahova) and the variation of muon flux with the Channels Counting rate (p/s) altitude. This type of reading technique combined with the −3 mobility of the detector could be used easily in various appli- (1+2+3+4)∩ (5+6+7+8) (191 ± 2.3) ⋅10 −3 cations, like archaeology and volcanology, or as a scanner 1+6 (5 ± 0.4) ⋅ 10 −3 used in customs control. 4+7 (8 ± 0.5) ⋅ 10 −3 2+5 (4 ± 0.3) ⋅ 10 −3 Acknowledgment 3+8 (6 ± 0.4) ⋅ 10 −3 2+7 (4 ± 0.3) ⋅ 10 The Romanian authors would like to thank the support of the −3 3+6 (5 ± 0.4) ⋅ 10 Romanian Authority for Scientific Research by the Projects −3 (1 + 2) ∩ (7 + 8) (9 ± 0.5) ⋅ 10 Parteneriate 194/2012—CORONA and PN 09 37 01 05. −3 (3 + 4) ∩ (5 + 6) (26 ± 0.8) ⋅ 10 References

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Research Article Charge Coupled Devices as Particle Detectors

Dan A. Iordache,1,2 Paul E. Sterian,1,2 and Ionel Tunaru1

1 Physics Department, University “Politehnica” of Bucharest, 313 Splaiul Independentei, 060042 Bucharest, Romania 2 Section of Science and Technology of Information, Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania

Correspondence should be addressed to Ionel Tunaru; tunaru [email protected]

Received 1 October 2012; Accepted 10 February 2013

Academic Editor: Jacek Szabelski

Copyright © 2013 Dan A. Iordache et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

As it is well known, while the most important advantages of the charge coupled devices, as high energy particle detectors are related to their (a) extremely high sensitivity (very important for the underground laboratories, also) and (b) huge number of very 6 small independent components (pixels) of the magnitude order of 10 , which allow the separate impressions of many different “signatures” of (silicon lattice defects produced by) these particles, their main disadvantages refer to the (a) difficulty to distinguish between the capture traps (of free electrons and holes, resp.) produced by the radiation particles and the numerous types of traps due to the contamination or dopants and (b) huge number of types of lattice defects due to the irradiation. For these reasons, this work achieves a state of art of the (i) main experimental methods and (ii) physical parameters intended to the characterization of the main types of traps embedded in the silicon lattice of CCDs. There were identified also some new physical parameters useful in this aim, as the polarization degree of capture cross-sections and the state character, as well as some new useful notions, as the trans-Fermi level capture states.

1. Introduction example, [1, 3]. As it results from the works [4–6], the number of trap types induced by nuclear irradiation is huge (more As it was shown by the classical scientific monographs [1, 2] than 600 types only for the low energy He ion bombardment; on the charge coupled devices (CCDs), the silicon quality is e.g., the main physical parameters of the EHe584 trap type are extremely critical for the CCD sensors/detectors. Impurities −15 2 [4] 𝐸𝑐 − 0.58 ± 0.03 eV, 𝜎𝑛 = (1.0 ± 0.5) ⋅ 10 cm ). as gold, transition metals, or lattice imperfections can have The specialty literature involves also a rather large num- a profound effect on CCD performance. One of the most ber of nanoimpurities and nanodefect types that can affect important chapters of the main scientific monograph [1]on the quality of the silicon crystalline lattice. The study of these CCDs (the last one, 125 pages) and other 18 pages (from the nanoimpurities and defects began even before (see, e.g., [7– total of 24 pages) of final Appendices are dedicated to the 24]) the invention (in 1969) of the charge coupled devices, radiation damage. “culminated” with the elaboration of the main experimental Onefindsthespecificeffectsonsiliconoffluxesof methods used to identify and characterize them [25–38], and photons, electrons, muons, pions, protons, deuterons, helium continues nowadays (see, e.g., [39–41]). The CCDs image ions, and so forth [1, page 814]. The most important effects of 𝐸 −0.39 sensors are extremely sensitive to contamination by heavy the protons fluxes refer to the divacancy electron ( 𝑐 eV, metals, which form Shockley-Reed-Hall deep-level traps that 𝜎 = 4⋅10−15 2 𝐸 + 0.21 𝜎 =2⋅ 𝑛 cm ) and holes traps ( 𝑣 eV, 𝑝 generate dark current in the imager region of the silicon −16 2 10 cm ), as well as to some combinations of vacancies with device [28, 32]. This dark current from defects scattered certain dopants, as the P-V center (the so-called E-centers: among the imager pixels represents a source of pattern noise −16 2 𝐸𝑐 −0.45 eV, 𝜎𝑛 = 3.7⋅10 cm )andAs-VorO-Vcenter(the and may cause the pixels and even the imager to be defective. −14 2 so-called A-centers: 𝐸𝑐 − 0.175eV,𝜎𝑛 = 1⋅10 cm ); see, for The deep-level transient spectroscopy (DLTS [25–27]) and 2 Advances in High Energy Physics the dark current spectroscopy (DCS, [28–38]) methods allow choice and evaluation of the basic uniqueness parameters [52– the study of these deep-level traps in silicon at concentrations 54], and (iie) hidden corelations in complex semiconductors 7 3 even of only 10 nanotraps/cm . [55, 56]). Taking into account the complex character of semicon- The most important nuclear methods are the (C1) neutron ductors, they are described by a huge number of uniqueness activation analysis (e.g., the works [57–61]), (C2) tracers parameters. In fact, the existing nonnegligible measurement method (for some of its main works, see [62–66]), (C3), (C3) errors allow accurate evaluations only for few dominant nuclear irradiation methods (e.g., [39, 67, 68]). uniqueness parameters, specific to the physical processes The thorough study of the specialty literature points out characteristic to a certain experimental method. For this rea- that besides the dark current spectroscopy method, the most son, the achievement of some sufficiently complete physical important experimental methods intended to the characteri- characterizations of the nanoimpurities and/or nano-defects zation of impurities and/or defects from semiconductors are of a semiconductor lattice requires the use of two or more the DLTS method (especially) and the TSCa one. For the complementary measurement methods. above indicated reasons, many experimental works report the results obtained by means of both (a) DLTS and TSCa methods (e.g., [69–71]), (b) DLTS and EPR [72, 73], (c) DLTS 2. Short Review of the Main Experimental and Hall [74], (d) Hall and EPR methods [75, 76], and so Methods Used to Characterize forth. We have to underline that the DLTS method allows the Nanoparticles, Nanocomplexes, and/or to (a) point out the character (acceptor or donor, resp.) of Defects Embedded in the Si Lattice the impurity/defect state, (b) evaluate (i) its absolute position (energy) and (ii) the capture cross-sections corresponding to The physical characterization of the impurities and/or defects thefreeelectrons(𝜎𝑛) and holes (𝜎ℎ),respectively. from semiconductors presents a special importance for the Additionally, the basic DLTS work [25] achieves a detailed design and use of various semiconductor devices, as the comparison of this method with the capacitance techniques charge coupled devices [1, 2], the semiconductor solar cells (TSCa, AST, and photocapacitance), while the works [77](for [42–46], and so forth. Taking into account the complex the electrical data) and [78](forthebasicfeaturesofdeep- nature of many semiconductors, the number of their char- level states of the transition metals in Si) achieve some of the acteristic parameters is huge; hence usually only a unique most important state of art (reviews) of the basic methods and experimental method is not able to provide a complete results from this field (more than 400 citations of the work description of semiconductors. [78]). The most important experimental methods intended to Other detection procedures of the cosmic rays and the study of the energy levels of the impurities and/or the mathematical models of the corresponding dissipative defects from semiconductors belong mainly to 3 classes: (A) systems were studied in the frame of the works [79, 80]. spectroscopic methods,(B)electrical methods, and (C) nuclear methods. The most important experimental methods of the first class are those of the (A1) electron paramagnetic resonance 3. Theoretical Part: The Main Sources of (EPR,usedfirstlyin[7–9]) and (A2) luminescence (used to Dark Current identify the shallow impurities or defects, see, e.g., [10]). The most important sources of dark current in semiconduc- Similarly,themainelectricalmethodscanbeclassified tors are [1, pages 605–648], [2, pages 37–45] (a) the field-free as (B1) the classical electrical techniques, as those of the (B1a) regions (diffusion and substrate (dominant for very heavily temperature dependence of the resistivity (e.g., works [11, 12]) >∼ 17 −3 and the (B1b) Hall effect (see works [13, 14]) and (B2) Junction doped ( 10 cm ) semiconductors)) dark current, (b) the techniques,ofthetypes(B2a)non-transient techniques as depletion (or bulk) dark current generated in the depletion the (i) admittance spectroscopy (see, e.g., [15]) and (ii) the region, and (c) the surface dark current generated at the Si- thermally stimulated capacitance (TSCa, used by [16–19]) SiO2 interface. If the CCD is operated in a multipinned phase and (B2b) transient techniques, as the (i) p/n or Schottky (MPP) mode, then the interface is completely inverted with junctions technique (e.g., [20–22]), (ii) capacitance and current a high hole carrier concentration, hence the surface dark transients [23], the (iii) photocapacitance,particularly[24], currentfromtheSi-SiO2 interface will be almost completely and (iv) deep-level transient spectroscopy (DLTS), with its suppressed. The analysis of the field-free regions (diffusion basic work [25], and some of its first applications [26, 27], and and substrate) and depletion dark current, respectively, was the (f) dark current spectroscopy (DCS). achieved in the frame of various books on semiconductors, As it results from Table 1,themostimportantversions the more important being those of Grove [81]andSze[82]. of the dark current spectroscopy are (i) the classical one (basic work [28],andsomeofitsmostimportantapplications [14b–14f]), (ii) the DCS computational approach (represented 3.1. The Depletion Dark Current. Taking into account that mainly by the works leading to the evaluation of the (iia) the parameters of nanoparticles influence the dark current, preexponential factors of the diffusion and depletion dark we will study the contribution of the depletion processes to currents [36–38], (iib) activation energy [47, 48], as well as the dark current, given [36] by the expression (the present the study of the: (iic) Meyer-Neldel corelations [49–51], (iid) validity and usefulness of the Shockley-Read-Hall (SRH) Advances in High Energy Physics 3 model and statistics were confirmed also by the several recent where the depletion preexponential factor is given by the 𝑉 𝑁 studies (see, e.g., [46, 93]): expression ( th and 𝑡 are the thermal velocity and the traps concentration, resp.) 𝑥 ⋅𝑛2 ⋅𝐴 𝐷𝑒− =− dep 𝑖 pix , (1) 𝑥 𝐴 𝑐𝑛√𝜎𝑝𝜎𝑛 ⋅𝑉 𝑁𝑡 SRH 𝑈 𝐷𝑒− = dep pix th , (4󸀠) 0,dep 2 where the net generation-recombination rate 𝑈 corresponding to the impurities and/or imperfections of the semi- and“thepolarizationdegree”𝑑 of the capture cross-sections conductor lattice is described by the following relation (At for electrons and holes, respectively, is 𝑛⋅𝑝2 =𝑛 𝑈 =0 thermal equilibrium: 𝑖 ,hence dep (the 𝜎 −𝜎 recombination and generation rates being equal)): 𝑛 𝑝 pdg ≡𝑑=arg tanh ( ). (5) 𝜎𝑛 +𝜎𝑝 2 𝜎𝑝𝜎𝑛𝑉𝑡ℎ (𝑛 ⋅ 𝑝𝑖 −𝑛 )𝑁𝑡 𝑈= . (2) 𝜎𝑛[𝑛+𝑛𝑖 exp ((𝐸𝑡 −𝐸𝑖)/𝑘𝑇)]+𝜎𝑝[𝑛+𝑛𝑖 exp ((𝐸𝑖 −𝐸𝑡)/𝑘𝑇)] Taking into account the possible concomitant presence of different traps 𝑗 in each pixel, the previous expression (4) 𝑥 In the above expressions, dep is the width of the depletion becomes layer, 𝐴 is the pixel area, 𝜎𝑝,𝜎𝑛 arethecapturecross- pix 𝐸 𝐸 −𝐸 𝑉 − 3/2 𝑔 − 𝑡𝑗 𝑖 sections for holes and electrons, respectively, th is the 𝐷𝑒 =𝑇 ⋅ (− )⋅∑ 𝐷𝑒 [ +𝑑] 𝐸 𝑁 dep exp 0,dep.𝑗sech 𝑗 thermal velocity, 𝑖 is the intrinsic Fermi energy level, 𝑡 2𝑘𝑇 𝑗 𝑘𝑇 is the concentration of traps, that is, of bulk generation- 𝐸 𝑛, 𝑝 𝐸 recombination centers at the energy level 𝑡, while , − 3/2 𝑔 𝐸𝑡, −𝐸𝑖 =𝐷𝑒 ⋅𝑇 ⋅exp(− )⋅sech[ eff +𝑑 ], and 𝑛𝑖 are the electrons, the holes, and the intrinsic carrier 0,dep.eff. 2𝑘𝑇 𝑘𝑇 eff concentration, respectively, given by the expressions (5󸀠) 3/2 2𝜋 ⋅𝑛 𝑚 𝑘𝑇 𝜇−𝐸𝑐 − 𝑛=2( ) , where 𝐷𝑒 ,𝐸𝑡, .,and𝑑 . are the effective preexpo- ℎ2 exp 𝑘𝑇 0,dep.eff. eff eff 𝑒− ℎ (3) nential factor, trap energy, and polarization degree of , 2𝜋 ⋅ 𝑚 𝑘𝑇 3/2 𝐸 −𝜇 capture cross-sections, corresponding to the considered pixel. 𝑝=2( 𝑝 ) 𝑣 , ℎ2 exp 𝑘𝑇 Assuming equal capture cross-sections for holes and electrons, hence a null polarization degree, the expression of 3/2 the temperature dependence of the depletion dark current, 2𝜋√𝑚𝑛𝑚𝑝 ⋅𝑘𝑇 𝐸 𝑛 =2( ) ⋅ (− 𝑔 ) becomes 𝑖 ℎ2 exp 2𝑘𝑇 (3󸀠) 𝐸 𝐸 −𝐸 − − 3/2 𝑔 𝑡,eff 𝑖 𝐸 𝐷𝑒 =𝐷𝑒0, . . ⋅𝑇 ⋅exp (− )⋅sech [ ] . 3/2 𝑔 dep dep eff 2𝑘𝑇 𝑘𝑇 =𝑐𝑛 (𝑇) ⋅𝑇 ⋅ exp (− ), 2𝑘𝑇 (6) where 𝑚𝑛,𝑚𝑝 are the effective masses of the free electrons Because the temperature dependence of all physical and holes, respectively, 𝐸𝑐, 𝐸𝑣, 𝜇,and𝐸𝑔 are the lower/higher parameters of the preexponential factor seems to be very threshold of the conduction/valence band, the electrochemi- weak (in comparison with the exponential dependence of the cal potential, and the energy gap of the considered semicon- last 2 factors, especially), we can assume that the temperature ductor, respectively, which are also temperature dependent. dependence of the depletion dark current is due mainly to the One finds that expression3 ( ) is symmetrical relative to the last 3 factors of expression (6). permutation 𝑛,𝑛 𝜎 ,𝐸𝑡 −𝐸𝑖 ↔𝑝,𝜎𝑝,𝐸𝑖 −𝐸𝑡, which leads to the DCS possibility to evaluate |𝐸𝑡 −𝐸𝑖|, | ln 𝜎𝑛/𝜎𝑝|,andsoforth, 𝐸 −𝐸,𝜎,𝜎 3.3. Choice of the Uniqueness Parameters. Adding the expres- butnotoftheabsolutevalues 𝑡 𝑖 𝑛 𝑝,andsoforth sion of the free-field region (equivalent to the diffusion, for without additional elements given by other experimental weakly doped semiconductors) dark current [36–38, 83–85], methods. one finds (see also [54]) that the most suitable expression of the temperature dependence of the dark current in CCDs is 3.2.TheApproximationoftheCompletelyDepletedZone. given by the relation Assumingthat,inthedepletionzone,theelectricfieldsweeps the holes to the p-substrate and the electrons to the potential 𝐷𝑒− (𝑇) =𝐷𝑒− (𝑇) +𝐷𝑒− (𝑇) 2 diff dep wells, hence (in this region) 𝑛, 𝑝𝑖 ≪𝑛 ,thetemperature 𝐸 dependence of the depletion dark current will be described =𝑇3 ( 𝐷𝑒− − 𝑔 )+𝑇3/2 bytheexpression[seerelations(4)and(5)] exp ln 0,diff 𝑘𝑇 𝐸 𝐸 −𝐸 𝐸 𝐸 −𝐸 𝐷𝑒− =𝐷𝑒− ⋅𝑇3/2 ⋅ (− 𝑔 )⋅ [ 𝑡 𝑖 +𝑑], ⋅ ( 𝐷𝑒− − 𝑔 )⋅ [ 𝑡 𝑖 +𝑑]. dep 0,dep exp 2𝑘𝑇 sech 𝑘𝑇 exp ln 0,dep 2𝑘𝑇 sech 𝑘𝑇 (4) (7) 4 Advances in High Energy Physics

The detailed analysis accomplished in the frame of works with distinct values for the generation by 1 free [52–54] pointed out that the most convenient choice of electron capture (𝑟𝑛) or by 1 hole capture (𝑟𝑝), the uniqueness parameters corresponds to the order (a) 𝐷𝑒− 𝐷𝑒− (iii) the emission time, defined as ln 0,diff,ln 0,dep (logarithms of the preexponential fac- 𝐸 tors of the diffusion and depletion current, resp.) and 𝑔 1 𝑔 Δ𝐸 (the effective (temperature averaged) energy gap), (b) the 𝜏= = ⋅ ( ), 𝑒 𝑉 ⋅𝜎⋅𝑁 exp 𝑘𝑇 (10) difference 𝐸𝑡−𝐸𝑖 of the energies of the trap and of the intrinsic th 𝑏 Fermi level, respectively, or its modulus |𝐸𝑡 −𝐸𝑖| (when the fitting relation6 ( ) is used), and (c) the depolarization 𝑑 (c) the energy level, given by its absolute value: 𝐸𝑣 +𝐸𝑎 degree of the capture cross-sections of electrons and holes, 𝐸 −𝐸 respectively, given by relation (5). or 𝑐 𝑎 in terms of the energies corresponding to A synthesis of the main features of the basic versions of the upper/lower thresholds of the valence/conduction band and the activation energy, respectively, or by the the DCS method is presented in Table 1. |𝐸 −𝐸| The columns of Table 1 point out the (a) basic theoretical modulus 𝑡 𝑖 of the distance from the considered trap to the intrinsic Fermi level (taking into account relations of the classical McGrath-McColgin DCS method 𝐸 ≈1.08 andofourcomputationalDCSapproachand(b)thespecific that we have chosen the value 𝑔 eV for advantages of each procedure, related to a global investigation theeffective(averagedonthetemperatureinterval 222⋅⋅⋅291K)energygap;weusedforSithevalue𝐸𝑖 ≈ (the classical DCS method) and to the per pixel analysis (our 0.54 Computational approach). eV (see also [28])).

4. Study of the Possibilities of Identification of 4.2. Evaluation of the Polarization Degree of the Capture Cross- the Impurities and/or Defects Embedded in Sections of Free Electrons and Holes, Respectively. As it was found (see, e.g., relation (10)), the polarization degree 𝑑 of the Semiconductor Crystalline Lattice the capture cross-sections of the free electrons and holes, 4.1. Main Characteristic Parameters of the Impurities and/or respectively, intervenes in the expression of the depletion Defects. The main characteristic parameters of the impurities dark current, which is prevalent at low temperatures. For this and/or defects embedded in the forbidden band of a semicon- reason, even if the low temperatures dark currents are consid- ductor are erably weaker (hence, their use implies considerably higher errors) than those corresponding to higher temperatures, the (a) the capture cross-sections of the free electrons 𝜎𝑛 and evaluation of the polarization degree imposes the use of the holes 𝜎𝑝 by the different types of traps or their dark current for all 8 studied temperatures. Starting from the 𝜎 ≡𝜎= 𝜎 𝜎 evaluated values of the logarithms of preexponential factors geometrical average: ave √ 𝑛 𝑝 [28]and the corresponding polarization degree, defined in the corresponding to the diffusion ln Diff and depletion lnDep frame of this work: pdg ≡𝑑=arg tanh((𝜎𝑛−𝜎𝑝)/(𝜎𝑛+ dark current, respectively, as well as from the evaluated 𝐸 𝜎𝑝)), effective energy gap 𝑔, it is evaluated also the last factor of expression (10): (b) different (and related) generation rates of the charge carriers: 𝐸 −𝐸 𝑡,eff. 𝑖 Fact = sech [ +𝑑 .] , (11) (i) the emission rate, defined by the classical 𝑘𝑇 eff expression of the number of captures (through collisions) in the time unit, in terms of the mean for all studied temperatures. 𝑉 thermal velocity th and the considered traps In the following are determined the slope (𝐸𝑡 −𝐸𝑖)/𝑘 𝑛 type concentration 𝑡 inthevolumeunit[25]: and the intercept 𝑑 of the least squares (regression) straight ( ) = 𝐹(1/𝑇) Δ𝑁 𝑉 ⋅𝜎⋅𝑁 Δ𝐸 line, arg sech Fact , and the correlation coefficient 𝑒= =𝑉 ⋅𝜎 ⋅𝑛 = th 𝑏 ⋅ (− ), corresponding to this regression line. Δ𝑡 th em 𝑡 𝑔 exp 𝑘𝑇 (8)

where 𝑁𝑏 is the effective density of states at the 4.3. Basic Features of the Most Efficient Generation- border of the of the respective carriers band, 𝑔 Recombination Traps. Starting from the expression of is the degeneracy of the trap level, while Δ𝐸 is the effective generation-recombination life of electrical the energy separation (the so-called activation charge carriers in the depletion region (see, e.g., [28, 36]), energy) between the trap level and the border of

the corresponding carriers band, Δ 𝑛 𝑥 𝐴 𝑛𝑖 3 𝜏 = 𝑖 = dep pix (ii) the generation rate given by 1 trap in a cm , 2𝑈 2𝐷𝑒− dep defined as (12) 𝑒 1 Δ𝑁 𝜎𝑛 exp ((𝐸𝑡 −𝐸𝑖)/𝑘𝑇)+𝜎𝑝 exp ((𝐸𝑖 −𝐸𝑡)/𝑘𝑇) 𝑟= = ⋅ =𝑉 ⋅𝜎, = , th (9) 𝜎 𝜎 𝑉 𝑁 𝑛𝑡 𝑛𝑡 Δ𝑡 𝑝 𝑣 th 𝑡 Advances in High Energy Physics 5

Table 1: Comparison of the main versions of the classical and computational approach of the dark current spectroscopy (DCS) method.

The DCS method Basic Main evaluated Input data Accepted approximations version expression(s) parameter Histogram: 𝑛, 𝑝 ≪𝑛 The average number of pixels Deep-depletion mode: 𝑖 𝑗 = 𝜎 𝜎 ⋅𝑉 𝑛 𝑛 𝑞𝑊/2 (1) dark √ 𝑛 𝑝 th 𝑖 𝑡 cross-section Classical DCS Equal cross-sections: 𝜎𝑛 =𝜎𝑝 versus dark current 𝜎≡𝜎 = √𝜎 𝜎 method (ClDCS) [28] ave 𝑛 𝑝 (a) McGrath et al. Temperature [28] Deep-depletion mode: 𝑛, 𝑝𝑖 ≪𝑛 󵄨 󵄨 dependence of the 𝑗𝑑 ∝ exp [−|𝐸𝑡 −𝐸𝑖 |/𝑘𝑇] 󵄨𝐸𝑡 −𝐸𝑖󵄨 |𝐸𝑡 −𝐸𝑖|≲𝑘𝑇 (b) McColgin et dark current [31] al. Traps concentration The generation 𝑛 𝑛, 𝑝 ≪𝑛 [29–32] ( 𝑡) and carrier Deep-depletion mode: 𝑖 Δ𝑁 /Δ𝑡 = 1/𝜏 =𝑉 ⋅𝜎⋅𝑛 (emission) rate, 𝑉 𝜎 =𝜎 𝑐 th 𝑡 𝑒−/𝑠 velocity ( th)from Equal cross-sections: 𝑛 𝑝 , (c) Webster et al. other methods [30] 𝑒≡Δ𝑁𝑐/Δ𝑡 = 1/𝜏 [35] Temperature dependence of the Validity of the Arrhenius The activation energy, Δ𝑁𝑐/Δ𝑡 = 1/𝜏 ≡ 𝑘 =𝐴⋅ exp (−𝐸𝑎/𝑘𝑇) generation (emission) equation 𝐸𝑎 rate [33] 𝑛,𝑝≪𝑛 𝜎 =𝜎 𝑗 =𝐷 𝑇3 (−𝐸 /𝑘𝑇) Temperature 𝑖, 𝑛 𝑝 𝑑 0,diff. exp 𝑔 The preexponential dependence of the Very deep-level traps: factors 󵄨 󵄨 3/2 󵄨𝐸 −𝐸󵄨 ≪𝑘𝑇 +𝐷0 𝑇 (−𝐸𝑔/2𝑘𝑇) 𝐷 𝐷 →𝑛 dark current [36, 37] 󵄨 𝑡 𝑖󵄨 ,dep exp 0,diff.; 0,dep 𝑡 Idem and Arrhenius (2) Computational The Meyer-Neldel preexponential factor 𝑗 =𝐷 −Δ𝐸/𝑘𝑇 DCS approach The validity of the Arrhenius and 𝑑 0 exp ( ) energy 𝐸 and the dependence on the MN (CA-DCS) Meyer-Neldel relations 𝐷 =𝐷 (Δ𝐸/𝐸 ) preexponential factor activation energy 0 00 exp MN (a) Widenhorn et 𝐷00 al. [36, 37, 47–51] [36, 37, 47–56] Negligible effect on dark current 𝐷 ,𝐷 𝐸 =𝑓(𝑇) 0,diff. 0,dep, of 𝑔 ,relativetothoseof 3/2 The temperature 󵄨 󵄨 𝑗 =𝐷 𝑇 (−𝐸 /2𝑘𝑇) 𝐸𝑔 (effective (b) Widenhorn et 󵄨𝐸 −𝐸󵄨 𝑑,dep 0,dep exp 𝑔 dependence of the 󵄨 𝑡 𝑖󵄨 and even of parameter), al. 𝑑 = ⋅ [(𝐸 −𝐸)/𝑘𝑇+𝑑] energy gap 𝐸𝑔 [36, 82] sech 𝑡 𝑖 |𝐸𝑡 −𝐸𝑖|,and𝑑 [51–56] arg tan ℎ((𝜎𝑛 −𝜎𝑝)/(𝜎𝑛 +𝜎𝑝)) →𝜎𝑛,𝜎𝑝 and 𝑛, 𝑝𝑖 ≪𝑛 (c) Widenhorn et Correlations al. coefficients, [52–56] Results concerning high: 𝐷0 ,𝐷0 , ln 𝐷0 =𝑓(𝐸𝑔), ,diff. ,dep Single or double linear ,diff. 𝐸𝑔 (effective ln 𝐷0 = Idem corelations between some effective ,dep parameter), 𝑓(|𝐸𝑡 −𝐸𝑖|), 󵄨 󵄨 parameters 󵄨𝐸𝑡 −𝐸𝑖󵄨,and𝑑 medium values: 𝐷 =𝑓(𝐸 ) [52–54] ln 0,dep 𝑔 , low values: 𝐷 =𝑓(𝐸 ) ln Arrh 𝑔

it is very easy to find that this effective generation-recom- Because in the middle of the temperature interval studied bination life presents a sharp minimum (i.e., a maximum dark by us (≈260 K) we have (𝑘𝑇/2) ≅ 11.2125 meV, it results that current emission) for (i) |𝐸𝑡 −𝐸𝑖|/(𝐸𝑔/2) ≤ 0.2;hencethemostactiveimpurities correspond to a rather deep energy levels (near to the Fermi |𝐸 − 𝑑𝜏 1 𝜎 𝐸 −𝐸 𝜎 𝐸 −𝐸 level; and that is, they correspond to deep-level traps), (ii) 𝑡 0= = [ 𝑛 𝑡 𝑖 − 𝑝 𝑖 𝑡 ], 𝐸 |/(𝑘𝑇/2) ≅ 0.8 ⋅ ⋅5 𝑑𝐸 𝜎 𝜎 𝑉 𝑁 𝑘𝑇 exp 𝑘𝑇 𝑘𝑇 exp 𝑘𝑇 𝑖 ; it results that the polarization degree of 𝑡 𝑝 𝑛 th 𝑡 the capture cross-sections of holes and electrons, respectively, (13) hastoberatherlarge(ofthemagnitudeorderof1). Of course, the experimentally found depletion dark cur- equivalent to the condition rent does not correspond exactly to the emission maximum; hence (a) some specific numerical calculations are necessary, but (b) the assumption on the possibility to consider the 𝜎 𝑘𝑇 𝑝 󸀠 capture cross-sections of holes and electrons as equal seems 𝐸𝑡 =𝐸𝑖 + ln ( ). (13 ) 2 𝜎𝑛 to be wrong. 6 Advances in High Energy Physics

Table 2: Some known values of the traps energy levels, of both capture cross-sections of free electrons and holes, respectively, in silicon, as well as of their polarization degree (pdg), implicitly.

∘ 2 2 𝑘=𝜎/𝜎 U (55 C) Trap Group Energy (eV) 𝜎𝑛 (cm ) 𝜎𝑝 (cm ) 𝑛 𝑝 pdg Reference − e /s [9] −16 −15 − − 𝐸𝑖 − 0.01 1.4 × 10 7. 6 × 10 0.01842 1.997 [86] Au𝑠 11 − − −4 5.0 × 10 16 1.0 × 10 15 ∝𝑇 0.5 −0.3466 [87] 565 −14 MnB 7; 13 𝐸𝑖 − 0.01 9.0 × 10 [88] + − + −12 −13 (Mn𝑖 B𝑠 ) 7; 13 𝐸𝑖 + 0.01 2.1 × 10 3.5 × 10 6.0 + 1.282 [89] + 1/2 Co𝑖 9 𝜎=(𝜎 ⋅𝜎 ) ≈ 6.6 × 10−15 + 𝐸𝑖 − 0.02 𝑛 𝑝 [90] 3700 Ni𝑖 10 − −15 −14 Pt𝑖 10 𝐸𝑖 + 0.02 4.5 × 10 1.09 × 10 2.42 +0.442 [91] 970 −16 CrAl 6; 13 𝐸𝑖 − 0.048 1.5 × 10 [88] −15 CrGa 6; 13 𝐸𝑖 − 0.058 1.5 × 10 [88] −− −19 −15 × − 5 − Zn𝑠 12 𝐸𝑖 + 0.07 1.3 × 10 6.6 × 10 1.97 10 5.417 [86] −15 MnAl 7; 13 𝐸𝑖 + 0.09 5.0 × 10 [88] + Mn𝑖 7 𝐸𝑖 + 0.09 9.4 +1.1204 [89] 1/2 − ≡ 𝜎=(𝜎 ⋅𝜎 ) ≈ 6.6 × 10−15 PVp 𝐸𝑖 + 0.10 𝑛 𝑝 [92] 70 14 E-center −16 𝐸𝑖 + 0.084 3.7 × 10 [92] − −15 VV 𝑒 trap 14 𝐸𝑖 + 0.15 4.0 × 10 [1,page820] + −14 −17 Fe𝑖 8 𝐸𝑖 − 0.16 5.0 × 10 7. 0 × 10 714.3 +3.286 [86] ++ −14 −18 V𝑖 5 𝐸𝑖 − 0.18 5.0 × 10 3.0 × 10 16667 +4.86 [86] + −14 Pt𝑠 10 𝐸𝑖 − 0.18 5.4 × 10 [91] − −15 −15 − Zn𝑠 12 𝐸𝑖 − 0.21 1.5 × 10 4.4 × 10 0.3409 0.538 [86] ++ 18.5 ÷ 28.3) Mn𝑖 7 𝐸𝑖 − 0.21 23.1 ( +1.57 [89] −14 −16 + 𝐸𝑖 − 0.26 1.6 × 10 6.0 × 10 26.67 +1.642 [93] Mo𝑖 6 −15 −16 𝐸𝑖 − 0.223 7. 8 × 10 6.0 × 10 13 +1.282 [93] + − − −15 −14 − (Cr𝑖 B𝑠 ) 6; 13 𝐸𝑖 − 0.26 5.0 × 10 1.0 × 10 0.5 0.3466 [94] + PV 14 𝐸𝑖 − 0.27 [92] 1.8 + −14 −15 Ti𝑖 4 𝐸𝑖 + 0.27 3.1 × 10 1.4 × 10 22.14 +1.549 [86] ++ −14 −17 Ti𝑖 4 𝐸𝑖 − 0.28 1.3 × 10 2.8 × 10 464.3 +3.070 [86] −14 −15 + − 𝐸𝑖 + 0.28 1.4 × 10 1.1 × 10 (Fe B )+ 8; 13 13 +1.282 [90] 𝑖 𝑠 (±0.02) (±0.02) (0.5 ÷ 2.5)

MnAu 7; 11 𝐸𝑖 + 0.30 + −15 Pt𝑠 10 𝐸𝑖 + 0.31 3.4 × 10 [91] −13 −13 ++ 𝐸𝑖 + 0.32 2.3 × 10 1.1 × 10 2.091 +0.369 [86] Cr𝑖 6 −14 −15 𝐸𝑖 + 0.30 2.0 × 10 4.0 × 10 5 +0.805 [94]

VV hole −16 14 𝐸𝑖 − 0.33 2.0 × 10 [1,page820] trap − OV ≡ 𝐸 + 0.37 × −14 A-center 16 𝑖 1.0 10 [1,page820] all Mn 1/2 −15 6 7 𝜎=(𝜎min ⋅𝜎max) ≈ 1.0 × 10 ;𝜎max/𝜎min ∼10 [32, 89] 6400 Traps

Table 3: Analysis of the physical meaning of the possible signs of the slope and intercept of the regression line (15).

Sign of the slope 𝑠 Sign of the intercept 𝑖 sc Value of |𝐸𝑡 −𝐸𝑖| Value of |pdg| >0 >0+1𝑠𝑖 >0 <0 −1 −sc ⋅𝑠=+𝑠 sc ⋅𝑖=−𝑖 <0 >0 −1sc⋅𝑠=−𝑠sc − ⋅𝑖=+𝑖 Advances in High Energy Physics 7 studied temperatures,% Accuracyfor8(or6) ]3.82% 32 /Co, Mn 2.59% (1.8%) 𝑖 Possible assignments | pdg 2.715 Fe 2.25% (2.3%) 1.630 Fe 5.99% (2.5%) 8.169 PV-donor 13.8% (0.91%) 7.644 PV-donor 267.8% (1.6%) ⋅| 6.880 PV-donor 7.99% (1.8%) 0.428 IN 1.8175 Fe 10.5% (2.6%) 1.5216 Mn 2.51% (2.2%) 1.7287 Fe 12.1% (2.6%) 3.9519 Trap 2 [ − − − − − − − − − − sc , | eV (the same values for all pixels and temperatures) 𝑖 −𝐸 𝑡 meV |𝐸 = 1.076 𝑔 2.23% 343.6 2.36% 310.8 7.055% 133.6 3.197% 126.4 2.294% 9.939 studied Accuracy for all 8 temperatures,% , 𝑖 + ) − )]| = 𝑓(1/𝑘𝑇) 𝐸 Au 𝑝 Au Au Au + Ni/Co MnAu, Possible =𝜎 Pt;Ni;Co; Pt; Mn;Co; 𝑛 assignments (Mn (𝜎 )] 𝑖 dep , | −𝐸 𝑡 /𝐷𝑒 pdg ⋅| 0.3114 Mn, Au 5.246% Instable 1.3896 Mn, Ni/Co 5.38% 347.6 0.1548 2 Mn, 1 Pt 2.472% 147.8 0.3274 1 Au 1 Mn 5.65% Instable diff 3.0746 1 MnAu 17.47% Instable [𝑑(𝐸 − − − − − sc where sc = sign , − Dark current spectroscopy (DCS) assignment of capture traps of same CCDs pixels | [𝐷𝑒 − 𝐷𝑒 𝑖 𝑡 𝐸 meV |𝐸 arg sech C) | ∘ Depletion generation rate (counts/sat 55 Regression line Table 4: Example of dark current spectroscopy (DCS) assignments of the capture traps of some CCDs pixels. eff 𝑔, (eV) 𝐸 ), 3/2 − 3/2 K − ⋅ K dep.eff ⋅ counts/ − 0, s 6 7.224 1.0745 289.5 30.85 2.541 1.0764 23.1 32.125 5.433 1.0755 125.9 24.39 +0.0187 1 Au & 1 Mn 3.57% Instable 9.530 1.0745 108.9 28.043 +0.7904 4 Au 6.99% 127.0 6.623 1.0745 139.1 24.66 +0.0455 1 Cr-Ga 2.36% Instable 6.022 1.0673 160.4 34.44 6.478 1.0745 132.1 8.49 +0.7733 3 Au 6.158% Instable 11.710 1.0745 217.9 33.588 +0.0154 32.120 1.0745 366.8 51.86 15.998 1.0745 306.3 28.029 +0.4381 Cr-Ga, Au 3.797% Instable 21.944 1.0745 415.4 31.21 +01169 1 Ni/Co; Mn 1.77% 74.79 40.792 1.0745 271.1 27.325 +1.369 66.386 1.0745 589.7 45.697 +0.397 𝐷 421.361 1.0745 911.6 2.16 105.688 1.0745 606.7 57.215 +0.1351 MnB, Pt 2.2798% 197.3 268.671 1.0745 369.6 42.793 +0.9105 254.039 1.0745 722.1 55.479 +0.2589 Pt, Mn, Fe 10 (Mcps 341; 420 261; 340 281; 360 Pixel Coordinates 32; 400 181; 260 121; 200 141; 220 101; 180 301; 380 188; 471 81; 160 61; 140 221; 300 201; 280 161; 240 31; 247 29; 88 8 Advances in High Energy Physics

5. Interpretation of the Found of the dark current spectroscopy (DCS) assignment criteria Numerical Results forcertainsmallgroupsofcapturetrapsofsomeCCDs,we studied the dark currents of 20 randomly chosen pixels of The main difficulties of our study correspond tothe a 512 × 512 SI003AB thinned CCD chip of a backside illu- minated Spectra Video camera manufactured by PixelVision, (i)possiblepresenceineachpixelofseveraltypes Beaverton (Oregon, USA), the corresponding numerical data of traps and/or impurities, which means that the being kindly indicated to us by Professors Erik Bodegom and obtained values are in fact averages over the present Ralf Widenhorn, from Portland State University (Oregon) traps/impurities, [52].Theaveragenumberoftraps/pixelwasofabout10[36]; (ii) complexity of the used SRH theoretical model, which hence we studied both some pixels with very small numbers determines an effective character of all evaluated of pixels and other pixels with some tens of such capture traps. uniqueness parameters. Excepting the pixels with the smallest dark currents and implicitly the smallest values of the depletion dark 𝐷𝑒− 5.1. Assignment Criteria of the Individual Capture Traps current preexponential factor 0,dep.eff.,wheretheevaluated from Semiconductors. The basic assignment criteria of the physical parameters could correspond to some individual 𝐷𝑒− individual capture traps due to contaminants, to the defects capturetraps,forthelargervaluesof 0,dep.eff. these values 󸀠 produced by high-energy radiation particles, or to some represent some rather intricate (see relation (5 )) averages combinations of these basic traps (as the E-centers, A- over 2 or more capture traps, being so effective parameters. centers, etc.) are (a) the trap energy level, expressed by means 𝐸 −𝐸 𝐸 +𝐸 Being the complex character of semiconductors (the tem- of the activation energy as (i) 𝑐 𝑎 and (ii) 𝑣 𝑎,orby perature dependence of their basic parameters, of the energy means of the intrinsic Fermi level energy as 𝐸𝑖 ±|𝐸𝑡 −𝐸𝑖|,(b) 𝐸 𝜎 𝜎 gap 𝑔, particularly), the experimental data processing can be the capture cross-sections of the free electrons 𝑛 or holes 𝑝, accomplished in 2 versions assuming (a) an effective (specific respectively, or by the geometrical average of cross-sections to the experimental data obtained for each pixel) energy gap 𝜎=√𝜎𝑛𝜎𝑝 [28] and the polarization degree of capture cross- 𝐸𝑔, . or (b) a constant value for all temperatures, common 𝑑= ((𝜎 −𝜎 )/(𝜎 +𝜎 )) eff sections arg tanh 𝑛 𝑝 𝑛 𝑝 , defined by this for all pixels, for example 𝐸𝑔 ≈ 1.076 eV. work, and (c) the generation-recombination rate by means of 𝐷𝑒− After the evaluation of the diffusion 0,diff. and depletion depletion processes [28, 36]andrelation(2) and the depletion − 󸀠 󸀠 𝐷𝑒 preexponential factors and of the effective value preexponential factor (4 ), (5 ). In order to achieve such 0,dep. of the energy gap 𝐸𝑔, ., concomitantly with a zero-order assignments of the traps states detected by the main present eff approximation of the modulus of the of the average value (for experimental methods, Table 2 presents the synthesis of the all traps of the considered CCD pixel) difference |𝐸𝑡 −𝐸𝑖| specialty literature results concerning the states whose basic of energies of the CCDs traps and of the intrinsic Fermi features specified above were already measured. level, it becomes possible to evaluate the factor sech(((𝐸𝑡 − Relative to the atoms and/or ions involved in Table 2, 𝐸𝑖)/𝑘𝑇) + 𝑑) (see relation (7)) for all 8 studied temperatures: we have to mention (a) several of these nanoparticles were 222,232,242,252,262,271,281,and291K[52]. Given that present in the experimental data of some previous works (e.g., theargumentofthehyperbolicsecantfunctionisaneven [52])and(b)accordingtoourknowledge,thepresentwork function, we will study the least squares fit (regression line) is the first one to accomplish a wide-scale analysis of free for the linear dependence electrons and holes, respectively, capture cross-sections, this 󵄨 󵄨 finding justifying the involvement of some elements rarely 󵄨𝐸𝑡 −𝐸𝑖 󵄨 1 󵄨 +𝑑󵄨 =𝑓( ). (15) metinCCDs,whichwillallowustheobtainmentinfollowing 󵄨 𝑘𝑇 󵄨 𝑘𝑇 of some new results. The analysis of the experimental data synthesized by OnefindsthatusingtheDCSmethod,itispossibleto Table 2 points out the possibility to classify the different evaluate only the |𝐸𝑡 −𝐸𝑖| and |𝑑| ≡pdg | |. Depending on capture traps states in terms of the newly defined here state the signs of the slope 𝑠 and intercept 𝑖 oftheregressionline character (symbol sc), defined as (15), it is possible to establish the value of the state character sc,asitisshowninTable 3. = [ ⋅ (𝐸 −𝐸)] . sc sign pdg 𝑡 𝑖 (14) One finds that the general relation between the intercept 𝑖 From Table 2 one finds that while for the so-called “nor- of the least-squares (regression) line (15)andthemodulusof + + + − − + + − − thepolarizationdegreepdgofthecapturecross-sectionsis mal” states (as those of Ti𝑖 ,Cr𝑖 , (Cr𝑖 B𝑠 ) ,Mn𝑖 , (Mn𝑖 B𝑠 ) , ( + −)− − − + 󵄨 󵄨 Fe𝑖 B𝑠 ,Au𝑠 ,Zn𝑠 ,Pt𝑖 ) the state character has the value 𝑖=sc ⋅ 󵄨pdg󵄨 . (16) sc =+1,forthe“trans-Fermi level acceptor/donor states” ++ ++ + ++ + −− (Ti𝑖 , V𝑖 , Mo𝑖 , Mn𝑖 , Fe𝑖 , Zn𝑠 ) it has the value sc =−1. The priority order of the dark current spectroscopy (DCS) Thisfindingwillbeusefulfortheidentificationofthecapture assignment criteria of the capture traps of a CCD pixel traps states in the case of small groups of traps inside some refers mainly to the values of the (a) preexponential factor 𝐷𝑒− CCDs pixels. 0,dep.eff. of the depletion dark current, which can indicate the magnitude order of the number of traps inside the con- 5.2. DCS Assignment Criteria for the Small Groups of Capture sidered CCD pixel, (b) the modulus of the energies difference Traps of Some CCD Pixels. As an example of application |𝐸𝑡 −𝐸𝑖|, (c) the capture cross-sections of different traps, Advances in High Energy Physics 9

(d) the state character sc, and (e) the generation rate 𝑈.Of both the important differences between the basic notions 𝐷𝑒− course, the traps states with the smallest values of 0,dep.eff. and parameters of the dark current spectroscopy method correspond to the lowest numbers of traps. As it results from (DCS) and of the deep-level transient spectroscopy (the most Table 4, from the studied CCD pixels, that of coordinates 321, important present alternative experimental method) one the 400 seems to have the lowest traps population, maybe only possibilities to combine their results. one trap. Given that the corresponding depletion dark current is very weak, the corresponding measurement errors are very Acknowledgments large, and the trap assignment is rather difficult. As it results from the study of the specialty literature [86, 89, 90, 95], the The authors thank very much Professors Erik Bodegom and main “candidates” for this pixel trap are mainly the electronic Ralf Widenhorn from the Physics Department of the Port- states of Au and Mn. But, as it results from Table 2, while the land State University for the important awarded information electronic states of Au are usually “normal” ones (sc =+1), andsuggestions,aswellastheleadershipofthePortland someofthenumerouselectronicstatesofMncanbelong State University (Oregon, USA) for the Memorandum of also to the trans-Fermi capture states (i.e., sc =+1, e.g., the ++ Understanding 9908/March 6, 2006–2011, with University electronic state Mn𝑖 ). Given that the electronic state of the “Politehnica” from Bucharest, which allowed this coopera- MnAu nanocomplex presents the value |𝐸𝑡 −𝐸𝑖| = 0.30 eV, we tion. consider this complex and its atoms Mn and Au as the most justified to correspond to the first 3 pixels from Table 4 (with the lowest value of the depletion preexponential factor). References The analysis of the results synthesized by Table 4 points [1] J. R. Janesick, Scientific Charge-Coupled Devices,SPIEPress, out also that the strong nonlinearity of the SRH model Bellingham, Wash, USA, 2000. relations (2) and (7), as well as of the temperature dependence [2] R. Widenhorn, Charge Coupled Devices,VDM,Saarbruecken, of the semiconductors energy gaps 𝐸𝑔 (see, e.g., [36, 82], 𝐸 Germany, 2008. etc.), imposes the use of the effective parameter 𝑔,eff. (pixel) depending on all DCS physical results referring to a given [3] J. B. Spratt, B. C. Passenheim, and R. E. 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Research Article Precise 3D Track Reconstruction Algorithm for the ICARUS T600 Liquid Argon Time Projection Chamber Detector

M. Antonello,1 B. Baibussinov,2 P. Benetti,3 E. Calligarich,3 N. Canci,1 S. Centro,2 A. Cesana,4 K. Cieslik,5 D. B. Cline,6 A. G. Cocco,7 A. Dabrowska,5 D. Dequal,2 A. Dermenev,8 R. Dolfini,3 C. Farnese,2 A. Fava,2 A. Ferrari,9 G. Fiorillo,7 D. Gibin,2 S. Gninenko,8 A. Guglielmi,2 M. Haranczyk,5 J. Holeczek,10 A. Ivashkin,8 J. Kisiel,10 I. Kochanek,10 J. Lagoda,11 S. Mania,10 A. Menegolli,3 G. Meng,2 C. Montanari,3 S. Otwinowski,6 A. Piazzoli,3 P. Picchi,12 F. Pietropaolo,2 P. Plonski,13 A. Rappoldi,3 G. L. Raselli,3 M. Rossella,3 C. Rubbia,1,9 P. Sala,4 A. Scaramelli,4 E. Segreto,1 F. Sergiampietri,14 D. Stefan,1 J. Stepaniak,11 R. Sulej,1,11 M. Szarska,5 M. Terrani,4 F. Varanini,2 S. Ventura,2 C. Vignoli,1 H. Wang,6 X. Yang,6 A. Zalewska,5 and K. Zaremba13

1 Laboratori Nazionali del Gran Sasso dell’INFN, S.S. 17 BIS km. 18.910, 67010 Assergi, Italy 2 Dipartimento di Fisica e Astronomia e INFN, Universita` di Padova, Via Marzolo 8, 35131 Padova, Italy 3 Dipartimento di Fisica e INFN, Universita` di Pavia, Via Bassi 6, 27100 Pavia, Italy 4 INFN, Sezione di Milano e Politecnico, Via Celoria 16, 20133 Milano, Italy 5 Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Science, ul. Radzikowskiego 152, 31-342 Krakow,´ Poland 6 Department of Physics and Astronomy, University of California, 430 Portola Plaza, P.O. Box 951547, Los Angeles, CA 90095-1547, USA 7 Dipartimento di Scienze Fisiche e INFN, UniversitaFedericoII,ViaCintia,80126Napoli,Italy` 8 INR RAS, Prospekt 60-letiya Oktyabrya 7a, Moscow 117312, Russia 9 CERN, 1211 Geneve´ 23, Switzerland 10InstituteofPhysics,UniversityofSilesia,Uniwersytecka4,40-007Katowice,Poland 11National Centre for Nuclear Research, Andrzeja Soltana 7, 05-400 Otwock, Swierk, Poland 12Laboratori Nazionali di Frascati (INFN), Via Fermi 40, 00044 Frascati, Italy 13Institute of Radioelectronics, Warsaw University of Technology, Nowowiejska 15/19, 00-665 Warsaw, Poland 14INFN, Sezione di Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy

Correspondence should be addressed to D. Stefan; [email protected] and R. Sulej; [email protected]

Received 22 October 2012; Revised 10 January 2013; Accepted 15 January 2013

Academic Editor: Maury Goodman

Copyright © 2013 M. Antonello et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Liquid Argon Time Projection Chamber (LAr TPC) detectors offer charged particle imaging capability with remarkable spatial resolution. Precise event reconstruction procedures are critical in order to fully exploit the potential of this technology. In this paper we present a new, general approach to 3D reconstruction for the LAr TPC with a practical application to the track reconstruction. The efficiency of the method is evaluated on a sample of simulated tracks. We present also the application of the method tothe analysis of stopping particle tracks collected during the ICARUS T600 detector operation with the CNGS neutrino beam.

1. Introduction particles with the level of details comparable to bubble chamber technology. The concept is now exploited in several The LAr TPC detector idea, proposed in 1977 by Rubbia1 [ ], projects around the world [2–5]withtheICARUST600 provides spatial and calorimetric measurement of charged [6, 7] being the largest presently operating detector, located at 2 Advances in High Energy Physics

Cathode Induction1 Induction2 Collection

Induction1 Induction2 Collection

− e − −e e − e 𝑋 + + + − 𝑋 e + 𝑍 𝜇 𝜇 𝐸 +

𝑌, time 𝑍

(a) (b)

Figure 1: Schematic view of the ICARUS T600 readout principle; one of four TPCs is shown: (a) 3D view with marked 𝜇 track and the − ionization electrons e drifting in the electric field 𝐸 toward the readout wire planes; (b) the XZ projection with marked actual intersections of the particle track and readout wires (green and orange points) and an example of points on the reconstructed track that may be obtained by associating wire signals from Induction2 and Collection planes using drift timing (black crosses).

Gran Sasso underground National Laboratory, on the CNGS with the identification of individual signals on wires, the neutrino beam. The LAr TPC technique is of interest for a so-called hits. At this point the position and calorimetric wide physics program including studies of neutrino oscilla- information are assigned to hits. In the next step hits are tion parameters, sterile neutrinos, CP violation, violation of aggregated in clusters forming 2D structures: tracks and baryonic number conservation, and dark matter searches. showers. Hit clustering is a challenging image recognition The operating principle of the LAr TPC detector as imple- taskinitselfgiventhecomplexityandvarietyofpossible mented in the ICARUS T600 is illustrated in Figure 1(a).A event topologies. A solution based on the DBSCAN algorithm charged particle produces ionization electrons and scintilla- has been proposed in [2]; however the techniques that tion light along its path. Free electrons drift in a uniform are efficient at reconstructing complex topologies are being electric field toward the anode that is composed of three under study. Independently from the clustering method, 3D wire planes. Diffusion of the drifting electrons is low enough, objects are reconstructed using 2D hit clusters associated in 2 4.8 cm /s, [7], to preserve details of the ionizing particle at least two wire planes. 3D reconstruction provides informa- track. A signal is induced in a nondestructive way on the tion necessary for further analysis; particularly directions of first two wire planes, Induction1 and Induction2, which are particles and their momenta are crucial for the reconstruction practically transparent to the drifting electrons. The signal on oftheeventkinematics.Alsotheparticleidentificationof the third wire plane, Collection, is formed by collecting the low energy hadrons is based on the energy losses along their ionization charge, which is also the source of the calorimetric tracks, 𝑑𝐸/𝑑𝑥, and it is dependent on the precision of the measurement. Different orientation of the wires in the anodic spatial reconstruction. ∘ ∘ ∘ planes (0 ,+60, −60 with respect to the horizontal, with Typical approaches to the track 3D reconstruction pre- 3 mm wire spacing in each plane) allows localization of the sented in recent papers [2, 3, 6, 7]arebasedonmatching signal source in the XZ plane as shown in Figure 1(b),while the hits or the track end points from the individual 2D wire the Y coordinate, which defines the distance to the wire planes by their drift timing. Examples of reconstructed events planes, is calculated from the wire signal timing and the were shown, however without the evaluation of the algorithm electron drift velocity, 1.59 mm/𝜇s. Wire signals are amplified efficiency on a large sample of tracks. and digitized with 2.5 MHz sampling frequency which results The first limitation of the approach based on the drift in 0.64 mm spatial resolution along the drift coordinate. The time matching is illustrated in Figure 1(b).TheXZ position absolute event timing, 𝑡0,isprovidedbythepromptsignal of the 3D point is obtained as the crossing point of the from the photomultipliers collecting the scintillation light. wires containing the matched pair of 2D hits. This leads to a 2 Finally, digitized waveforms from consecutive wires placed position quantization in the XZ plane, 3.5×3.5 mm assuming ∘ nexttoeachotherform2Dprojectionimagesofanevent,like 3 mm wire-to-wire spacing and 60 inclination between wires in the example of neutrino interaction shown in Figure 2. of the consecutive readout planes. Moreover, any spurious The reconstruction of an event is split into a series of hit matching adds an additional error of 3.5 mm per each several steps realized with independent algorithms. It starts wire shift with respect to the correct matching. This effect Advances in High Energy Physics 3

0.5 m Electromagnetic showers

Muon track

Time Primary vertex Hadron tracks Wire no. CNGS beam direction

(a) 0.5 m Electromagnetic showers

Muon track Hadron tracks Time Primary vertex Wire no. CNGS beam direction

(b) 0.5 m

Electromagnetic showers

Muon track

Time Hadron tracks

Wire no. Primary vertex CNGS beam direction

(c)

Figure 2: Data: CNGS ]𝜇 charge current interaction in the ICARUS T600 detector, a fragment of the wire data in one of the detector modules: (a) Collection plane; (b) Induction2 plane; (c) Induction1 plane. The horizontal wires of the Induction1 plane form the projection on XY plane and give the frontal view of the event while the Collection and Induction1 planes form YZ projections and give the top views of the event seen at two angles. introduces kinks and distortions to the track constructed with (b) simultaneous use of the three wire planes is not matching hit by hit, visible also in the track examples shown straightforward and was not developed according to in [6, 7]. On the other hand, the straight line approximation is our knowledge; not sufficient to reproduce the particle trajectory in all details (c) a robust algorithm requires preprocessing, such as hit available with LAr technology, such as elastic scatterings of sorting, in each 2D projection independently before the low energy particles. the projections matching; we found this difficult in Another drawback of the approach based on the drift time case of the sophisticated track topologies, particularly matching is the inefficiency of the reconstruction of tracks in case of scatterings at a sharp angle in the 2D parallel to the wire planes. The low variation in the hit drift projection. timing along the track increases ambiguities in the individual hit association between the wire planes. In data, tracks with spurious reconstruction are difficult The disadvantages that we also observed during the to distinguish from tracks with correctly reconstructed fea- studies of the drift time-based matching of 2D projections tures. This motivated us to search for a different concept of3D include reconstruction that would be capable of reproducing details along the whole track, at any track orientation. (a) incomplete information, for example, missing parts of In this paper we propose to build 3D objects by simul- the track in one of the wire planes due to a hardware taneous optimization of their 2D projections to match data problem, is difficult to manage; in the wire planes. A single fit function is constructed to 4 Advances in High Energy Physics combine all pieces of information available in data with Hits with adjacent drift time windows form a group that the constraints specific to the considered object type. The isfittedasitwouldbeforasinglewindow.Thefitfunctionfor proposednewapproachisappliedinthispapertotracks,but each drift time window reads the idea is general and may be explored in the reconstruction 𝑁𝑝 of cascade-like objects, detailed reconstruction of interaction 𝑓 (𝑡) =𝐵+∑ 𝑝 (𝑡) , vertex regions as well as in global event reconstruction. It is 𝑤 𝑖 𝑖=1 (2) also straightforward to adapt the implementation to detector −1 readout concepts different from wire planes, for example, −(𝑡−𝑡𝑝𝑖)/𝜏1 −(𝑡−𝑡𝑝𝑖)/𝜏2 𝑝𝑖 (𝑡) =𝐴𝑖𝑒 (1 + 𝑒 ) , basedonlargeelectronmultipliers(LEMs)[8]. In Section 2 we describe the general algorithm idea where 𝑝(𝑡) is the function describing the impulse response and its practical implementation details. Then we show ofthewirereadoutelectronics,laterintextcalledapulse; (Section 3) the algorithm performance evaluated on sim- 𝐴𝑖 is the 𝑖th pulse amplitude; 𝑡𝑝𝑖 is the 𝑖th pulse timing; 𝜏1 ulated particle tracks, compared with the results obtained and 𝜏2 are the rising and falling time constants, respectively, from the previously developed hit matching algorithm. The with common values for all pulses in the fit; and 𝐵 is the proposed method is cross-checked on a sample of stopping fit baseline. The fit parameter values and the number of 2 particlesselectedintheeventscollectedduringtheCNGS pulses, 𝑁𝑝, are iteratively optimized to minimize 𝜒 = run (Section 4). Finally, in Section 5,wesummarizeresults ∑ [ (𝑡) − 𝑓 (𝑡)]2/𝑁 𝑁 =𝑁 −(2𝑁 + 𝑡 ADC 𝑤 free where free ADC 𝑝 and comment on possible future enhancements. 3) 𝑁 is the number of degrees of freedom of the fit, ADC is the number of ADC samples in the drift time window, and 2. Algorithm 2𝑁𝑝 +3is the total number of 𝑓𝑤(𝑡) parameters. Pulses 𝑝𝑖(𝑡) become the new hits that replace those initially found at the 𝑇 The particle real track is observed in the detector as a set hit identification stage. The maxima of pulses are considered 𝑃 (𝑇) 𝑃 (𝑇) 𝑃 (𝑇) of three 2D projections 𝐼1 , 𝐼2 , 𝐶 to Induction1, as the drift coordinate positions of the new hits, 𝑡𝑑. Induction2, and Collection wire planes, respectively. In prac- The particle energy deposit observed in a hit is calculated 𝑡 /𝜏 tice these projections consist of 2D hits. The 3D fit trajectory 𝑞 =𝑞 𝑊 𝑑 𝑒 𝑞 𝐹 as 𝐸 𝐶 e eV, where 𝐶 is the hit charge calculated as may be projected to the wire planes according to the same the integral of the corresponding pulse 𝑝(𝑡) scaled according operators 𝑃(𝐹).Weproposetobuildthefit𝐹 by minimizing a −4 to the calibration factor 152 ± 2 × 10 fC/(ADC ×𝜇s), as measure of the distance 𝐷 between the fit projections and the evaluatedin[10]. 𝑊 is the average energy needed for the track hits in all wire planes simultaneously, with constraints +0.5 creation of an electron-ion pair, 23.6−0.3 eV [11], and 𝜏𝑒 is the 𝐶𝑗(𝐹) that may include factors such as trajectory curvature anddistancetothealreadyidentifiedandreconstructed free electron lifetime, which is monitored during the detector interaction vertices. This may be expressed with an objective operation, as presented in [6]. function 𝐺(𝐹): Particle tracks perpendicular to the drift direction produce signals that are fitted with a single pulse per wire, while 𝐺 (𝐹) = ∑ 𝛼 𝐷[𝑃 (𝑇) ,𝑃 (𝐹)]+∑ 𝛽 𝐶 (𝐹) , wire signals induced by tracks more parallel to the drift 𝑖 𝑖 𝑖 𝑗 𝑗 (1) 𝑖 𝑗 direction need to be considered as sequences of pulses with varying amplitudes and timings (Figure 3). where wire planes, denoted with the index 𝑖,andconstraint The uncertainty on the energy deposit of the recon- factors, denoted with the index 𝑗, have a weighted impact on structed hits was estimated from reconstruction of the sim- the overall 𝐺(𝐹) value according to the 𝛼𝑖 and 𝛽𝑗 coefficients. ulated signal with added electronics noise based on data. The For the practical implementation of constructing the best uncertainty is almost independent from the actual hit energy fit track we have adopted the Polygonal Line Algorithm deposit value, and it is constant at the level of 𝜎 = 0.06 MeV [9], PLA, described in more detail in Section 2.2;however (Figure 4). The lowest amplitude hits observed on the particle any other approach, even straight line approximations, may tracks are related to the minimum ionizing muons; energy follow the same concept of simultaneous optimization of 2D deposit of such hits is on the level of 0.5–0.7 MeV. The projections. resulting worst case inaccuracy of the energy deposit per hit is roughly 10%. 2.1. Hit Reconstruction. Webriefly describe the method of the individual hit reconstruction since it is the essential base for 2.2. Track Reconstruction. The objective function 𝐺(𝐹) (1) thespatialandcalorimetricmeasurements. has been inspired by the PLA formulation, which is an Inthefirststagehitsareidentifiedinallwireplanes efficient algorithm for the principal curve finding problem following the algorithm presented in [7]. As a result hit [9]. The principal curve, in our case the best track fit 𝐹, positions in the drift coordinate are obtained together with is approximated with the polygonal line determined by 3D the drift time windows, which cover the hit ADC waveform points, called later nodes, interconnected with straight 3D with a margin required for the second stage. segments. The difference from the original PLA application In the second stage fitting hits within the drift time is that we are looking for the principal curve in 3D while the windows is applied to the Collection plane. This improves distance to data points is given in 2D projections. The track the hit positioning, resolves overlapping hits, and allows the fit shape and its projections distances to the 2D hits need to reconstruction of the individual hit energy deposits. be optimized to allow unbiased reconstruction of the track Advances in High Energy Physics 5

3 5 cm

n 1 2 2

C N 1 ADC count co nt Time TimTTimeme Wire no.

(a) (b)

Figure 3: Data: Collection wire signal fragment: (a) raw ADC (blue) and the fit function (red); (b) fragment of the 2D wire view; red arrow indicates the wire shown in (a). Hits (1, 2) are induced by the tracks perpendicular to the wires and are fitted with single pulses; hit (3) is induced by the track more parallel to the wires; this hit was split into two hits in the second stage of the hit reconstruction algorithm. The feature marked with (N) in the raw ADC is too low to be recognized as hit during the signal fit optimization.

0.6 Initialization 0.4 250 0.2 200 (MeV) 0 150 MC Projection

−𝑞 −0.2 100

reco −0.4 50 𝑞 Optimization Add node −0.6 0 1 10

𝑞MC (MeV) Convergence N Figure 4: Simulation: the absolute difference between the recon- 𝑞 Y structed hit energy deposit ( reco) and the simulated hit energy 𝑞 𝑞 deposit ( MC) as a function of MC.Thehitsshownareoriginating 𝐾≥𝐾 max from muon tracks simulated with isotropic initial direction. The tail N 𝑞 < 0.4 of the distribution with MC MeVcorrespondstothehits Y at track end points, only partially crossing the distance between End consecutive wires. The peak of the distribution corresponds to the 𝑞 hits of minimum ionizing particles; the points at high values of MC Figure 5: Fit optimization diagram. The inner loop contains the hit come from low energy, highly ionizing parts of tracks. assignment to nodes and segments of the fit (projection step) and the optimization of node 3D positions. New nodes are introduced to the fit in the outer loop until the 𝐾max numberofnodesisreached. features, such as scatterings and decay points, taking into accountalsothehitpositionsaccuracy. The diagram in Figure 5 shows the main steps of the PLA algorithm. In the initialization the first segment with two During the optimization step the node positions are nodes is placed in the 3D space, according to the procedure updated to minimize the objective function (1). To reduce described in Section 2.2.1.Thenthetrackfit𝐹 is constructed the computational complexity we use a local version of in an iterative way by adding new nodes and rebuilding the objective function (we use a gradient descent method segments. After adding a new node, the positions of all nodes, with the finite differences approximation of the gradient 𝜕𝐺(𝐹)/𝜕n denoted with n𝑘 where 𝑘=1...𝐾,areoptimizedintheinner 𝑘; therefore it is convenient to express the objective 𝐺(𝐹) = loop of the algorithm. Simultaneously with changes of the function as a sum of independent components): ∑ 𝑔(n ) 𝑔(n ) node positions, the fit 2D projections to the wire planes are 𝑘 𝑘 where 𝑘 is a function assigned to the kth node updated. of the fit: The 2D projections of the track fit 𝐹 are determined by the node 2D projections, 𝑃𝑖(n𝑘), which also describe segment 2D 𝑔(n𝑘)=𝑑(n𝑘)+𝛽V𝑐V (n𝑘)+𝛽𝑎𝑐𝑎 (n𝑘) (3) projections. The algorithm stops when the maximum number of nodes, 𝐾max,isreached. The inner loop of the algorithm consists of two steps: the anditconsistsofthefollowingcomponents: projection and the optimization. In the projection step, 2D hitsareassignedtothefitsegmentornode.Thisisdoneby finding the segment/node 2D projections with the minimal (a)weightedaverageofthesquareddistanceofthefit distancetothe2Dhit,asitisillustratedinFigure 6. projection to the 2D hits that are assigned to the kth 6 Advances in High Energy Physics

node and segments connected to that node, in all wire n4 planes: n2 𝑃(𝑇) 𝑃(𝐹) 1 󵄩 󵄩2 𝑑(n )= ∑ (𝛼 ∑ 𝜔 󵄩 h𝑖 −𝑓 (h𝑖 ) 󵄩 ), 𝑆23 𝑘 𝑖 𝑛󵄩 𝑛 2D 𝑛 󵄩 (4) 𝑁𝑘 𝑆12 𝑖 𝑛∈𝑁𝑖𝑘 𝑆 𝛾 34 2D 𝑁 𝑁 where 𝑘 is the number of considered hits, 𝑖𝑘 Time 𝑖 includes indices of hits in the th wire plane among n h𝑖 3 all hits considered with kth node, 𝑛 is the position n 𝑛 𝑖 𝑓 h𝑖 1 of the th hit in the wire plane ,and 2D ( 𝑛)isthe position of this hit projection to the fit 2D projection, Wire 𝑃𝑖(𝐹),asillustratedinFigure 6; 𝜔𝑛 is the coefficient Figure 6: Schematic view of the track 𝑃(𝑇) (red) and fit 𝑃(𝐹) (blue) used to weight the contribution of the individual projections in the wire plane. 2D hits (orange dots) are marked on hits to 𝑑(n𝑘) value; we calculate 𝜔𝑛 as the ratio of 𝑃(𝐹) 𝑛 the track projection intersections with wires; hit projections to th hit amplitude over the maximum hit amplitude are marked as green dots; hit distances to 𝑃(𝐹) are marked with black among hits considered in the inner sum of (4), which sections. Hits from grey shaded regions 𝑠𝑥𝑦 are assigned to segments; 𝑛 𝛾 efficiently suppresses the impact of the noise hits hits from white regions 𝑥 are assigned to nodes. Indicated angle 2D spuriously accounted to the track, usually of the much is the 2D projection of the 𝛾 angle between the fit segments in 3D (see lower amplitudes than the signal hits; (7)intext). (b) the average squared distance of the fit to the 3D vertices created independently from the track reconstruction algorithm: considered hits), 𝜂 is an arbitrary factor assigned to the end nodes (𝜂 value was determined empirically as 1 󵄩 󵄩2 𝑐 (n )= ∑ 󵄩 v −𝑓 (v ) 󵄩 , 0.05 to avoid excessive stretching of the end segments V 𝑘 󵄩 𝑚 3D 𝑚 󵄩 (5) 𝑀 𝑚∈𝑀 or shortening the whole track fit (however precise 𝑘 tuning has no strong effect on the obtained fit)), 𝑝 𝑀 𝑀 scale factor allows to shape the contribution of where isthenumberofallusedvertices, 𝑘 the constraint while 𝐾 (the number of the nodes) includes indices of vertices assigned to the kth node is growing (we use 𝑝=1.8to allow slow decrease and segments connected to that node, v𝑚 is the 𝑚 𝑓 (v ) of the constraint while approaching the minimum of position of the th vertex, and 3D 𝑚 is the position the objective function), and the constraint on the fit of this vertex projection to the fit; in the present stage segment angles allows to keep a smooth track fit along we do not differentiate accuracy of the individual the particle trajectory. vertex positions; however it is straightforward to 𝜔 introduce a coefficient similar to 𝑛 in (4)when Coefficients 𝛼𝑖, 𝛽𝑎, 𝛽V in (3)and(4) correspond to 𝛼𝑖 and thereconstructionaccuracyisavailable;identification 𝛽𝑖 in (1)andallowtokeepbalancebetweenoverfittingto and reconstruction of the 3D vertices is beyond the the noise in hit/vertex positions and ability to reconstruct scopeofthispaper;thereforeweonlynotethatsuch correctly the significant track features. The actual values of vertices may tag the particle interaction, decay points, these coefficients depend on the noise conditions ofthe or delta ray spots identified along the particle track; readout wire planes. (The coefficient values used for the 𝛼 = 1.0 𝛼 = (c) constraint on the angles 𝛾 between the consecutive ICARUS T600 data are the following: Coll , Ind2 0.8 𝛼 = 0.2 3Dsegmentsandonthelengthoftheoutermost , Ind1 (for Collection, Induction2, and Induction1 𝛽 = 1.0 𝛽 =2.0 segments where the angle 𝛾 cannot be calculated: planes resp.); V ; 𝑎 .Valueswereadjusted empirically to maximize the reconstruction efficiency.) The 𝑝 𝑐𝑎 (n𝑘) =𝐾 [𝜋 (n𝑥=𝑘−1) +𝜋(n𝑥=𝑘) +𝜋(n𝑥=𝑘+1)] , (6) performance in the localization of track features, scattering, and decay points, is illustrated in the examples of simulated 𝜋(n𝑥) tracks in Section 3 and in the example of decaying kaon in Section 4. 𝑟2 (1 + 𝛾 )𝑥∈⟨2; 𝐾 − 1⟩ { 𝑥 cos 𝑥 inner nodes The node positions optimization step is finished when { 󵄩 󵄩2 𝐺(𝐹) 𝜂⋅󵄩n𝑥+1 − n𝑥󵄩 𝑥=1 first node the minimization of converges to a stable value. (The = 󵄩 󵄩2 {𝜂⋅󵄩n − n 󵄩 𝑥=𝐾 relative change of 𝐺(𝐹) is calculated after each step of the { 󵄩 𝑥 𝑥−1󵄩 last node minimization algorithm, which updates all node positions. {0 𝑥<1 𝑥>𝐾, or The value of 𝐺(𝐹) is considered as stable when the relative −4 (7) change is below 10 ;howeverinthefirststagesofbuilding the track we use higher values to speed up the computations.) where 𝑟𝑥 is the radius of the hits assigned to the Then the new node is added to the segment with the 𝑥th node and connected segments (the maximum maximumnumberofhitsassignedintheprojectionstep.The distancebetweenthehitandthemeanpositionofall position of the new node is chosen as the one that separates Advances in High Energy Physics 7 Time Time

Wire no. 25 cm Wire no. 25 cm

(a) (b)

Figure 7: Muon track (data, CNGS ]휇 CC interaction) observed in the Induction1 view and reconstructed using the Collection and the Induction2 plane hits with different delay values between these planes: (a) Induction1 raw data view; (b) 3D track reconstructed with three different delay values and then projected to Induction1 view, orange-optimal delay, blue and green, over- and underestimated delay, respectively.

the selected segment into two parts containing the same end point pairs. Then the two possibilities are tested, and the number of hits. one with smaller resulting 퐺(퐹) is chosen. The stopping condition of the algorithm, the maximum 1/3 number of nodes 퐾max = min(푁/5, 7푁 ),isbasedonthe 2.2.2. Wire Plane Spacing. The timing difference between the number of hits 푁; it reflects the track length and allows to corresponding signals observed on successive wire planes is keep a higher number of hits per segment for high energy the combination of the electron drift time between the wire particles with long tracks. Short tracks with 푁≤5are planes and the delays in the electronics. Inaccurate estimation approximated with a single segment. Stopping condition of the overall delay may cause strong systematic effects in parameters were optimized to maximize the spatial recon- terms of the expected precision of the reconstruction. The struction efficiency measures shown in Section 3. delay value for the ICARUS T600 data has been fine-tuned Finally, the 3D positions corresponding to the 2D hits are empirically, by reconstructing the tracks using two wire calculated: planes and minimizing the distance between fit projection and track hits in the third wire plane (Figure 7). (a) if the hit is assigned to the fit segment: the hit projec- Long tracks, almost parallel to the wire planes, were used 푓 (h) tion to the fit segment projection, 2D , determines in the tuning since they are the most sensitive to changes in the 3D hit position since the relative distance from the the timing delay between planes. segment beginning with respect to the segment length is the same in 2D projection and in 3D space; 2.2.3. Calorimetric Measurement. The sequence of the ion- 푑푄 푑푥 푑푄/푑푥 (b)ifthehitisassignedtothefitnode:thehit3Dposition ization charge collected per track length, , issimplythenodeposition. isevaluatedfromthechargesandthe3Dpositionsofthe Collection plane hits. Since tracks nearly parallel to the drift direction can contain several hits within a small range along 2.2.1. Initialization. The fit optimization starts from two the drift direction, it is convenient to limit the minimal 푑푥 nodes connected with a single segment. The initial 3D lengthtoavalueclosetothewirespacingdistance,inour positions of the first two nodes should roughly correspond to application 2.7 mm. The hit charge is assigned to the 훿푥 length the track end points. We assume that hits in the individual surrounding the hit, calculated as (푥1+푥2)/2,where푥1 and 푥2 wire views are not ordered and the exact matching of hits are the distances to the preceding and subsequent Collection corresponding to the actual track end points is not possible. hits, respectively. Hit charges and 훿푥 lengths are summed up The initial node positions are evaluated as follows: a straight until the minimum value of 푑푥 is reached. In this way 푑푥 line is fitted to the hits within the wire plane using the linear values are comparable for any track orientation with respect regression; two outermost projections of hits to the fitted to the Collection wires direction. Then the correction due to line are considered as 2D end points; end points from two the recombination effect [12]maybeappliedtoobtainthe wire planes are paired by the minimal drift time difference to actual value of the energy deposit per track 푑푥 length, 푑퐸/푑푥, obtain 3D node positions. (This rough approximation of 3D according to the Birk’s semiempirical formula, which can be position may fall out of the actual detector volume. In such a expressed as case we simply limit the obtained position to the nearest one 푑푄 푘 푑푄 inside the detector.) Then the minimization of the objective 푑퐸 = ,푅=퐴− ⋅ , function 퐺(퐹) is performed to find the optimal positions of 푅 휀⋅휌 푑푥 (8) the first nodes. In case of short tracks parallel to wire planes it is possible to obtain wrong matching of 2D end points due where 푅 is the correction factor, calculated with the param- 2 to the small drift time difference of two combinations of 2D eters 퐴 = 0.81, 푘 = 0.055 (kV/cm)(g/cm )/MeV, 휀= 8 Advances in High Energy Physics

3 0.5 kV/cm and 휌 = 1.4 g/cm that were obtained from data shown in Figure 9,illustratesanarrowanglebetweentwo collected during the detector test run [12]. tracks in a decay chain. Such an event topology was not manageable with our implementation of conventional hit 3. Algorithm Performance on matching approach. Simulated Tracks 3.1. Reconstruction Efficiency Dependence on the Track Inclina- The algorithm performance was evaluated on samples of tion. Since the reconstruction depends on the track orienta- simulated stopping protons and muons, two species with tion with respect to the readout wires we present an efficiency different track properties: low and medium energy protons evaluation as a function of the angle 휃푤 between the normal produce relatively straight tracks characterized by high ion- to the wires direction and the initial particle direction in ization while muons of the comparable range are more scat- 2D projections. Samples of 5000 protons and muons were tered and give signals of much lower amplitude. Particles were simulated with isotropic direction, with initial kinetic energy transported in LAr using the FLUKA simulation package 퐸푘푝 = 232 MeV and 퐸푘휇 = 100 MeV, respectively, in [13, 14], including all physical interactions such as delta rays, order to ensure comparable range (30 cm) of both kinds of inelastic scatterings, decays, and absorptions. The ionization particles. The particles that are stopping or decaying at rest charge along the track was subject to the recombination effect were selected for further tests. [12]. In order to evaluate the geometrical reconstruction effi- Cases with all distances of MC cells to the fit below ciency the volume of the detector was divided into elements of 5 mm were considered as correctly reconstructed tracks. The 3 3mm , called later MC cells, used to accumulate the resulting fraction of correctly reconstructed tracks as a function of 휃푤 charge without any instrumental effect. Simultaneously, the is shown in Figure 10. The comparison of results obtained charge was also collected in bidimensional structures that with the new method and the hit matching based approach reproducethe2Dwireviewskeepingthesamewirespacing is shown on the proton track sample in Figure 10(a).The and orientation as in the real detector and a drift coordinate spatial reconstruction is better with the new 3D approach granularity finer than the one corresponding to the ADC even if applied to the relatively simple proton tracks. The sampling. The resulting charge deposition was convoluted problems pointed in the Introduction section and illustrated with the readout channel response using packages dedicated with the example in Figure 8 arecauseofthesignificant to the ICARUS T600 detector. Finally, the electronics noise inefficiencies of the traditional method in the detailed spatial has been applied to the wire signals, with use of the noise reconstruction of tracks. parameters obtained from data. Then the hit and track The worsening of the reconstruction efficiency of the ∘ ∘ reconstruction procedures were applied and compared with proposed method, seen at 휃푤 =0, 180 , is related to tracks the unperturbed MC cells. parallel to the wire planes with a short projection (a few The presented tests are the reconstruction of isolated hits) in one of the planes. A second source of the inefficiency tracks, without added information about vertices. The simple is the ambiguity of the fit initialization when the straight topologies of the simulated tracks allow to show basic proper- track in the XZ plane has two possible 3D fit solutions. The ∘ ties of the proposed method. The tests include reconstruction inefficiency seen around 휃푤 =90 is related to tracks nearly oftheparticleinitialdirectionbasedonthecomparisonwith parallel to the drift direction, which produce long signals on the simulated initial momentum vector, the spatial recon- a few wires, more difficult to resolve in the Induction2 plane. struction along the track based on MC cells positions, and cal- The efficiency obtained for muon tracks is smaller than the orimetric reconstruction of the particle kinetic energy. Two one for protons due to the spurious assignment of the muon examples are shown to illustrate the algorithm properties. decayproducthitstothemuontrackandviceversa.Theeffect The reconstruction results obtained with the proposed caused by the wrong hit assignment is increased at the muon ∘ method are compared to the results of a previously devel- track inclinations close to 휃푤 =90. oped algorithm. This previous approach was based on the Adding information from the Induction1 plane independent reconstruction of the two 2D projections of the (Figure 10(c)) reduces significantly spurious reconstruction, track, with the application of the PLA [9]. Hits from the track especially for the tracks parallel to the wire planes. The projection in the Collection plane were paired with the hits efficiency gain is higher in case of the muon tracks which are on the track projection in the Induction plane using drift scattered more than protons at energies considered here, and timing. Hits ordering obtained from PLA was used to resolve they are more likely to have track bends visible only in the XZ ambiguities in choosing the best matching pair if several hits view. When three wire planes are used, the reconstruction werefoundwiththeclosedrifttimevalues.Matchedhitpairs fails mostly in case of straight tracks oriented strictly in the were used to obtain the 3D track points. The comparison of Z direction, which is more likely for proton tracks. (Also both methods is shown on the proton track samples in the these cases may be recovered in the further development following subsections. of the algorithm. A short track projection (i.e., 1-2 hits) in The effects pointed out in the Introduction section, such one of the views in the present form of the algorithm has as the spurious 2D hit matching and the quantization of 3D negligible impact on the overall objective function 퐺(퐹), positions in the XZ plane, are well visible in the reconstruc- while it should help to exclude impossible solutions. This tion of tracks nearly parallel to the XZ plane, as it is shown maybeachievedbyafuzzyassignmentofall2Dhitstoall in the example in Figure 8. These problems are practically fit segments, weighted with the distance of the hit to the eliminated in the proposed algorithm. The second example, segment projection in 2D.) The other source of inefficiency, Advances in High Energy Physics 9 Time Time

Wire no. 10 cm Wire no. 10 cm

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Figure 8: Simulation and reconstruction of a proton track: (a) Collection wire view; (b) Induction2 wire view; (c) and (d), respectively, YZ and XZ views of the MC cells (orange dots) and the track reconstructed: using matching 2D projections by drift timing (blue curve) and using 3D fit optimized to 2D projections (green curve). Time Time Time

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+ + + Figure 9: Simulated decay chain of 퐾 →휇]휇 →푒]푒]휇: (a) Collection view; (b) Induction2 view; (c) Induction1 view; (d) 3D reconstruction; MC cells are marked with orange dots, and reconstructed track is marked with blue curve. The tracks of all three particles were reconstructed together to show the capability of reconstructing narrow angles between tracks. 10 Advances in High Energy Physics

1.2 1.1

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Figure 10: Fraction of the reconstructed proton and muon tracks with the maximum MC cell distance to the reconstructed track below 5 mm as a function of the initial track direction with respect to the normal to wires of Collection and Induction2 planes: (a) comparison of the new 3D method with the approach based on 2D hit matching, proton tracks reconstructed using Collection and Induction2 planes only; (b) muon and proton tracks reconstructed with the new 3D method using Collection and Induction2 planes; (c) muon and proton tracks reconstructed with the new 3D method using Collection, Induction2, and Induction1 planes.

which is the ambiguity related to the fit initial orientation, the sample of tracks with a fixed initial kinetic energy 퐸푘 may be solved by the correct association of the track end (protons: 232 MeV; muons: 100 MeV) and on a sample of points, for example, reconstructed 3D vertex associated with tracks with a range of particle initial 퐸푘 (protons: 10–350 MeV; the track or an observation of the increasing ionization in muons: 10–185 MeV). Tracks were reconstructed using the case of particles that are stopping or decaying at rest. Collection and the Induction2 planes. The angle 휓 between the reconstructed and the simulated 3.2. Reconstruction of the Particle Initial Direction. Recon- initial directions is shown in Figure 11. The minimum reason- struction of the particle initial direction was performed on able energy for proton track identification and reconstruction Advances in High Energy Physics 11

1 700 ∘ 0.998 3 600 0.996 ∘ 5 500 0.994 0.992 400 0.99 cos 휓 300 0.988 0.986 200 ∘ 0.984 10 100 0.982

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Figure 11: Distribution of the angle 휓 between the reconstructed and the simulated particle initial directions: (a) protons, initial 퐸푘 = 232 MeV (range 30 cm); the new 3D reconstruction-black curve, 2D hit matching-red curve; (b) protons, initial 퐸푘: (10–350) MeV (range up to 60 cm); dots color: 1, 2 hits in the track-blue, 3 hits in the track-red, 4 and more hits in the track-green; (c) muons, initial 퐸푘 = 100 MeV (range 30 cm); (d) muons, initial 퐸푘: (10–185) MeV (range up to 60 cm); colors are the same as in (b).

is about 50 MeV, which corresponds to tracks with more The estimation of the initial direction of muon tracks than 3 hits. The initial direction reconstruction at this energy (Figures 11(c) and 11(d)) is less precise due to the higher ∘ threshold is better than 10 in 98% of tracks in the simulated scattering along the track and lower amplitude of muon hits. sample. The angle 휓 quickly decreases for protons with higher The initial direction is reconstructed in the muon sample with ∘ energies and for initial 퐸푘 > 232 MeV (30 cm and longer 휓<10 for 96% of events with initial 퐸푘 >50MeV. ∘ tracks) 휓 stays below 3 in 92% of all events. In Figure 11(a) For events with the initial 퐸푘 > 100 MeV (30 cm and the new reconstruction method is compared with the hit longer tracks) the initial direction is reconstructed with 휓< ∘ ∘ matchingbasedapproachonthesampleof30cmproton 3 in 67% of events and with 휓<5 in 90% of events. tracks. In this sample the initial direction is reconstructed ∘ with 휓<3 in 83% and 32% of events for the new method and 3.3. Calorimetric Reconstruction. The calorimetric recon- thehitmatchingbasedapproach,respectively.Thefractionof ∘ struction was performed on the track samples used in the events with 휓<5 is 94% and 52% for the new method and previous tests. The hit charges along the track were corrected thehitmatchingbasedapproach,respectively. for the recombination effect according to the procedure given 12 Advances in High Energy Physics

700 100 New 3D 80 Entries 3360 600 60 Mean −0.02192

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Figure 12: Calorimetric reconstruction: (a) protons, initial 퐸푘 = 232 MeV, range 30 cm; the new 3D reconstruction-black curve, 2D hit matching-red curve; (b) protons, initial 퐸푘:(10–350)MeV,rangeupto60cm;dotscolor:1,2hitsinthetrack-blue,3hitsinthetrack-red,4 and more hits in the track-green; (c) muons, initial 퐸푘 = 100 MeV, range 30 cm; (d) muons, initial 퐸푘:(10–185)MeV,rangeupto60cm;color is the same as in (b). in Section 2.2. However, the charges of the first hit and the overall particle energy calculation, as seen in Figure 12(b). last hit in the track need a different approach due to the high Theeffectisdecreasingwiththegrowinglengthofthetrack; uncertainty of the outermost 푑푥 lengths, where the particle however it is still visible as the asymmetry of the distribution partially crosses the distance between consecutive wires. of the reconstruction error of the proton tracks with initial These charges were corrected in a conservative way, using 퐸푘 = 232 MeV (corresponding to 30 cm tracks), shown in a constant factor corresponding to the minimum ionizing Figure 12(a). The energy underestimation is observed also in particle, 푅 = 0.7, according to (8). The results of the particle case of low energy muon tracks, but in a much smaller extent energy reconstruction are shown in Figure 12. (Figure 12(d)). In the presented test we assume that the particle is not The energy reconstruction of the tracks with low ampli- identified; otherwise it would allow for the differentiation tude hits, present for minimum ionizing muons, is limited by of the correction factor 푅 applied to the outermost hits. the electronics noise that affects both the hit charge and the Therefore the treatment of these hits has a strong effect in hit position reconstruction. This leads to larger errors of the case of the highly ionizing, low energy protons whose tracks recombination correction and of the energy reconstruction of are composed of a few hits. In such cases the underestimated themuontracksthanincaseofprotontracks.Theasymmetry charge of the outermost hits has a major contribution to the in the energy reconstruction error distribution of the muon Advances in High Energy Physics 13 tracks in Figure 12(c) is originating from the nonlinearity of compatible with 휇/휋 hypothesis are well distinguishable from the recombination correction. the main band of the proton contribution, as it is shown in Results of the energy reconstruction are compared for Figure 13(a).Figures13(b)–13(d) present comparison of the tracks obtained from the new method with those obtained reconstruction of the data tracks and the simulated proton fromthehitmatchingapproach,usingthesampleofproton and muon tracks. The small shift of the proton data 푑퐸/푑푥 tracks with initial 퐸푘 = 232 MeV (Figure 12(a)). More distribution toward the lower values may originate from accurate reconstruction of the particle trajectory allows appli- the interacting protons contamination in the selected track cation of more precisely calculated recombination correction. sample (Figure 13(c)). In addition to the described data analysis, we show the 4. Tests on Data Tracks example of a kaon decay which was identified in one of the CNGS events, and it is shown in Figures 14(a) and 14(b), The new reconstruction procedure was applied to tracks of in Collection view and Induction2 view, respectively. This stopping particles selected from data collected with the CNGS topology is characteristic for the proton decay searches in 푝→퐾+] beam. The correction of the recombination effect was applied the channel . Hits that belong to the chain of the according to the procedure described in Section 2.2.Thegoal decay (kaon, muon, and electron/positron) were used in the of the test was to compare the theoretical Bethe-Bloch curves reconstruction as they were a single track. The 3D view of describing 푑퐸/푑푥 evolution along the stopping particle track theobtainedtracksisshowninFigure 14(c).Eventhoughin with the 푑퐸/푑푥 sequence reconstructed for data tracks. At the theInduction2thedecayofkaonintomuonhappenedatthe same time the performed analysis is a test of the Birk’s low narrow angle and the electron/positron is crossing the kaon application to the energy correction due to the recombination track, the 3D topology is resolved. effect [12]. Since the kaon and the muon decay at rest, it is possible to 푑퐸/푑푥 The main attention had been paid to low energy protons identify them according to the dependence of versus because they are relatively easy to be recognized in manual residual range along the tracks. The particle identification scanning: they are highly ionizing, not decaying particles. description is out of the scope of this paper, and here we 푑퐸/푑푥 295 tracks in total were selected visually, according to the present only the measurement of sequence of both the following criteria: kaonandthemuontracks,Figure 14(d).Themeasurement was done selecting manually the end points of tracks. In case (1)therearenovisibledecayproducts; ofthemuon,30cmofthetrackresidualrangewasusedto (2) ionization is increasing at the track end; distinguish it from other particles. In case of kaon, the track residual range was taken from the point of the particle decay (3) hits in the Collection view are not overlapping with to the point of the elastic scattering, which is seen as a kinked other tracks and cascades; trajectory on Figures 14(a)–14(c) and which corresponds to (4)trackhasatleast5hitsintheCollectionview. 8.5 cm of the track residual range.

The above conditions select mostly the stopping proton 5. Summary and Future Development Remarks tracks, with a small fraction of the protons interacting inelas- tically at low energies producing neutral or undetectable A new approach to the 3D reconstruction for LAr TPC charged secondaries. The sample contains also a fraction of detectors was proposed and applied to the reconstruction of muons and pions absorbed at rest. Kaons are unlikely to meet data tracks collected with the ICARUS T600 detector. The the selection criteria. The fraction of kaon tracks that could be main advantage of the proposed idea is the full exploitation of misidentified as stopping particles, with no visible secondary all available pieces of information. The reconstructed object particles, is about 0.3% according to the FLUKA simulation isbuiltinthe3Dspacetomatchdatasimultaneouslyinallits with the selection criteria applied as for data tracks. 2D projections, with a set of object-specific constraints, for Tracks from the selected sample were reconstructed auto- example, the curvature and the distance to 3D vertices in the 푑퐸/푑푥 matically and the sequence of values was evaluated. track reconstruction. In contrast to the usual approach in for- 푑퐸/푑푥 The particle identification is based on the versus track mer works related to LAr TPC, the troublesome matching of range, which is computed from the point where the particle 2D points by the drift timing is no longer needed. Moreover, stops, called later residual range. The particle identification in case of the application to the track reconstruction: was performed in order to distinguish tracks compatible with the proton hypothesis from the 휇/휋 hypothesis. A detailed (a) 2D hits projected to the reconstructed 3D trajectory description of the particle identification procedure will be are not constrained to the wire crossing points in the given in a forthcoming paper. The results in comparison XZ plane and allow precise hit-by-hit analysis of the with the theoretical curves are shown in Figure 13(a).The charge deposition; theoretical stopping power curves of Bethe-Bloch have been (b) missing parts of the track in one of the wire planes are calculated taking into account LAr’s properties, shell cor- properlytakenintoaccount; rections, and the density effect. The delta rays produced by particles in the examined momenta range have an energy (c) the method is much more efficient than hit matching low enough to be undistinguishable from the particle track; approach in the reconstruction of tracks parallel to therefore no delta rays energy restriction has been set. Tracks wire planes. 14 Advances in High Energy Physics

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30 MC data 100 MC muons Entries 24494 Entries 34708 Mean 6.987 25 Mean 3.142 RMS 1.087 80 RMS 0.9126 Data 20 MC pions Entries 1262 Entries 24498 60 Mean 6.924 Mean 3.403 RMS 1.393 15 RMS 0.8901

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Figure 13: (a) The selected sample of data tracks identified as proton or 휇/휋 tracks; (b) mean value of 푑퐸/푑푥 distributions in 6 mm bins of residual range: black-data tracks identified as protons; blue-simulated proton tracks; points in the background-data tracks identified as protons; (c) 푑퐸/푑푥 in 8–12 cm residual range for tracks identified as protons, compared to simulated proton tracks; (d) 푑퐸/푑푥 in 8–12 cm residual range for tracks identified as 휇/휋,comparedtosimulatedmuonandpiontracks.

The efficiency of the proposed track reconstruction In this paper we focused on the track reconstruction; methodwasdemonstratedonsamplesofsimulatedstopping however the projection, the distance, and the constraint proton and muon tracks. We also presented the results of operators (1) may be constructed for showers, vertices, or the application to data, such as 푑퐸/푑푥 reconstruction on a any other object. For example, an electromagnetic shower sample of stopping particles selected from CNGS neutrino axis may be reconstructed as a single 3D segment optimized interactions observed with ICARUS T600 detector. The to the hits in wire projections, similarly to the initialization presented data tests show a very good agreement with the procedure given in Section 2.2.1. Another example could be MC simulation and the theoretical expectations of the 푑퐸/푑푥 the simultaneous optimization of several tracks with the evolution of the stopping particles. common starting fit node which acts as the interaction Advances in High Energy Physics 15

Cathode Cathode

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Figure 14: Example of a decaying kaon candidate observed in the CNGS data (퐾: 90 cm, 325 MeV; 휇: 54 cm, 147 MeV; 푒:13cm,27MeV):(a) the Collection view; (b) the Induction2 view; (c) the 3D reconstruction (fit nodes are marked with the red dots); (d) 푑퐸/푑푥 sequence for the kaon track (cyan dots) and the muon track (violet dots) superimposed on the theoretical Bethe-Bloch curves. The muon data points with the high 푑퐸/푑푥 are due to the additional energy of delta rays. They are attached to the muon track (visible black dots on the muon track in the Collection view). Their energy contribution is in agreement with the energy loss distribution expected for a muon track.

vertex. These ideas are now under study. Issues specific to in particular the CNGS staff, for the successful operation of the detector readout design such as merging objects from the neutrino beam facility. multiple TPC modules or LEM units may be accommodated bythealgorithmaswell.Weconsidertheproposedapproach as the optimal utilization of all the spatial information References contained in the LAr TPC data. [1] C. Rubbia, “The Liquid-Argon Time Projection Chamber: a new concept for neutrino detectors,” CERN Report, 1977. Acknowledgments [2] C. Anderson, M. Antonello, B. Baller et al., “The ArgoNeuT detector in the NuMI low-energy beam line at Fermilab,” The ICARUS Collaboration acknowledges the fundamental Journal of Instrumentation,vol.7,ArticleIDP10019,2012. contribution of INFN to the construction and operation of [3] O. Araoka, A. Badertscher, A. Curioni et al., “Performance of a the experiment. In particular the authors are indebted to 250L liquid Argon TPC for sub-GeV charged particle identifi- the LNGS Laboratory for the continuous support to the cation,” http://128.84.158.119/abs/1206.1181v1. experiment. The Polish groups acknowledge the support of [4] H. Chen, J. Farrell, F. Lanni et al., “Proposal for a new experi- the Ministry of Science and Higher Education in Poland, ment using the booster and NuMI neutrino beamlines: Micro- including project 637/MOB/2011/0. Finally they thank CERN, BooNE,” FERMILAB-PROPOSAL 0974, 2007. 16 Advances in High Energy Physics

[5]D.Autiero,J.Ayst¨ o,¨ A. Badertscher et al., “Large underground, liquid based detectors for astro-particle physics in Europe: scientific case and prospects,” Journal of Cosmology and Astroparticle Physics, no. 11, article 011, 2007. [6] C. Rubbia, M. Antonello, P. Aprili et al., “Underground operation of the ICARUS T600 LAr-TPC: first results,” Journal of Instrumentation, vol. 6, Article ID P07011, 2011. [7] S. Amerio, S. Amoruso, M. Antonello et al., “Design, construction and tests of the ICARUS T600 detector,” Nuclear Instruments and Methods in Physics Research A,vol.527,no.3, pp.329–410,2004. [8] A. Badertscher, A. Curioni, L. Knecht et al., “First operation of a double phase LAr Large Electron Multiplier Time Projection Chamber with a two-dimensional projective readout anode,” Nuclear Instruments and Methods in Physics Research A,vol.641, no. 1, pp. 48–57, 2011. [9] B. Kegl,´ A. Krzyzak, T. Linder, and K. Zeger, “Learning and design of principal curves,” IEEE Transactions on Pattern Analysis and Machine Intelligence,vol.22,no.3,pp.281–297, 2000. [10] S. Amoruso, M. Antonello, P.Aprili et al., “Analysis of the liquid argonpurityintheICARUST600TPC,”Nuclear Instruments and Methods in Physics Research A,vol.516,no.1,pp.68–79, 2004. [11] M. Miyajima, T. Takahashi, S. Konno et al., “Average energy expended per ion pair in liquid argon,” Physical Review A,vol. 9, no. 3, pp. 1438–1443, 1974. [12] S. Amoruso, M. Antonello, P. Aprili et al., “Study of electron recombination in liquid argon with the ICARUS TPC,” Nuclear Instruments and Methods in Physics Research A,vol.523,pp. 275–2286, 2004. [13]G.Battistoni,S.Muraro,P.R.Salaetal.,“TheFLUKAcode: description and benchmarking,” in Proceedings of the Hadronic Shower Simulation Workshop,M.AlbrowandR.Raja,Eds.,vol. 896 of AIP Conference Proceeding, pp. 31–49, September 2007. [14]A.Ferrari,P.R.Sala,A.Fasso,andJ.Ranft,“FLUKA:a multi-particle transport code,” CERN-2005-10 (2005) INFN/ TC 05/11, SLAC-R-773. Hindawi Publishing Corporation Advances in High Energy Physics Volume 2013, Article ID 839570, 6 pages http://dx.doi.org/10.1155/2013/839570

Research Article The Structure of an Automatic Decision System for a Large Number of Independent Particle Detectors

Andreea Rodica Sterian

Academic Center of Optical Engineering and Photonics, Polytechnic University of Bucharest, 313 Splaiul Independentei, 060042 Bucharest, Romania

Correspondence should be addressed to Andreea Rodica Sterian; [email protected]

Received 27 December 2012; Accepted 1 March 2013

Academic Editor: Bogdan Mitrica

Copyright © 2013 Andreea Rodica Sterian. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The interest for large underground particle detector is increasing. Phenomena as proton decay and long base line neutrino oscillation are subject for many research projects over the world. Large detectors present also some problems regarding the large number of signals from independent photo multiplier tubes (PMTs). A realistic statistical model for numerical simulation of signal processing and sampling has been developed for the case of a large number of independent particle detectors (LNIPDs). Based on this analytical model of Poisson type, the structure of an automatic decision system based on the decision criterion of maximum a posteriori probability (MAP) or the maximum likelihood (ML) criterion is proposed. The purpose of the system is to analyze the exit from the measurement process and to decode the message transmitted, taking into account the presence of the noise which generates errors in the decoder. The system can be used later for detailed simulation of different types of huge underground particle detectors (like LAGUNA-LBNO experiment), where the large number of signals could become a real problem.

1. Introduction This paper proposes to use the mathematical model of Poisson detection based on the response function that corre- We know that the abstract models are often used for the lates the random variables in a studied case of a large number resolution of various problems. Starting from a detector of independent particle detectors (LNIPDs) providing a response function that presents the relationship between knowntypefunctionofthesecomplexprocesses.Wedefinea the input factors and the output ones, we investigate a response function and show that the measurement to detect relaistic statistical model for numerical simulation of signal 𝑘 particles in the interval (𝑡, 𝑡 + 𝑇) is the type conditional processing and sampling for the case of a large number Poisson. The further processing of the information obtained of independent particle detectors (LNIPDs) and Poisson from the detection processes is based on decision criteria statistics of the detection process [1–6]. In the obtained similar to the criteria from the information transmission equation, the statistical behaviour of the analyzed processes theory.Inthiscontext,weproposeareal-timemethodof is essential. The basic criterion by which we can make automatic implementation of the decision-making process a distinction between the different form of the detection based on the information that results in the LNIPD [15–19]. process is the nature of the detection statistics which may In the paper, in order to process the data obtained be of Poisson type, Laguerre type, and so on. The nature of from the study of the detection process in the LNIPD the detection statistics depends on the real situation by many case, we proposed to use known decision criteria from the factors as the number and size of the used detectors, the types theory of information transmission. The method of automatic of particles detected, the strength of the signal to be detected, implementation of this decision process, which was described and the extent by which the detected information needs to be in this paper, based on the real-time information collected processed after detection [7–14]. from LNIPD, is a major step forward in the implementation 2 Advances in High Energy Physics of the strategy proposed for the large underground particle at the point 𝑟⃗ at the moment 𝑡 corresponds to the following detector implementation. transition rate 𝑑𝑃/𝑑𝑡: There are interconnections for which the optimal data 𝑑𝑃 analyses can be made automatically, in real time and in differ- 𝑡 =𝛼𝐼(𝑡, 𝑟)⃗ Δ𝑟,⃗ (3) ent conditions and situations. In the situations characterized 𝑑𝑡 by two random variables as in the case of LNIPD, the suitable where 𝐼(𝑡, 𝑟)⃗ is the intensity of the field at the detector situated statistical distribution is of the Poisson conditional type. in point (𝑟,⃗ 𝑡) and 𝛼 is a proportionality constant. For an optimal and efficient settlement of the measure- This problem consists of calculating the probability that ment equipments with minimum costs, automatic machines all the LNIPD detectors emit 𝑘 electrons by their area 𝐴 in need to be built, which secure a real-time analysis and assure the interval (𝑡, 𝑡 + 𝑇). us of suitable correct decisions, being followed by adequate We must calculate composed probability in order to automatic data after detection processing [20–28]. obtain 𝑘 electrons from all the LNIPD detectors. It results [8, 22]that 2. Detection Statistics (𝑚 )𝑘 𝑃 (𝑘) = V [−𝑚 ] 𝑘≥0, (4) Study of detection statistics represents an essential operation 𝑘 𝑘! exp V in the realization of an automatic decision system for large number of independent particle detectors (LNIPDs). where, by definition,

⃗ ⃗ 2.1. The Detector Response Function. Each electron makes a 𝑚V =𝛼∫ 𝐼(𝑉)𝑉 𝑑 (5) contribution to the output current which is converted into 𝑉 voltage by passing through the load resistance. Conversion or process is a stochastic process in nature. From mathematical 𝑡+𝑇 point of view, the output current is a superposition of the 𝑚V =𝛼∫ ∫ 𝐼(𝜌,𝑟)⃗ 𝑑𝜌𝑑𝑟,⃗ (6) effects produced by each electron emitted. A single electron 𝐴 𝑡 produces a current response function ℎ(𝑡): 𝑚V being the probability level. ∞ −19 Therefore, (4) is also written under the following form [8]: ∫ ℎ (𝑡) 𝑑𝑡=𝑒=1,6⋅10 𝐶. (1) 0 𝑘 (𝑚V) Pos (𝑘,V 𝑚 )= exp [−𝑚V], (7) A measurement done at the moment 𝑡𝑚 produces the 𝑘! response ℎ(𝑡 −𝑚 𝑡 ),sothatingeneralweobtainthetotal 𝑚 response where V,theparameterofPoissonprobability,isdimension- less. 𝑘(0,𝑡) According to (5), in the energetic space, 𝛼 has the reversed 𝑥 (𝑡) = ∑ ℎ(𝑡−𝑡𝑚), (2) size of energy. 𝑚=1 The quantity 𝑛(𝑡, 𝑟)⃗ can be defined as “count intensity” by where 𝑘(0, 𝑡) represents the number of photoelectrons the relation (0, 𝑡) 𝑡 obtained in the interval , 𝑚 being the moment of 𝑛 (𝑡, 𝑟)⃗ =𝛼𝐼(𝑡, 𝑟) , (8) measuring 𝑚.Theprocessiscalled“counting.”Theresponse 𝑥(𝑡) depends on two random variables: which represents a normalized intensity. The integral of 𝑛(𝑡, 𝑟)⃗ gives directly the level of probability (i) random localizations of the measuring moments, 𝑡𝑚; (ii) random values of the measured quantity, 𝑘(0, 𝑡). 𝑡+𝑇 𝑚V = ∫ ∫ 𝑛(𝜌,𝑡)𝑑𝜌𝑑𝑟.⃗ (9) 𝐴 𝑡 Because 𝑡𝑚 and 𝑘(0, 𝑡) are random variables, 𝑥(𝑡) is a 𝑥(𝑡) relatively complicated process to study because does not Alternately, explicitly contain the properties of the incident particles. Therefore, we aim to find under what form the properties 𝑛 (𝑡) = ∫ 𝑛 (𝑡, 𝑟)⃗ 𝑑𝑟=𝛼⃗ ∫ 𝐼 (𝑡, 𝑟)⃗ 𝑑𝑟.⃗ (10) of the detected field are contained in the response signal and 𝐴 𝐴 to highlight them. So, 2.2. Mathematical Model of the Detection Process. The model 𝑡+𝑇 𝑚V = ∫ 𝑛(𝜌)𝑑𝜌. (11) is represented by the probability that the detection process 𝑡 leads to 𝑘 photoelectrons in the interval (𝑡, 𝑡 + 𝑇). According to Fermi rule for the transition rate extended It results that variable 𝑘 is a Poisson type. to that study, for a detector element Δ𝑟,⃗ localized in point 𝑟⃗ The probability (7) is actually a conditional Poisson on the radius of observer, we can see that the probability 𝑃𝑡 probability or double stochastic Poisson probability because of an electron to be emitted by an element of area Δ𝑟⃗ located it depends on 𝑚V which is a random variable (integral of Advances in High Energy Physics 3

a random variable). Therefore (in more precise case), 𝑃𝑘(𝑘) 3.2.2. The Maximum Likelihood (ML) Criterion. According to requires additional media over 𝑚V of Pos(𝑘,V 𝑚 ) as it can be this criterion, considered a random variable with density 𝑝𝑚 (𝑚) for 0≤ V Λ 𝑖 𝑚≤∞. (i) we define the plausibility function 𝑖 for byte by the It results that relation ∞ 𝑘⃗ Λ =𝑃( ) 𝑃𝑘 (𝑘) = ∫ Pos (𝑘,V 𝑚 )𝑝𝑚 (𝑚) 𝑑𝑚 𝑖 (14) 0 V 𝑖

∞ 𝑘 (12) 𝑚 −𝑚 ⃗ = ∫ 𝑝𝑚 (𝑚) [ 𝑒 ]𝑑𝑚. which means the probability of detecting vector 𝑘 0 V 𝑘! when particle 𝑖 is incident (byte 𝑖) on one photodetector; 3. Processing of Information (ii) we calculate the functions Λ 𝑖; Obtained from LNIPD (iii) we decide on byte 𝑖 if For the two types of emission, processes studied of Poisson type and Poisson conditioned type output level of the signal Λ 𝑖 = max (Λ 𝑗). (15) statistics are closely related as has been shown with intensity statistics. In the considered case of binary decisions [8], it is Thus, formula (2) reveals proportionality of the photode- expressed as equivalent as follows: tector output process with the emission of electrons. Also, the formulas (5)and(8)showthatforsufficiently Λ 1 ≥Λ0 (16) large values of statistical intensity, the strength of the response of photodetector is determined basically by the incident field. or In order to process the data obtained from the LNIPD, the proposal of the paper is to use the known decision log Λ 1 ≥ log Λ 0 (17) criteria from the theory of information. The method of automatic implementation of the decision process, which because the “log” function increases monotonically with its will be described later, based on the real-time information argument. collected from the LNIPD, is a major step forward in the implementation of the automatic decision system in the case 4. Implementation of an Electronic Decoder of a large number of independent particle detectors. for the Automatic Data Processing 3.1. Characterization of Decision Criteria. The decisions are The role of MAP decoder (or ML) is to analyze the infor- basedonthedetectionstatisticsofphotoelectrons,Inthe mation resulted from LNIPD and to offer us correct data on binary systems, we define the messages associated to binary the measuring process. The presence of different noise types symbols “one” or “zero” as bytes. Byte 1 is associated to the determines errors in the decoder’s decision. presenceoftheparticleandbyte0tothenoise,intheabsence of it. 4.1. Structure of Decoder in Case of Poisson Detection. We consider the distribution 3.2. Formulation of Optimal Decision Criteria 𝑘𝑗 𝑘𝑗 𝑃 ( ) = Pos ( ) , (18) 3.2.1. Decision Criterion of Maximum A Posteriori Probability 𝑖 𝜇𝑖𝑗 +𝜇𝑏 (MAP). According to this criterion, where 𝜇𝑖𝑗 is the “energy” number of the signal; 𝜇𝑏 is the (i) detectors measure the the incident field on the inter- average “energy” number of noise. val of a byte; Equation (18) defines the probability that in the counting 𝑗 𝑘 𝑖 (ii) on the basis of detection statistics, we calculate the interval are measured 𝑗 when byte was realised. ⃗ From (18), 𝑃(𝑘𝑗/𝑖) is explicitly written as follows: probability 𝑃(𝑖, 𝑘) oftheparticleincidence(byte𝑖) 𝑘⃗ when the vector was detected; 𝑘𝑗 2𝐵𝑛𝑇 (𝜇 +𝜇 ) ⃗ 𝑖𝑗 𝑏 (iii) it decides on the byte 𝑖 if: 𝑃(𝑘, 𝑖) = ∏ exp [− (𝐾𝑖 +𝐾𝑏)] , (19) 𝑗=1 𝑘𝑗! ⃗ 𝑗 𝑃(𝑖,𝑘) = max 𝑃( ), (13) 2𝐵 𝑇 𝑘⃗ where 𝑛 is the number of counting intervals in the time interval [0, 𝑇], 𝐵𝑛 is the signal bandwidth and 𝐾𝑖, 𝐾𝑏 are averagenumbersofsignalandnoiseinthesameinterval where 𝑖, 𝑗 = 0,1. [0, 𝑇]. 4 Advances in High Energy Physics

Computational block ̃ Λ 0 Output 𝑘 Maximum Comparator

Computational block ̃ Λ 1

Processing and decision block

Figure 1: The block scheme of the processing and decision system.

𝑛 (𝑡) log [1 + 1 ] −𝐾 𝑛 1 𝑏 𝑇 𝑛 (𝑡) ∫ 𝑘 log [1 + 1 ]𝑑𝑡 0 𝑛𝑏 +

Maximum 1 comparator 𝑘

log Λ 1 > log Λ 0 log Λ 1 < log Λ 0 0

𝑇 𝑛 (𝑡) ∫ 𝑘 log [1 + 0 ]𝑑𝑡 + 0 𝑛𝑏 𝑛 (𝑡) log [1 + 0 ] −𝐾0 𝑛𝑏 Figure 2: Integrated version of Poisson decoder.

The expression of logarithmic plausibility function is[8, 4.2. Discrete Version of Poisson Decoder. In the structure, it 9] has a pair of weighted summations circuits of detected signals according to expression (21), followed by a comparator of 2𝐵 𝑇 𝑛 𝜇𝑖𝑗 maximum. Λ = ∑ 𝑘 (1 + )−𝐾 ⃗ log 𝑖 𝑗 log 𝑖 Summationsarediscretecorrelationsof𝑘 to the corre- 𝑗=1 𝜇𝑏 sponding logarithmic intensity vector. Because the maximal (20) correlation function is the self-correlation, by the appro- 2𝐵𝑛𝑇 [ ] priate adjustment of polarizations 𝐾1 and 𝐾0,comparator + ∑ (𝑘𝑗 log 𝜇𝑏)−log 𝑘𝑗! −𝐾𝑏. of maximum determines correct decisions regarding the [ 𝑗=1 ] transmission of bytes “1” and “0.” The expression (20) can be simplified because the last bracket does not depend on 𝑖;so,ithasthesamevaluefor 4.3. Integrated Version of the Poisson Decoder. The discrete both bytes 𝑖 = (0, 1). Therefore, it can be neglected in the version of the decoder is very appropriate for the operational application of the decision test. analysis of this type of decoder. In the integrated version Consequently, we must evaluate only the quantity [5] of decoder [8], summations are replaced with integration circuits (Figure 2). 2𝐵 𝑇 𝑛 𝜇 Λ̂ = Λ ≅ ∑ 𝑘 (1+ 𝑖𝑗 ) −𝐾 𝑖 log 𝑖 𝑗 log 𝜇 𝑖 (21) 𝑗=1 𝑏 5. Conclusions for 𝑖=0,1, and we compare the results. The detector response function is used for obtaining the The block scheme of the processing and decision system probability as that in the measuring process to determine 𝑘 is presented in Figure 1. photoelectrons in the interval (𝑡, 𝑡 + 𝑇).Thisprobabilityis The signals 𝐾𝑖 appear as a bias adjustment for the of conditional Poisson type. For processing the data obtained difference of energy in transmission of bytes. from observing the detectors response, we have proposed the Advances in High Energy Physics 5

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Nuclear Physics B—Proceedings Supplements,vol.196,no.C,pp. 462–465, 2009. [28] I.Lazanuetal.,“Aboutthepossibilitytomeasuresomestandard model parameters and search for new physics with low energy neutrinos,” Romanian Reports in Physics,vol.64,no.1,pp.24– 32, 2012. Hindawi Publishing Corporation Advances in High Energy Physics Volume 2013, Article ID 461764, 12 pages http://dx.doi.org/10.1155/2013/461764

Research Article Site Assessment for Astroparticle Detector Location in Evaporites of the Polkowice-Sieroszowice Copper Ore Mine, Poland

Jaroslaw Slizowski, Zenon Pilecki, Kazimierz Urbanczyk, Elzbieta Pilecka, Leszek Lankof, and Rafal Czarny Mineral and Energy Economy Research Institute, Polish Academy of Sciences, Wybickiego 7, 31-261 Krakow, Poland

Correspondence should be addressed to Zenon Pilecki; [email protected]

Received 10 December 2012; Accepted 18 January 2013

Academic Editor: Jacek Szabelski

Copyright © 2013 Jaroslaw Slizowski et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The aim of the work was to evaluate the possibilities of excavating a chamber for the Glacier detector, a cylinder with a 74 m diameter and 38 m height filled with 100 kT of liquid argon, in the Polkowice-Sieroszowice copper ore mine in the Legnica-Glogow Copper Area(LGOM).Twopotentiallocationswereanalyzedinarocksaltlayermorethan100mthickatthedepthof1000mandinthe anhydrite layer of about 100 m thick at the depth of 650 m, both lying above the copper ore deposit. The numerical analyses, based on geological, geophysical, and geomechanical research, were carried out to determine the behavior of the system of the chamber and surrounding rock mass. Two creep laws have been adopted for rock salt in the numerical models, Norton and Lubby2. Their coefficients have been adjusted for in situ measurements of the mine galleries convergence starting from the results of laboratory tests. Displacement and stresses of the rock salt in the chamber vicinity are much greater for the Lubby2 law. The displacements indicated at the chamber contour are the reason that the alternative location in the anhydrite layer was more advantageous.

1. Introduction This work concerns the location of the detector in the deep underground Polkowice-Sieroszowice copper ore mine The principal goal of the first project phase of Large Appa- in Poland. It was planned to host a Glacier detector, a giant ratus studying Grand Unification and Neutrino Astrophysics cylinder 74 m in diameter and 38 meters high filled with (LAGUNA) was to assess the feasibility of a deep under- 100kTofliquidargon.Therocksaltlayerover100mthick ground chamber able to host the giant neutrino detector [1]. at the depth of about 1000 m lying above the copper deposit The observatory was expected to provide new and unique was analyzed as a host rock mass in the preliminary study. scientific opportunities and to lead to the discoveries in the The main advantages of this location were the very low field of astroparticle physics. Seven potential locations were level of natural radioactivity background registered there and being considered in the project: the Boulby potash mine in no water hazard. The rock salt layer seemed to have adequate the UK [2], the Frejus´ tunnel in France [3], the Caso tunnel thickness and homogeneity. Some chambers were already in Italy, the Canfranc tunnel in Spain [4], the Pyhasalmi¨ mined; the largest about 100 m long and 15 m wide and 15 m metal ore mine in Finland [5, 6], the Unirea salt mine in highhasbeenstableforseveralyearsandwasusedafewtimes Romania [7], and the Polkowice-Sieroszowice copper ore for astrophysical experiments. mine in the Legnica-Glogow Copper Area (LGOM) in Poland The favorable location of the Polkowice-Sieroszowice [8, 9]. The location of these sites, with the underlined location mine near to the A-4 motorway and the airport for transport of the Polkowice-Sieroszowice copper ore mine, is shown in detector construction and further operation of the laboratory Figure 1. should also be noted. 2 Advances in High Energy Physics

Pyhäsalmi

Berlin Warszawa Polkowice Boulby Praga

Wiedeń km Polkowice 1050 2300 Gdańsk Olsztyn

km km Szczecin Białystok 950 Gorzów Bydgoszcz Wielkop. Poznań CERN 1200 km Warszawa km łódż 630 Slanic Frejus 730 Polkowice Lublin km Wrocław Kielce Canfranc 130 km Opole Katowice Rzeszów Gran Sasso Kraków Polkowice Legnica Wrocław Jelenia Góra

Wałbrzych

Figure 1: The sites considered in the LAGUNA project with the underlined location of the Polkowice-Sieroszowice copper ore minein Polkowice town, Poland (on the basis of [1, 13]).

A disadvantage of the analyzed location is the depth— Quaternary periods. The individual rock formations occur about 1000 m—which is considerable, from a geotechnical discordantly, and themselves discordantly, and they are sepa- point of view for a huge excavation in rock salt. Active mine rated by stratigraphic breaks. Permian formations begin with operations, having an impact on the surroundings and also a formation of Red Sandstone. They are built from a conglom- inducing seismicity, can also be problematic. The location of erate, sandstone, and shale floor in two similar sequences up the detector chamber in the anhydrite layer occurring above toabout450–500minthicknessofstrata.Thecopperore the rock salt was also taken into account as an alternative to deposit occurs in the floor segments. Permian limestone of the rock salt layer. themonoclineoftheSudeticForelandisdevelopedinthe The aim of this work is to present of the preliminary form of four evaporite cyclothems: Werra, Stassfurt, Leine, evaluation of the properties and structure of the host rock andAller.Themostdevelopedcyclothem,Werra,beginswith mass and to consider the possibility of constructing a cham- cupriferous shale deposits. The carbonate deposits, including ber. This paper presents the results of geological, geophysical, carbonate of limes and dolomite rocks from 5 to 70 m in and geomechanical research carried out in the Polkowice- depth of strata, are lying above cupriferous shale. Dolomite Sieroszowice copper ore mine. A large part of these studies rocks which often contain copper sulfide predominate in was published in the works of Slizowski et al. [10, 11]. the southern part of the monocline. Lower anhydrites from about several dozens up to over hundred meters in thickness 2. Geological Conditions of strata are lying over the carbonate deposits. The oldest, bright-grey, coarse- and medium-crystalline rock salt occurs The field of research lies within the monocline of the Sudetic on the lower anhydrites in the northeastern part of the Foreland [12, 13]. The monocline of the Sudetic Foreland monocline of the Sudetic Foreland. Rock salt beds stretch is built of three main rock formations in a broad outline from several dozens up to a few hundred meters in depth of (Figure 2). A rock bed of the monocline, the so-called meta- strata, and it can be observed that the general tendency of this morphic of the interior Oder River, is formed by crystalline increase is in a northerly direction. A rock salt seat occurs at and sedimentary rocks from the Proterozoic and the older a depth of 631 up to 1229 meters and a roof at a depth of 628 Paleozoic periods. Permian and Triassic sedimentary systems up to 1099 meters. occur over them. The Cenozoic complex forms the monocline The thickness of strata of the rock salt deposit all over cover—there are deposits from the Paleogene, Neogen, and the mining area of the Polkowice-Sieroszowice mine is from Advances in High Energy Physics 3

SW NE 𝑆-364 𝑆-373 𝑆 279 𝑆-351 𝑆 37 𝑆-104 - 200.8 179 𝑆-1 𝑆-71 - 165.6 192.9 138 136.9 139.7 143.4 0

−250

−500

Depth (m) −750

−1000

Sands, gravel, clay Holocene, Pleistocene Sandstone Motley sandstone Triassic Mesozoic Sandstone/shale Gravel, sands, claystone, Pliocene clay/sand Clayey shale Lignite Gypsum, anhydrite Clay, clay/lignite, mud, Miocene Cenozoic Rock salt Zechstein sand/clay, claystone, clay/sand/gravel Dolomite, limestone Permian Paleozoic Copper bearing shales Lignite Oligocene Gray sandstone Clay/sandstone/mudstone, Red ﬂoor sandstone sands, gravel Red sandstone Crystalline rock

Faults identified in mine excavations Faults anticipated

Figure 2: The cross-section of the southern part of the mining areas for the Legnica-Glogow Copper Area (LGOM)[13].

0 to 186 meters—65 meters on average. It is distinguished by The faults are usually grouped into tectonic zones of a lot of salt varieties in the rock salt bed which show different irregular course, from several dozens of meters up to above contents of NaCl. The coarse- and high-crystalline variety one kilometer in width to over ten and twenty kilometers is characterized by the greatest content of NaCl. A medium in length. The faults running in parallel create systems of content of NaCl is determined at a level of 98.2%. Upper horsts and rift valleys. The length of individual faults ranges anhydrites, in which end up deposits of cyclothem Werra, from 200 to 1000 meters. The average gradient of fault surface ∘ occur above the rock salt. The depth of strata of the upper varies from 71 to 75 , and thrusts are generally small; about anhydrites does not exceed hundred meters. 60% of them do not exceed one meter. The thickness of strata differentiation of evaporites is The block tectonics exerted influence on the present layer closely bound up with weathering processes, as evidenced structure of the rock salt. The fault system in the rock salt by clay-anhydrite and gypsum breccia layers often having layer floor does not diverge from the system determined at heavydepthsofstrataaswell.Thegeneraldipofbedson thePermianlimestonelevel.ThefaultsoccurinanNW-SE ∘ the monocline of the Sudetic Foreland is 2–5 in a northeast and W-E direction. A part of them goes out from the bed on ∘ direction. The locally occurring larger declines of up to 25 account of the salt’s plastic properties. The floor part of the are connected with roof elevation angle slopes of sandstone rock salt bed is displaced to a smaller degree, with larger faults deposits. in this connection, but, in contact with the upper anhydrites, The biggest influence on the structural composition of minor faults can occur with a limited range. the monocline area of the Sudetic Foreland was exerted Two main water-bearing complexes may be singled out by tectonic movements of the Laramie phase between the on the analyzed monocline area of Sudetic Foreland: Cretaceous and Paleogene. Earlier earth movements also had an essential meaning for the tectonics of the monocline. At the turn of Keuper, the complex of limestone and schist, had (i) the Cenozoic—comprised of loose deposits of the arisen the oldest fault system in a NW-SE direction, together Neogene and Paleogene periods with intergranular with accompanying fissures in the old-Kymeric phase. The water circulation, fault system in the NW-SE direction creates blocks dropping in an NE direction which are built of red sandstone deposits, (ii) the Triassic-Permian—occurring in cohesive, porous Permian limestone, and the Bunter. They are characterized and fissured-cavernous rocks of the Bunter, Permian compressively. The remaining groups of faults on a longitu- limestoneaswellasRedSandstonewithmainly dinal and latitudinal course are less important. fissured and porous-fissured water circulation. 4 Advances in High Energy Physics

These complexes differ markedly in lithological develop- A more complex situation occurs in the case of rock salt ment, the way of formation and chemistry of water resources, on account of its high plasticity. The fraction of reversible and thus hydrogeological parameters. elastic strains in total strain is small. The characteristics throughout its range are nonlinear, mostly due to nonlinearity of plastic strengthening. Young’s modulus was determined (𝐸 ,𝐸 ,𝐸 ,𝐸 ) 𝜎 𝜀 3. Rock and Rock Mass Properties at different states 0 1 2 3 .Thestress( 1)—strain ( 1) curves are shown in Figure 4. 3.1. Geophysical Examinations. The rock salt layer is slightly Experiences with the numerical calculations, however, fractured and faulted. A different geomechanical situation show that the parameter values of elasticity are of secondary occurs in the case of the adjoining anhydrite and dolomite importance, not significantly affecting the state of deforma- layers which are fractured on the whole and may be water- tions and stresses of rock mass surrounded by underground logged in a diversified manner. The least preferred conditions workings in the rock salt [16]. The rheological properties are aretobeexpectedinthecontactzonesbetweenthese more important. layers. Surveys of seismic direct P-wave velocity changes and fissuring degree in rock mass were made by applying seismic and georadar profiling with the use of a shielded 100 MHz 3.2.2. The Rheological Properties of Rock Salt. Analysis of the antenna [14]. Seismic surveys were also aimed at determining rheological properties of rock salt in cyclothem Werra from the static deformation modules for the separate layers by the Polkowice-Sieroszowice copper ore mine is based on two Barton’s empirical formula [15]. series of experiments described in [10]. The investigations in Investigations were made in the side walls of excavations 1991 lasted 175 days in the case of uniaxial creep tests, while carried out at different intervals: almost twenty years ago (Ps- they lasted 147 days in the case of triaxial creep tests, and 3 gallery) for the contact zone of the rock salt and anhydrite, were made only at room temperature. The duration of all the as well as in a gallery “freshly” prepared by using the heading tests in 2001 amounted to 115 days, in addition to which the ∘ machineinthecontactzoneofanhydriteanddolomite(Ps-1 temperature was raised to 40 C as regards the samples in the gallery). The underground workings were located at a depth triaxial stress state, corresponding to the temperature of the of about 1000 meters. Georadar profiling carried out in the rocks in the Polkowice-Sieroszowice mine at a depth of about Ps-3 gallery showed a fracturing structure of anhydrite and 1000 meters. rock salt layers (Figure 3). The discontinuity and lithological Figure 5 shows an example of the results of triaxial borders were noticeable on an echogram. Intense fracturing creep test for two values of effective stresses, while Figure 6 in a segment of several meters in the contact zone of presents the creep test results of two samples at the changed anhydrite and rock salt layers was recorded. Damage along temperatureaswellaseffectivestress. thesidewallwasobserved,inparticularoccurrenceina There was a clear difference in the testing of creep rate of segmentofanhydrite.Brecciazonesoccurredlocallyinthe salt samples due to the varying thickness of the grains, which anhydrite. There might be lenses of postsedimentary rock may even be a factor of ten. The creep law parameters that can salt. Larger discontinuities were not observed outside the be obtained in these tests may not be precise. However, the side wall zone. Reconnaissance further away from the side research results indicate that the rock salt in the cyclothem wall revealed probably the lithological boundary between the Werra from the Polkowice-Sieroszowice mine is very fast anhydrite and rock salt. The degree of fracturing of rock salt creeping. is significantly lower in comparison to anhydrite. Figure 7 shows the creep rates of salt samples from the Seismic studies have shown significant differences in P- Polkowice-Sieroszowice mine obtained at room temperature. wave velocity and static deformation modulus in the ana- Two lines representing creep laws known in the literature as lyzed rock layers (Table 1). The most advantageous elastic BGRa and BGRb [17, 18] are presented for reference purposes. propertiesarestatedfortheanhydriteanddolomitelayers. The seismic P-wave velocities are decidedly larger in “freshly” made underground workings as a result of a shorter period of 3.2.3. Strength Properties. Strength tests were performed for weathering and rheological processes. The elastic properties various samples of different rock salt of difference grain thick- of the strongly disturbed layer of anhydrite are similar to the ness,aswellasforanhydritefromcyclothemWerra(Table 3). properties of the rock salt layer. Inthecaseofrocksalts,theresultswereobtainedbySlizowski et al. [10] based on uniaxial and triaxial compression tests, tension (direct and Brazilian methods), and shear test at 3.2. Laboratory Tests different angles between the direction of the compressive force and the shear plane. As regards the anhydrite, the 3.2.1. Elastic Properties. In the case of rocks with high elastic- tests were conducted by KGHM Cuprum, based on uniaxial ity, amongst which anhydrites are numbered, a determination compressionandtensionusingthedirectmethod[10]. of elasticity parameters is not complicated. The values of In rock salt, there is a visible dependence on the param- Young’s modulus and Poisson ratio are presented in Table 2. eters of the orientation of the sample in relation to the It should be noted that Young’s modulus values have a bedding, especially evident in the uniaxial compression tests. considerably smaller scatter in the case of a specific sampling Ingeneralitwasfoundthattheuniaxialstrengthchangesof location. rock salt are mainly due to the differentiation of its grains. Advances in High Energy Physics 5

Table 1: Seismic properties of rock mass in two galleries: Ps-1 and Ps-3 [13].

∗ 𝑃-wave velocity (m/s) Deformation modulus (GPa) Type of rock mas/Ps-1 and Ps-3 Range Mean Range Mean Rock salt layer Ps-1 — — — — Ps-3 4400–5150 4817 8.4–18.0 13.9 Anhydrite layer Ps-1 5950–6700 6440 50.4–119.4 88.6 Ps-3 5000–5480 5310 16.9–29.3 24.1 Dolomite layer Ps-1 5900–6350 6260 47.6–70.8 72.0 Ps-3 — — — — ∗ Static modulus by Barton’s empirical formula [15].

Table 2: Elastic parameters obtained for rock salt and anhydrite laboratory tests.

Rock salt Anhydrite Parameter Range Mean Range Mean Young’s modulus (GPa) 0.5–30.0 8.0 52.4–68.2 59.0 Poisson ratio (−) 0.15–0.30 0.20 0.22–0.26 0.25

Geotechnical research of the rock salt mechanical prop- One study that was carried out was the rock temperature erties showed that different parts of the deposit differ strongly on the side walls as well as at three points into the rock mass, with strength parameters and creep rate, in spite of being of the furthest of which was at 2.7 meters deep in a gallery thesameorigin—oldesthaliteNa1belongingtocyclothem and operating chamber. The achieved results showed that the Werra. Values of uniaxial compression strength were higher temperature at all points was almost the same and averaged ∘ (25.3–38.8 MPa) for samples of fine-grained impure salt, 35.5 C. cut perpendicularly to the bedding of the deposit than for samples of coarse-grain pure salt, and cut parallel to the bedding (20.1–29.7 MPa). 4. Determination of Creep Law Coefficients The strength of anhydrite obtained under laboratory conditionsvariesanddecreasesinthepresenceofinterlayers. The calculations were performed using two creep laws— Norton and Lubby2 [19]. Norton law describing the stationary creep is as follows: 3.3. Determination of Rock Mass Mechanical Properties. The properties of the rock salt layer are slightly different from the properties of rock salt samples determined under laboratory −(𝑄/𝑅𝑇) 𝑛 𝜀𝑒𝑓̇ =𝐴𝑒 𝜎𝑒𝑓 , (1) conditions. Undoubtedly, the unfavorable elements in the saline layers are the fractures and faults occurring to a small extent, mainly in the contact zone. However, the mechanical −1 −1 where 𝑄—activation energy, 𝑅—8,3144 J⋅mol K —gas properties of the anhydrite layer differ significantly from ∘ constant, 𝑇—absolute temperature [ K], 𝐴, 𝑛—empirical the parameters determined under laboratory conditions. A constants, commonly known Maxwell creep law may be preliminary observation of the rock mass in the mine, as well regarded as a special case of Norton law with assumptions as results of conducted geophysical surveys, clearly shows the 𝑛=1and distinct fractures of the anhydrite layers, the presence of weak zones in the form of breccia, and relatively high fissuring in the areas of contact with adjoining rocks (Figure 12). 𝑒𝑄/𝑅𝑇 𝜂 (𝑇) = . (2) An RQD index as well as other parameters was measured 𝐴 forpurposesofRMR89 rating calculations (Bieniawski 1989) in Ps-1 gallery. The rock mass parameters were calculated by applying the RocLab program developed by Hoek (Table 4). The coefficients 𝐴, 𝑛 and the quotient value 𝑄/𝑅 are The parameters of strata adjacent to a layer of rock salt are determined empirically on the basis of creep tests performed clearly less favorable than those obtained under laboratory at different temperatures and stresses. conditions presented in Tables 2 and 3. Lubby2 creep law, being a generalization of Burger’s The parameters collated in Table 4 were accepted for rheological model, describes both stationary and primary numerical calculations. The parameters of the rock salt layer creep. In other words, Lubby2 creep law describes the formula were not subjected to reduction as shown in Tables 2 and 3. analogoustoBurger’smodel,inwhichthecoefficientsarenot 6 Advances in High Energy Physics

Table 3: Strength parameters of rock salt and anhydrite with rock salt impurities from the Polkowice-Sieroszowice mine [10].

Parameter Rock salt Anhydrite Anhydrite with impurities ∗ 𝑅𝑐 (MPa) 25.3–38.8/20.1–29.7 92.3 63.84 ∗∗ 𝑅𝑐𝑡 (MPa) 57.2/79.47/94.2/ —— ∗ 𝑅𝑟 (MPa) 0.25/1.0 4.9 3.8 ∗ 𝑅𝑠 (MPa) 2.9/2.3 —— ∗ ∗∗ Perpendicular/parallel to the bedding; 𝜎3 =2MPa/𝜎3 =5MPa/𝜎3 =10; 𝑅𝑐: uniaxial compressive strength; 𝑅𝑐𝑡: triaxial compressive strength; 𝑅𝑟:uniaxial tension strength; 𝑅𝑠:uniaxialshearstrength.

Table 4: Calculation values of strength and elastic parameters for anhydrite and neighboring layers used for numerical calculations [13].

Rock mass type 𝑅𝑐 (MPa) 𝑅𝑟 (MPa) 𝑐 (MPa) 𝜑 (deg) 𝐸 (MPa) 𝜈 (−) Sandstone 6.43 0.06 2.1 30.1 44.7 0.26 Shale 1.47 0.003 0.6 24.7 1.3 0.29 Anhydrite upper 16.51 0.20 4.2 34.3 11.3 0.24 Anhydrite lower 27.55 0.36 6.3 37.6 18.3 0.23 Dolomite, limestone 105.0 1.49 20.0 53.3 67.5 0.18

𝑅𝑐: uniaxial compressive strength; 𝑅𝑟: uniaxial tension strength; 𝑐: cohesion; 𝜑: internal friction angle; 𝐸:Young’smodulus;𝜈: Poisson ratio. constant but are exponential functions of effective stress or better results were given by Lubby2, because it includes both effective stress and temperature (stationary creep): the primary creeping and stationary creeping. Finally, the adopted coefficients were as follows: 𝜀𝑐𝑟 𝑐𝑟 1 𝑒𝑓 𝜀̇ (𝜀 )= [ (1 − 𝐺 (𝜎 )) −5 𝑒𝑓 𝑒𝑓 𝐾 𝑒𝑓 (i) Norton law: 𝑛 = 5; 𝐴 = 0, 010772 MPa ;𝑄/𝑅= 3𝜂 (𝜎 ) 𝜎𝑒𝑓 𝐾 𝑒𝑓 5750 K, −1 1 (ii) Lubby2 law: 𝐺𝐾 = 8091 MPa; 𝑘1 = −0, 150 MPa ; + ]𝜎𝑒𝑓 , −1 3𝜂 (𝜎 ,𝑇) (3) 𝜂𝐾 = 89633 MPa⋅d; 𝑘2 = −0, 150 MPa ; 𝜂𝑀 = 𝑀 𝑒𝑓 −1 24075000 MPa⋅d (at 313 K); 𝑚=−0.30MPa . 𝑘1𝜎𝑒𝑓 𝑘2𝜎𝑒𝑓 𝐺𝐾 (𝜎𝑒𝑓 )=𝐺0𝑒 ,𝜂𝐾 (𝜎𝑒𝑓 )=𝜂0𝑒 ,

𝑚𝜎𝑒𝑓 𝑙𝑇 5. Stability Assessment 𝜂𝑀 (𝜎𝑒𝑓 ,𝑇)=𝜂0𝑒 𝑒 , The section refers to the most interesting results from the where 𝐺𝐾—Kelvin shear modulus, 𝜂𝐾—Kelvin viscosity, perspective of stability assessment. Two potential locations 𝜂𝑀—Maxwell viscosity, 𝑘1, 𝑘2, 𝑚, 𝑙—empirical constants. for the Glacier detector chamber and its dimensions are Asignificantfeatureofthetestedrocksaltisthestrong schematically presented in Figure 9. Axisymmetrical models influence of temperature on the creep rate. It was impossible of FLAC2D and FLAC3D were used to simulate the behavior to derive reliable coefficients of creep laws from dispersed of rock formation around the detector chamber. Excavation values of laboratory creep rate. Fortunately, convergence support by bolting was not taken into account in the prelim- measurements performed in the mine gallery could be used inary calculations presented in the following section. to validate the creep laws. The gallery was about 5.0 m high and 6.5m wide. Horizontal displacement benchmarks were 5.1. Rock Salt Layer. The rock salt layer of the Werra placed on the gallery wall 1.5 m above the bottom, opposite to cyclothem in the Polkowice-Sieroszowice mine is situated each other; vertical displacement benchmarks were placed at between two layers of anhydrite (Figure 9), a rock mass the center of the gallery roof and bottom. Three benchmarks with a high value of Young’s modulus. Therefore, it could were placed at each location—stabilized at 0.2 m, 2.5 m, and be expected that the location of the chamber near the 5.0 m inside the rock salt. layers of anhydrite significantly reduces the value of the Finally, two creep laws have been adopted for the numer- displacement. Numerical simulations were carried out for ical models—Norton and Lubby2, whose coefficients have several models of different geological configurations. Two of been validated using in situ measurements of the mine gallery them are compared in Table 5: side wall displacements after several modelings with different coefficients from the range given by laboratory tests. (i) chamber in very thick salt layer (no anhydrite layers It was found that both laws give similar qualitative results in the chamber vicinity), (Figure 8), but considering the horizontal displacements, better results were obtained for Lubby2, as opposed to (ii) chamber in salt layer between two layers of anhydrite vertical displacements, where better results were obtained— 15mbelowthechamberfloorand30mabovethe for Norton’s law. It is not surprising that, in general, slightly chamber roof. Advances in High Energy Physics 7

Table 5: Maximal horizontal displacement of chamber wall and vertical displacement of the chamber bottom and roof [10].

Maximal displacement (m) Model Creep law Wall Bottom Roof Norton 𝑛=5 2.42 3.11 2.75 Rock salt Lubby2 3.93 5.06 4.46 Norton 𝑛=5 1.34 0.16 1.01 Rock salt with anhydrite Lubby2 2.34 0.26 1.74

Rock salt Anhydrite Rock salt Anhydrite (m) 0 10 20 30 40 50 60 70 80 90 100 110 0 0 Breccia Breccia 5 Disturbed zone 5 Breccia 10 10 (m) 15 15 (m)

20 20

25 25

Discontinuities Disturbed zone

Figure 3: Georadar cross-section through the contact zone between rock salt and anhydrite layer along the side wall of the Ps-3 gallery [10].

20 𝑇=40∘

16 )

15 ‰ 𝜎 −𝜎 ( 1 2 = 14.5 MPa 1

𝜀 12 𝐸1 10 𝐸2 (𝑀𝑃𝑎) 𝐸 8 1 3 𝜎 −𝜎

𝜎 1 2 = 12.5 MPa 𝐸0

5 Axial strain ∘ 𝜎1 −𝜎2 = 10 MPa 4 ∘ 𝑇=22 𝜀0 𝑇=40 0 1234567891011 0 20 40 60 80 100 120 140 𝜀1(‰) Time (days)

Figure 4: Typical stress-strain characteristics of rock salt in a cyclic Figure 6: Triaxial creep of rock salt samples at different temper- uniaxial compression test [10]. atures (𝑇) and stress conditions (𝜎1 −𝜎2) from the Polkowice- Sieroszowice copper ore mine [10]. 28 24 𝜎1 AscanbeseenfromTable 5, the vicinity of anhydrite 20 (‰) 𝜎2 𝜎2 layers strongly reduces the vertical displacements of the floor, 16 while the horizontal displacements of the wall are reduced by 12 𝜎1 nearly 50%. Such a result could be regarded as beneficial if the 𝜎 >𝜎 8 1 2 contact zones of salt and anhydrite rocks were not disturbed. Axial strain 4 However, based on observations of the mine’s workings and results of geophysical surveys, it has been noted that a 0 0 20 40 60 80 100 120 140 strongly disturbed zone occurs at the border between the salt Time (days) and anhydrite layers which has a thickness of several meters. Therefore, the chamber cannot be located in such a close 𝜎 −𝜎 1 2 = 10 MPa proximity to the layers of anhydrite. On the other hand, the 𝜎1 −𝜎2 = 15 MPa influence of anhydrite layers decreases with the distance from Figure 5: Selected triaxial creep tests results obtained for rock salt these layers. For example, in the case of the model where samples from the Polkowice-Sieroszowice copper ore mine [10]. the anhydrite layers occurred 70 m below the bottom and 8 Advances in High Energy Physics

1 rock mass due to water drainage and ventilation. Aside from the favorable geological conditions, the site must be distant 0.1 fromthezonedisturbedbythecopperoreminingoperations.

/day) 0.01 Numerical calculations were also performed, adopting ‰ much less favorable properties of anhydrite rock mass in 0.001 comparison with the results obtained from laboratory tests of rock samples. Despite such conservative assumptions, the

Strain rate ( rate Strain 0.0001 calculations showed that situating the chamber in the layer 0.00001 of anhydrite is acceptable from the geomechanical point of 0 510152025 view.TheareaoftheventilationshaftofthePolkowice- 𝜎𝑒𝑓 (MPa) Sieroszowice mine was selected as a most promising location. Nevertheless, confirmation of this location requires excava- Laboratory test tion of access galleries and detailed geophysical surveys. BGRa BGRb 5.2. Anhydrite Layer. Thesufficientdepthforproperfunc- Figure 7: Comparison of stationary creep rate of rock salt samples tioning of the Glacier detector is 600 meters of water (tests done in 1991—mean values, in 2001—all the values) with BGRa equivalent which, under local conditions for the Polkowice- and BGRb [10]. Sieroszowice mine, corresponds to depth of 250–300 m. As a consequence, an anhydrite layer occurring in the mine at a depth of 650 m was considered as an alternative location. 60 m above the roof, the values of vertical and horizontal The main advantages of this location are the high strength displacements were lower by only a few percent compared to oftheanhydriterockmassandtheshallowerdepthallowing the model with no anhydrite layer. the chamber to be placed at 650 m. Disadvantages of such a The stress-strain state in the rock mass for the demanded location are the widely varying properties of the anhydrite time of laboratory operation (approximately 40–50 years) is rockmassduetotectonicengagementandwaterhazard. highly dependent on the applied creep law. The difference in Numerical simulations were performed using the calcu- the values of displacements obtained using the Norton and lation values for rock parameters given in Table 4.Several Lubby2 creep laws is an important feature of the results and models were considered which differed in primary stress canbeseeninTable 5. states in the rock formation: The next aspect analyzed was the value of the stress in the rock salt surrounding the chamber. The greatest values (i) model 1: chamber in very thick anhydrite layer (no of effective stress—and consequently the failure factor (the otherrockstakenintoaccount)whereprimaryhori- inverse of the safety factor)—are observed at the chamber zontal stress components are equal to the vertical; that walls. The following two strength criterions were used to is, 𝜎𝑥 =𝜎𝑦 =𝜎𝑧 =𝛾𝐻, assess the rock mass stability: (ii) model 2: other rocks underlying and overlying the (i) Burzynski, an optimistic criterion [16]whereinterme- anhydrite layer taken into account, where primary stresses are in elastic geostatistical formation; that is, diate principal stress has no influence on the strength, 𝜎 =𝜎 =𝜎𝜈/(1 − 𝜈) = 𝛾𝐻𝜈/(1 −𝜈) and the failure factor is given by relation of Burzynski 𝑥 𝑦 𝑧 , stress to uniaxial compression strength; a value of 0.3 (iii) model 3: other rocks underlying and overlying the should guarantee long-term stability, anhydrite layer taken into account, where primary horizontal stresses are 36% higher than the vertical; (ii) Hunsche [17], a conservative criterion describing the that is, 𝜎𝑥 =𝜎𝑦 = 1.36𝜎𝑧 = 1.36𝛾𝐻, strength of the weakest salt, and the failure factor isgivenbyrelationofeffectivestresstomaximum (iv) model 4: other rocks underlying and overlying the allowable value according to Hunsche; a value of 0.5 anhydrite layer taken into account, where primary should guarantee long-term stability. horizontal stresses are different, 40% of the vertical in the 𝑥-direction and 80% of the vertical in the 𝑦- The corresponding failure factor distributions along the direction; that is, 𝜎𝑥 = 0.4𝜎𝑧; 𝜎𝑦 =0.8𝜎𝑧, chamber wall are shown in Figure 10.Thehighvaluesofthe (v) model 5: other rocks underlying and overlying the failure factor obtained with the Hunsche criterion indicate anhydrite layer taken into account, where primary that the presence of the weakest salt in the chamber vicinity horizontal stresses are different, 40% of the vertical mayleadtorockspallingatthechamberwalls.Theresultsled in the 𝑥-direction and 120% of the vertical in the 𝑦- to the conclusion that chamber stability can be achieved only direction; that is, 𝜎𝑥 = 0.4𝜎𝑧; 𝜎𝑦 =1.2𝜎𝑧. in the case of favorable geological conditions at the chamber site. The following two strength criterions were used to assess Very probably, favorable conditions could be the reason the rock mass stability: forthegoodstabilityofthelargechambermadeinthemine several years ago. Partially, these conditions may also be (i) Burzynski criterion [16]with𝑅𝑐 = 27.5 MPa; 𝛼= ∘ associated with a decrease in the temperature by 5–7 Cinthe 𝑅𝑟/𝑅𝑐 = 0.05, Advances in High Energy Physics 9

Time (days) Time (days) 0 200 400 600 800 1000 1200 1400 1600 0 200 400 600 800 1000 1200 1400 1600 0 0 −20 −20 −40 −40 −60 −60 −80 −80 −100 −100 −120 5.0 m −120 −140 −140 5.0 m −160 −160 −180 −180 2.5 m −200 −200 −220 −220 2.5 m −240 −240 Horizontal displacement (mm) displacement Horizontal Vertical displacement (mm) displacement Vertical −260 −260 −280 −280 −300 −300 −320 0.2 m −320 0.2 m −340 −340

In situ measurements Norton In situ measurements Lubby2 Norton Lubby2 (a) (b)

Figure 8: Validation of creep law parameters used in the study; changes of horizontal (a) and vertical (b) displacement versus time in the side wall of the gallery at a 1000 m depth in the Polkowice-Sieroszowice copper ore mine [11].

∘ (ii) Coulomb-Mohr criterion with 𝑐 = 6.3 MPa; 𝜑 =38. the impact range of the chamber was very large due to fast creeping of the rock salt layer, leading to a reduction in The Coulomb-Mohr criterion leads to a lower failure effective stress at the chamber contour and an increase at factor than the Burzynski criterion (Figure 11), but even then, larger distances. The main problem for the detector chamber the values do not exceed 0.8, and according to the accepted will be large displacements of the chamber walls and bottom criteria, the localization of the Glacier detector chamber in exceeding 3 m over 50 years. Although the neighboring the considered anhydrite layer can be recommended as the anhydrite layers can reduce the displacements of salt rock most promising. massatthechamberroofandbottom,thesalt-anhydrite contact zone had to be avoided as well. Another disadvantage of a chamber location at a depth of about 1000 m was the close 6. Resume proximity to the impact zone of active mine operations, also The paper presents geotechnical aspects of the feasibility inducing seismicity. study for locating the giant astroparticle detector in a very The location in anhydrite is recommended mainly due large size chamber in the Polkowice-Sieroszowice mine. Two to two factors—the depth at 650 m below the surface and locations were taken into account, a rock salt layer and an the insignificant viscoplastic properties of anhydrite rock at anhydrite layer. this depth. The numerical calculations indicate that from a The main advantages of the rock salt location were geomechanical point of view it is possible to cut a large- adequate thickness (more than 100 m) at the depth of dimension chamber at a depth 650 m; however, a stability of about 1000 m, no fractures, and no water hazard. Another the chamber can be improved by bolting as shown in Figure 9 advantage of this location was the very low level of natural or shotcreting. background radioactivity registered there. Parameters of the anhydrite rock in situ are, in fact, much Themainprobleminvolvedinchamberconstructionin less favorable than those obtained in laboratory tests and a rock salt layer resulted from the chamber’s convergence, aregettingworseovertime.Ontheotherhand,thereisthe that is, the loss of chamber volume over time. The issue possibility of the occurrence of diverse tectonic stresses, a was analyzed based on numerical simulation of the rock phenomenon which is particularly unfavorable when there salt behavior in the chamber’s vicinity using two- and three- is a large difference in the values of the two components of dimensional numerical models. Two creep laws were applied horizontal stress. in calculations leading to results which differ significantly. Summarizing, the location of the chamber in the anhy- Displacements and effective stresses were much greater for drite layer is the most promising in geological and mining the Lubby2 than for the Norton creep law. In both cases, conditions of the Polkowice-Sieroszowice mine. 10 Advances in High Energy Physics

NW SE 𝑆𝑊-4 𝑆𝐺-1 𝑃𝐼-𝑃𝐼𝐼 𝑃𝐼𝐼𝐼-𝑃𝐼𝑉 𝑆𝑊-1 𝑃𝑉-𝑃𝑉𝐼 0 0 −100 −100 −200 −200 −300 −300 −400 −400 −500 −500 −600 −600 −700 −700 Depth (m) −800 −800 Depth (m) −900 −900 −1000 −1000 −1100 −1100 −1200 −1200 −1300

The quaternary: sands, 𝑄 𝑃22-3 ℎ Faults (amplitudes in m) gravel, clay Zechstein: rock salt –10.5 m 𝑇 The tertiary: clay, sands, 𝑃 𝑃𝐼-𝑃𝐼𝐼 r gravel, brown coal 22-3 Zechstein: main dolomite Existing shafts Zechstein: carbonate series: 𝑇 Motley sandstone, 𝑝21 𝑆𝑊-4 Designed shaft 1 fine-grained sandstones dolomite, limestone, shale

𝑝24 Zechstein: clay shale series, 𝑃 Red ﬂoor sandstone: claystone, gypsum 1 gray and red sandstone Zechstein: anhydrite series, 𝑃22-3 Copper ore seam anhydrite with dolomite inclusions

(a) 72 m 3 12 m 15.5 m

R60

R39.5 47.5 m 27 m 32.5 m R218

74 m 79 m

(b)

Figure 9: Proposed detector locations (a) and Glacier chamber dimension in meters (b) used in the numerical modeling on the basis of [13]. Advances in High Energy Physics 11

−970 −970

−975 −975

−980 −980

−985 −985 Depth (m) Depth (m) −990 −990

−995 𝑅𝑐 = 23.64 −995

𝛼 = 𝑅𝑟/𝑅𝑐 = 0.064 −1000 −1000 0 0.5 0.1 0.15 0.2 0.25 0.3 0.3 0.35 0.4 0.45 0.5 0.55 0.6 Burzynski factor Hunsche factor Salt, Norton Salt, Lubby2 Salt, Norton Salt, Lubby2 Salt + anhydrite, Norton Salt + anhydrite, lubby2 Salt + anhydrite, Norton Salt + anhydrite, lubby2 (a) (b)

Figure 10: Failure factor according to Burzynski criterion (a) and to Hunsche criterion (b) along the chamber wall for the detector chamber in rock salt [11].

−615 −615

−620 −620

−625 −625

−630 −630

−635

−635 Depth (m)

Depth (m)

−640 −640

−645 −645

−650 −650 0 0.2 0.4 0.6 0.8 1 0.3 0.4 0.5 0.6 Burzynski factor Coulomb-Mohr factor 𝜎 0.4𝜎𝑧 0.4 𝑧 𝜎 1.2𝜎𝑧 1.2 𝑧 𝜎 1.36𝜎𝑧 1.36 𝑧 (a) (b)

Figure 11: Failure factor according to Burzynski criterion (a) and to Coulomb-Mohr criterion (b) along the chamber wall for the detector chamber in anhydrite [11]. 12 Advances in High Energy Physics

[10] J. Slizowski, K. Urbanczyk, D. Wiewiorka, M. Kowalski, and K. Serbin, Excavation stability in LGOM bedded evaporates for underground laboratory construction. Monographs no. 168 [M.S. thesis], IGSMiE PAN, Krakow, Poland, 2011. [11] J. Slizowski, K. Urbanczyk, and K. Serbin, “Salt chamber for the astroparticle detector-LAGUNA project,” in Proceedings of the Conference on Mechanical Behavior of Salt VIII, P. Berest, M. Ghoreychi, F. Hadj-Hassen, and M. Tijani, Eds., pp. 209–214, Paris, France, April 2012. [12] J. Klapcinski and T. M. Peryt, Geology of Przedsudecka Mono- cline, Monography of KGHM Polska Miedz S.A. (Piestrzynski), Lubin, Poland, 2007. [13] Laguna Design Study (Sunlab)-Underground Infrastructure and Engineering Interim Report. Report of KGHM Cuprum CBR Wroclaw, KGHM Polska Miedz SA, Polkowice- Sieroszowice, IGSMiE PAN Krakow, 2012. [14] Z. Pilecki, DeterminationofRockMassParametersUsing Figure 12: Crack in the contact zone of rock salt (a) and anhydrite Geotechnical Classifications,Drukrol,Krakow,Poland,2002. (b) in the side wall of the Ps-1 gallery [10]. [15] N. Barton, Rock Quality, Seismic Velocity, Attenuation and Anisotropy,Taylor&FrancisGroup,London,UK,2007. [16] J. Slizowski and K. Urbanczyk, Influence of Depth on Rock Acknowledgments Salt Effort around the Single Chamber,IGSMiEPAN,Krakow, Poland, 2004. The LAGUNA design study was financed by the FP7 Research [17] U. Hunshe, “True triaxial tests on cubic rock salt samples- Infrastructure “Design Studies” Grant Agreement no. 212343 experimental methods and results,” in Proceedings of the Iutam FP7-INFRA-2007-1. Researches were carried out by MEERI Symposium on Finite Inelastic Deformations-Theory and Appli- PAS and KGHM CUPRUM CBR. Special thanks are extended cations, D. Besdo and E. Stein, Eds., pp. 525–536, Hannover, to the management of the Polkowice-Sieroszowice copper Germany, August 1991. ore mine, who provided considerable and comprehensive [18] I. Plischke, “Determination of mechanical homogeneous areas assistance. in the rock salt mass using creep properties for a classification scheme,” in 6th Conference on the Mechanical Behavior of Salt References ’SALTMECH6’ - The Mechanical Behavior of Salt - Understand- ing of THMC Processes in Salt, pp. 321–325, deu, May 2007. [1] A. Rubbia, “The Laguna design study-towards giant liquid [19] K. H. Lux and S. Heusermann, “Creep test on rock salt with based underground detectors for neutrino physics and astro- changing load as a basis for the verification of theoretical mate- physics and proton decay searches,” Acta Physica Polonica B,vol. rial laws,” in Proceedings of the 6th International Symposium 41,no.7,pp.1727–1732,2010. on Salt Symposium, vol. 1, pp. 417–435, Salt Institute, Toronto, [2]E.Tziaferi,M.J.Carson,V.A.Kudryavtsevetal.,“First Canada, 1883. measurement of low intensity fast neutron background from rock at the Boulby Underground Laboratory,” Astroparticle Physics, vol. 27, no. 5, pp. 326–338, 2007. [3] L. Mosca, “Frejus´ site for the LAGUNA projects,” Acta Physica Polonica B,vol.41,no.7,pp.1773–1778,2010. [4] L. Labarga, “LAGUNA and the LSC,” Acta Physica Polonica B, vol.41,no.7,pp.1765–1772,2010. [5]W.H.Trzaska,T.Kalliokoski,andK.Loo,“LAGUNAin Pyhasalmi,”¨ Acta Physica Polonica B,vol.41,no.7,pp.1779–1787, 2010. [6]W.H.Trzaska,T.Enqvist,J.Joutsenvaaraetal.,“Advantagesof locating LAGUNA in Pyhasalmi¨ mine,” Progress in Particle and Nuclear Physics,vol.66,no.2,pp.463–467,2011. [7] S.Arad,V.Arad,I.Onicaetal.,“Stabilitystudyforalargecavern in salt rock from Slanic Prahova,” Acta Physica Polonica B,vol. 41, no. 7, pp. 1789–1802, 2010. [8] A. Zalewska, W. Pytel, M. Chorowski et al., “LAGUNA in Polkowice-Sieroszowice mine in Poland,” Acta Physica Polonica B,vol.41,no.7,pp.1803–1812,2010. [9] J. Kisiel, M. Budzanowski, J. Dorda et al., “Measurements of natural radioactivity in the salt cavern of the Polkowice- Sieroszowice copper mine,” Acta Physica Polonica B,vol.41,no. 7, pp. 1813–1819, 2010. Hindawi Publishing Corporation Advances in High Energy Physics Volume 2013, Article ID 876870, 11 pages http://dx.doi.org/10.1155/2013/876870

Research Article Classic (Nonquantic) Algorithm for Observations and Measurements Based on Statistical Strategies of Particles Fields

D. Savastru,1 Simona Dontu,1 Roxana Savastru,1 and Andreea Rodica Sterian2

1 Department of Constructive and Technological Engineering for Lasers and Fibre Optic Communications, National Institute of R&D for Optoelectronics INOE 2000, 409 Atomistilor Street, P.O. Box MG-5, 077125 Magurele, Romania 2 Academic Center for Optical Engineering and Photonics, Faculty of Applied Sciences, University Politehnica of Bucharest, 060042 Bucharest, Romania

Correspondence should be addressed to Simona Dontu; [email protected]

Received 10 October 2012; Revised 21 December 2012; Accepted 16 January 2013

Academic Editor: Bogdan Mitrica

Copyright © 2013 D. Savastru et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Our knowledge about surroundings can be achieved by observations and measurements but both are influenced by errors (noise). Therefore one of the first tasks is to try to eliminate the noise by constructing instruments with high accuracy. But any real observed and measured system is characterized by natural limits due to the deterministic nature of the measured information. The present work is dedicated to the identification of these limits. We havenalyzed a some algorithms for selection and estimation based on statistical hypothesis and we have developed a theoretical method for their validation. A classic (non-quantic) algorithm for observations and measurements based on statistical strategies of optical field is presented in detail. A generalized statistical strategy for observations and measurements on the nuclear particles, is based on these results, taking into account the particular type of statistics resulting from the measuring process also.

1. Introduction solar neutrino spectroscopy. They have a decisive role as an energy-loss channel for understanding stellar evolution also. The methods of testing statistical hypothesis and parameters The observed astrophysical neutrino sources other than the estimation, built up in the frame of mathematical statistics, Sun help us in understanding supernova physics as stellar represent algorithms which confirm the “functionality” of core collapse as well as the dynamics of supernova explosions experimental systems [1–4]. The aim of this paper is to and nucleosynthesis [15–24]. identify natural limits by building up “observation” and The methods of statistical physics we will discuss in “estimation” algorithms based on “statistical strategies” of thepaperareinseparablyintertwinedinthestrategyfor “assessment and control” of these limits. In the experimental observations and measurements on the nuclear particles, as systems as optical communications a large interest is focused neutrinos. on observation and measurement of signals with entropy A high-statistics neutrino observation provides us with bigger than the noise level. Thus, the signal/noise ratio is used very important data about other low-mass particles which as a main observable for validation of correct operation of a determine large-scale experiments in which new types of communication system [5–12]. particle detectors will be developed and built. Concomitantly A classic (non-quantic) algorithm based on statistical with the neutrino observation, a lot of theoretical and numer- strategies for an optical field is presented in detail. A gen- ical work remains to be done, based on statistical physics eralized statistical strategy based on observations and mea- methods giving us crucial information for the accuracy of the surements on the nuclear particles as neutrinos can be also experiments to be developed and built. developed [13, 14]. The neutrinos physics and engineering Two application examples are given: one is based on the are related very closely to that of the stars. The chemical bilateral test for validation of statistical hypothesis (validation composition of the solar interior is one of the frontiers of of mean value for a given dispersion) and another one for 2 Advances in High Energy Physics

󳨀→ validation of the mean value for an unknown dispersion [6– We define the risk function 𝑊𝑖( 𝑉 ) in choosing statistical 12, 15, 25]. ̂ hypothesis {𝐻𝑖} as follows: To eliminate the noise by construction of instruments with high accuracy it is very important to mention that 󳨀→ 𝑀 󳨀→ 𝑊 ( )=∑𝜉 𝐶 𝑃 ( ). statistical validation of some communication systems based 𝑖 𝑉 𝑗 𝑖𝑗 𝑗 𝑉 (6) on control statistical strategies points out that the signal/noise 𝑗=1 ratio is not the essential parameter in characterising such a Using (6), the value of average risk leads to the following system but the structure of the statistical strategy. Therefore expression: a system with high signal/noise ratio will not solve the validation (good working of this system) from the point of 𝑀 󳨀→ ←󳨀 󳨀→ 𝐶=∫ ∑𝑊 ( ) 𝜋̂ (𝑉)[𝑑 ]. view of multistochastic processes that generate noise. 𝑖 𝑉 𝑖 𝑉 (7) 𝑖=1 The problem consists in finding a number of 𝑀 functions 2. Theoretical Considerations 󳨀→ {𝜋̂𝑖( 𝑉 )}, which satisfy the conditions: We define the set of measurements for the considered signal as follows: 󳨀→ 0≤𝜋̂𝑖 ( 𝑉 )≤1, 󳨀→ 𝑉 ={𝑉1,𝑉2,𝑉3,...𝑉𝑛}. (1) 𝑀 󳨀→ Starting with this, we intend to calculate the false alarm ∑𝜋̂𝑖 ( 𝑉 )=1, 𝑖=1 (8) probability (𝑄0), the detection probability (𝑄𝑑),andthe physical system state [7]. We assume that a physical system is 𝑀 󳨀→ 󳨀→ 󳨀→ in 𝑀 statistical states, described by 𝑀 statistical hypothesis 𝛿𝐶=𝛿∫ ∑𝑊 ( 𝑉 ) 𝜋̂ ( 𝑉 )[𝑑 𝑉 ]=0. ̂ ̂ 𝑖 𝑖 {𝐻𝑗}.Ifan𝑀 physical system is characterized by {𝐻𝑗} 𝑗=1 statistical state, the detected signal will be, [8], The value of minimum risk is defined as follows: ̂ {𝐻𝑗}:𝑉(𝑡) =𝑠𝑗 (𝑡) +𝑛(𝑡) , (2) 󳨀→ def 󳨀→ Γ(𝑉 ) = min 𝑊𝑗 ( 𝑉 ) (𝑗) (9) where 𝑠𝑗(𝑡) represents the useful signal and 𝑛(𝑡) the random signal. or in other form: 󳨀→ We assume that the observation vector { 𝑉 } is a random 󳨀→ 𝑀 󳨀→ 󳨀→ variable described by the probability density function: Γ ( 𝑉 ) = ∑𝑊𝑖 ( 𝑉 ) 𝜋̂𝑖 ( 𝑉 ) , (10) 𝑖=1 󳨀→ 𝑃𝑗 =𝑃𝑗( 𝑉 ) . (3) 𝑗=1,2,3,4...,𝑀 where: 󳨀→ 󳨀→ Thus, the “strategy” consists in associating the statistical 𝐶min = ∫ Γ(𝑉 )[𝑑 𝑉 ]. (11) 󳨀→ 󳨀→ {𝐻̂ } { } 𝜋̂ ( ) hypothesis 𝑗 to the event 𝑉 ,withriskprobability 𝑗 𝑉 󳨀→ (classic measurement operator). The risk functions {𝑊𝑖( 𝑉 )} are directly proportional to the 󳨀→ 󳨀→ The {𝜋̂𝑖( 𝑉 )}𝑖=1,2,...𝑀 functions represent a “random strat- risks defined “a posteriori” {𝑟𝑖( 𝑉 )} as it is presented in the egy” for choosing the best statistical hypothesis. We define the following: {𝐻̂ } probability of choosing the statistical hypothesis 𝑖 when 󳨀→ 𝑀 𝑊 ( 𝑉 ) the physical system is characterized by statistical hypothesis 󳨀→ 𝐻̂ 𝑖 ̂ 𝑟 ( ) def= ∑𝐶 𝑃 { 𝑘 }= , {𝐻𝑗} [9] as follows: 𝑖 𝑉 𝑖𝑘 𝑟 󳨀→ 󳨀→ (12) 𝑘=1 𝑉 𝑃(𝑉 ) ̂ 𝑖 󳨀→ 󳨀→ 󳨀→ {𝐻𝑗}:𝑃𝑟 { }=∫ 𝜋̂𝑖 ( 𝑉 )𝑃𝑗 ( 𝑉 )[𝑑 𝑉 ], (4) 𝑗 ̂ 󳨀→ 󳨀→ 󳨀→ where 𝑃𝑟{𝐻𝑘/ 𝑉 }=𝜉𝑘(𝑃𝑘( 𝑉 )/𝑃( 𝑉 )) represents “a posteri- 󳨀→ ̂ ori” probability for statistical hypothesis {𝐻𝑘}: where [𝑑 𝑉 ]=𝑑𝑉1𝑑𝑉2𝑑𝑉3 ...𝑑𝑉𝑛. The statistical event (given by 𝑃𝑟{𝑖/𝑗} probability) is 󳨀→ 𝑀 󳨀→ described by {𝐶𝑖𝑗 } risk. Using the prior probability {𝜉𝑗},the 𝑃 ( 𝑉 ) = ∑𝜉𝑗𝑃𝑗 ( 𝑉 ) . (13) value of average risk for immediate strategy leads to 𝑖=1 𝑀 𝑖 Also,theaposterioriprobabilitycouldbedefinedinrelation 𝐶=𝐶[𝜋̂𝑖]= ∑ 𝜉𝑗𝐶𝑖𝑗 𝑃𝑟 { } to verisimilitude ratio under the expression: 𝑖, 𝑗=1 𝑗 󳨀→ Λ ( ) (5) 𝐻̂ 𝑘 𝑉 𝑀 󳨀→ 󳨀→ 󳨀→ 𝑃 { 𝑘 }=𝜉 = ∑ 𝜉 𝐶 ∫ 𝜋̂ ( 𝑉 )𝑃 ( 𝑉 )[𝑑 𝑉 ]. 𝑟 󳨀→ 𝑘 󳨀→ (14) 𝑗 𝑖𝑗 𝑖 𝑗 𝑉 ∑𝑀 𝜉 Λ ( 𝑉 ) 𝑖, 𝑗=1 𝑗=1 𝑗 𝑗 Advances in High Energy Physics 3

󳨀→ 󳨀→ 𝑄 (𝜋)̂ and the verisimilitude ratio can be written as, Λ 𝑘( 𝑉 )=𝑃𝑘( 𝑉 )/ 𝑑 󳨀→ 𝑃( 𝑉 ), 𝑃(𝑄0,𝑄𝑑)

󳨀→ 󳨀→ 󸀠 lim Λ 𝑘 ( 𝑉 )=Λ[𝑉 (𝑡)]󳨀→Functional. (14 ) 𝑘→∞ (Γ1)

3. Structure of Statistical Strategy for Two (𝐿) Statistical Hypotheses 𝑄0(𝜋)̂ Let us consider two statistical hypotheses defined as follows: (𝑄 ,𝑄 ) ̂ Figure 1: Simple convex region 𝑑 0 . 𝐻0 :𝑉(𝑡) =𝑛(𝑡) , (15) 𝐻̂ :𝑉(𝑡) =𝑠(𝑡) +𝑛(𝑡) . 1 ̂ We calculate the probability to choose {𝐻1} hypothesis for a ̂ From measurements, we obtained system retrieved in {𝐻0} hypothesis:

󳨀→ 󳨀→ 𝑉 (𝑡) ={𝑉 (𝑡) ,𝑉 (𝑡) ...𝑉 (𝑡)}. (16) {𝐻 } 󳨀→ 󳨀→ 󳨀→ 1 2 𝑛 𝑄 def=𝑃 1 = ∫ 𝜋̂ ( )𝑃 ( )[𝑑 ] 0 𝑟 { 󳨀→ } 1 𝑉 0 𝑉 𝑉 (22) Probability densities associated with the statistical hypothesis {𝐻0 } will be 𝑃0(𝑉),1 𝑃 (𝑉) [10]: andalsowecalculatetheprobabilitytochooseforaselected ̂ {𝐻̂ } 𝐻0 󳨀→ null hypoyhesis, physical system the 1 hypothesis which can be found in ̂ (17) the {𝐻1} hypothesis ̂ 𝐻1 󳨀→ alternative hypothesis. def 𝐻̂ 󳨀→ 󳨀→ 󳨀→ 𝑄 =𝑃{ 1 }=∫ 𝜋̂ ( 𝑉 )𝑃 ( 𝑉 )[𝑑 𝑉 ]. The risk functions are calculated as follows: 𝑑 𝑟 ̂ 1 1 (23) 𝐻1 󳨀→ 󳨀→ 󳨀→ 𝑊 ( )=𝜉𝐶 𝑃 ( )+𝜉 𝐶 𝑃 ( ), 1 𝑉 1 11 1 𝑉 0 10 0 𝑉 Actually, the strategy consists in 𝑄𝑑 maximization for a (18) certain given value of 𝑄0 (the Neyman-Pearson criteria). 󳨀→ 󳨀→ 󳨀→ In this case, if the verisimilitude ratio has the form: 𝑊0 ( 𝑉 )=𝜉1𝐶01𝑃1 ( 𝑉 )+𝜉0𝐶00𝑃0 ( 𝑉 ). 󳨀→ 𝑃 ( 𝑉 ) {𝐻̂ } 1 Bayes’ strategy consists in choosing statistical hypothesis 1 Λ [𝑉 (𝑡)] = (24) if the following relation is valid: 󳨀→ 𝑃0 ( 𝑉 ) 󳨀→ 󳨀→ 𝑊 ( 𝑉 )<𝑊 ( 𝑉 ), 1 0 (19) then for (22)and(23)weobtain,[11],

󳨀→ 󳨀→ 󳨀→ (see [10]). 𝑄0 (𝜋̂) = ∫ 𝜋(̂ 𝑉 )𝑃0 ( 𝑉 )[𝑑 𝑉 ], From (18)and(19)onecanget (25) 󳨀→ 󳨀→ 󳨀→ 󳨀→ 𝑄𝑑 (𝜋̂) = ∫ 𝜋(̂ 𝑉 )Λ[𝑉 (𝑡)] 𝑃0 ( 𝑉 )[𝑑 𝑉 ]. 𝑃1 ( 𝑉 ) 𝜉 (𝐶 −𝐶 ) > 0 10 00 , 󳨀→ 𝜉 (𝐶 −𝐶 ) 𝑃 ( 𝑉 ) 1 01 11 Let us define a phase space (𝑄0,𝑄𝑑) with parameter function 0 󳨀→ (20) {𝜋(̂ 𝑉 )}. This is a simple convex space: 󳨀→ 𝑃 ( 𝑉 ) 1 0≤𝑄 ≤1, Λ = . 0 1 󳨀→ (26) 𝑃 ( 𝑉 ) 0 0≤𝑄𝑑 ≤1.

The a posteriori probability has the form: D (a simple convex region) is the field of possible values for 𝑄0 and 𝑄𝑑(0),asshowninFigure1. 𝐻̂ 1 A reliability assessment of equipment compliance indi- 𝑃 { 0 }= , 𝑏 𝑟 󳨀→ 1+(𝜉 /𝜉 )(Λ /Λ ) cators based on these calculations is performed. Values st 𝑉 1 0 1 0 𝑟 𝑏 (21) and st are chosen to use the test plan for testing ( st— 𝜉 (𝐶 −𝐶 ) standardized coefficient calculated in one step). 0 10 00 𝑟 =0 𝑛𝑡/𝑇 Λ 0 = . At limits of compliance for 1 the value 0 𝜉1 (𝐶01 −𝐶11) 𝑛𝑡/𝑇 =𝑏 is calculated, the number of failures for 0 st is 4 Advances in High Energy Physics

󳨀→ ̂ determined and, in rectangular coordinate system, a trace line In the case of equality, Λ( 𝑉 )=𝜆,wechoose{𝐻1} as by the two points is obtained (Figure 2(a)). hypothesis, with the probability: 𝑛𝑡/𝑇 =0 For areas of inadequacy 0 the number of failures 󵄨 𝑟 𝑛𝑡/𝑡 𝑟=𝑟 󳨀→ 󵄨 2 is determined, the value 0 for st is calculated, and 𝑓=𝜋(̂ 𝑉 )󵄨 , 󵄨󳨀→ (34) a trace line by the two points is obtained (Figure 2(b)). 󵄨 𝑉 ∈𝑧 Achieve line is represented as a process that begins right 𝑧 → at point zero and coincides with the horizontal axis. where includes D the uncertainty region. 𝑄 𝑄 Let the curve equation (Γ1)whichupperlimitstheregion In this case, values of 0 and 𝑑 will have the expressions: Dbe 󳨀→ 𝑧 󳨀→ 𝜆 𝑄 =𝑓𝑃 { 𝑉 ∈ }+𝑃 {Λ ( 𝑉 )> }, 0 𝑟 ̂ 𝑟 ̂ 𝐻0 𝐻0 𝑄𝑑 =𝑔[𝑄0]. (27) (35) 󳨀→ 𝑧 󳨀→ 𝜆 𝑄𝑑 =𝑓𝑃𝑟 { 𝑉 ∈ }+𝑃𝑟 {Λ ( 𝑉 )> }. Since region D is convex, no tangent at Γ1 curve crosses the D ̂ ̂ 𝐻1 𝐻1 region. Let 𝑃 be the point of the {𝑄0,𝑄𝑑} coordinate tangent. The 󳨀→ [ 𝑉 ] line equation with 𝜆 slopehastheexpression: For a continuous structure on observable space (34)and (35)become

𝑔(𝑄0)−𝜆𝑄0 =𝑄𝑑 (𝜋̂) −𝜆𝑄0 (𝜋̂) . (28) 󳨀→ 𝜆 𝑄 =𝑃 {Λ ( 𝑉 )> }, 0 𝑟 ̂ 𝐻0 󳨀→ {𝜋(̂ )} (36) Whatever the 𝑉 values are, the points belonging to D 󳨀→ 𝜆 𝑄 =𝑃 {Λ ( 𝑉 )> }, region fulfill the condition: 𝑑 𝑟 ̂ 𝐻1 ̂ ̂ 𝑔(𝑄0)−𝜆𝑄0 ≥𝑄𝑑 (𝜋) −𝜆𝑄0 (𝜋) . (29) where [𝑧] region has null probability (𝑓 = 0) for any ̂ ̂ hypothesis {𝐻0, 𝐻1}. This can be rewritten as follows:

󳨀→ 󳨀→ 󳨀→ 󳨀→ 4. Calculation Algorithm of Statistical 𝑔(𝑄0)−𝜆𝑄0 ≥ ∫ 𝜋(̂ 𝑉 )[Λ(𝑉 −𝜆)]0 𝑃 ( 𝑉 )[𝑑 𝑉 ]. Strategy (Classic Case) for Observation (30) and Measurement of an Optical Signal in Presence of Gaussian Fluctuations In this case, the statistic strategy consists in maximization of Let us suppose that we consider the two statistical hypotheses the integral in (30): ̂ ̂ case {𝐻0, 𝐻1}:

󳨀→ 󳨀→ 󳨀→ 󳨀→ 󳨀→ 󳨀→ 𝐻̂ : 𝑉 (𝑡) = 𝑛 (𝑡) , 𝛿 ∫ 𝜋(̂ 𝑉 )[Λ(𝑉 ) − 𝜆]0 𝑃 ( 𝑉 )[𝑑 𝑉 ]=0. (31) 0 (37) 󳨀→ 󳨀→ 󳨀→ 𝐻̂ : 𝑉 (𝑡) = 𝑛 (𝑡) + 𝑠 (𝑡) , 󳨀→ 1 From (31) we obtain the parameter function, {𝜋(̂ 𝑉 )},which 󳨀→ 󳨀→ 𝑄 𝜋(̂ 𝑉 ) where 𝑛 (𝑡) represents the Gauss random distributed signal maximizes the value for 𝑑.The can have possible 󳨀→ values: (the Gauss noise) and 𝑠 (𝑡) the detectable useful signal. We suppose an averaging operator 𝐸̂ for statistical 󳨀→ 󳨀→ ̂ ̂ 𝜋(̂ 𝑉 )=1󳨀→Λ(𝑉 )−𝜆>0, hypothesis {𝐻0, 𝐻1} andthenwehavethecalculationrules: 󳨀→ 󳨀→ 󳨀→ 𝑛 (𝑡) 𝜋(̂ 𝑉 )=0󳨀→Λ(𝑉 )−𝜆>0, 𝐸[̂ ]=0, 𝐻̂ 󳨀→ 󳨀→ 󳨀→ 0 𝜋(̂ 𝑉 )=𝑓󳨀→Λ(𝑉 )=𝜆, 𝑉 ∈𝑧,{𝜆} ,0≤𝑓<1. 󳨀→ 𝑛 (𝑡) (32) 𝐸[̂ ]=0, ̂ (38) 𝐻1

And therefore 󳨀→ 󳨀→ 𝑛 (𝑡 ) 𝑛 (𝑡 ) 𝐸̂[ 1 2 ] =𝜑(𝑡,𝑡 ), 󳨀→ ̂ 1 2 ̂ 𝐻𝑖 Λ(𝑉 )>𝜆󳨀→we choose {𝐻1} hypothesis, [ ]𝑖=0, 1 (33) 󳨀→ where 𝜑(𝑡1,𝑡2) represents the correlation function of Gaus- Λ(𝑉 )<𝜆󳨀→ {𝐻̂ } , we choose 0 hypothesis sian noise. Advances in High Energy Physics 5

𝑟 𝑟 𝑟 𝑟 st st

𝑛𝑡 /𝑇0 𝑛𝑡/𝑇0 𝑁 𝑁 st st (a) (b)

Figure 2: The limits of a rectangular coordinate system.

󳨀→ 󳨀→ 󳨀→ The signal 𝑉 (𝑡) defined as 𝑉 (𝑡) = 1{𝑉 (𝑡),2 𝑉 (𝑡),3 𝑉 (𝑡), 󳨀→ { 𝑉 } 𝑃1 ( 𝑉 )=𝑃𝑟 ...,𝑉𝑛(𝑡)} must be “observed” and “measured” in (0, 𝑇) { ̂ } 𝐻1 period. { } For {𝑉𝑘}𝑘=1,...,𝑛 observables determination, which repre- 𝑚 {𝑓 } −𝑚/2 −1/2 1 sents latent vectors, and 𝑘 𝑘=1,...,𝑛 fundamental functions, we = (2𝜋) (det 𝜑) exp {− ∑ 𝜇𝑘 (𝑉𝑘 − 𝑉𝑘 ) 2 𝑙 1 can define the expansions: 𝑘, 𝑙=1

×(𝑉− 𝑉 )}, 𝑇 𝑙 𝑙1 𝑉𝑘 = ∫ 𝑓𝑘 (𝑡) 𝑉 (𝑡) 𝑑𝑡 (39) 0 (42)

where or from (37)itresultsthat 󳨀→ ̂ 𝑉𝑘 𝑉 𝑘 = 𝐸[ ]=0, 0 𝐻̂ 𝑇 0 𝑉 =𝑠 + ∫ 𝑓 (𝑡) 𝑛 (𝑡) 𝑑𝑡. 𝑘 𝑘 𝑘 (40) 󳨀→ 0 ̂ 𝑉𝑙 𝑉 𝑙 = 𝐸[ ]=0, 0 ̂ 𝐻0 (43) 󳨀→ 𝑇 Equation (39) represents spectral expansion defined by quan- ̂ 𝑉𝑘 {𝑉 ,𝑓} 𝑉 𝑘1 = 𝐸[ ]=𝑠𝑘 = ∫ 𝑓𝑘 (𝑡) 𝑠 (𝑡) 𝑑𝑡, tities 𝑘 𝑘 . 𝐻̂ 0 Let an observable space 1 𝑉 𝑇 𝑉 = 𝐸[̂ 𝑙 ]=𝑠 = ∫ 𝑓 (𝑡) 𝑠 (𝑡) 𝑑𝑡. 𝑙1 ̂ 𝑙 𝑙 󳨀→ 𝐻1 0 { 𝑉 }={𝑉1,𝑉2,...𝑉𝑛} (41) Also, we build the correlation matrices (for Gaussian noise): def ̂ ̂ (𝜑𝑘 ) = 𝐸[(𝑉𝑘 − 𝑉𝑘𝑖)(𝑉𝑙 − 𝑉𝑙𝑖) 𝐻𝑖] (44) be defined by Gaussian fluctuations, characterized by proba- 𝑙 𝑖=0, 1 𝑖=0, 1 󳨀→ 󳨀→ bility functions 𝑃0( 𝑉 ) and 𝑃1( 𝑉 ). Therefore we define or 𝑇 𝑇 (𝜑𝑘 ) = ∫ ∫ 𝑓𝑘 (𝑡1)𝜑(𝑡1,𝑡2)𝑓1 (𝑡2)𝑑𝑡1𝑑𝑡2. (45) 󳨀→ 𝑙 0, 1 0 0 󳨀→ { 𝑉 } 𝑃0 ( 𝑉 )=𝑃𝑟 { } (𝜇 ) 𝐻̂ The matrix 𝑘𝑙 is defined as { 0 } −1 𝑚 (𝜇𝑘 ) = (𝜑𝑘 ) (46) −𝑚/2 −1/2 1 𝑙 0, 1 𝑙 0, 1 = (2𝜋) (det 𝜑) exp {− ∑ 𝜇𝑘 (𝑉𝑘 − 𝑉𝑘 ) 2 𝑙 0 𝑘, 𝑙=1 Let correlation operator be:

𝑇 ×(𝑉− 𝑉 )}, 𝑇̂ = ∫ 𝜑 (𝑡 ,𝑡 ) 𝑑𝑡 . 𝑙 𝑙0 1 2 1 (47) 0 6 Advances in High Energy Physics

And let eigenvalues equation be but only if ̂ 2 𝑇𝑓𝑘 (𝑡1)=𝜆𝑘𝑓𝑘 (𝑡2), (48) 𝜑(𝑡1,𝑡2)=𝜎𝛿(𝑡2 −𝑡1), (55) where Then the result is 𝑇 𝑇 2 2 ∫ 𝜑 (𝑡1,𝑡2) 𝑓𝑘 (𝑡2) 𝑑𝑡2 =𝜆𝑘𝑓𝑘 (𝑡1) . (49) ∫ 𝜎 𝛿(𝑡2 −𝑡1)𝑓(𝑡1)𝑑𝑡1 =𝜎𝑓(𝑡2), ∀𝑓(𝑡) :𝑅󳨀→𝑅. 0 0 (56) Then we obtain the scalar matrix: (𝜑 )=𝜆 𝛿 , The signal/noise ratio becomes 𝑘𝑙 𝑘 𝑘𝑙 (50) 𝑆 1 𝑇 −1 ( )=[ ∫ 𝑓 (𝑡) 𝑠 (𝑡) 𝑑𝑡] . (𝜇𝑘 )=𝜆𝑘 𝛿𝑘 , (57) 𝑙 𝑙 𝑍 𝜎 0 where (𝜆𝑘) represents the measure of dispersion for every 󳨀→ 󳨀→ If probability distributions for the two statistical hypotheses measurement. The distribution functions 𝑃0( 𝑉 ) and 𝑃1( 𝑉 ) are characterized by a parameter, then we can write acquire a factorial expression (as if every sampling quantity ̂ has been Gaussian distributed). 𝐻0 :𝑃0 =𝑃0 [𝑉 (𝑡) ,𝜃0], (58) Thus, we have ̂ 𝐻1 :𝑃1 =𝑃1 [𝑉 (𝑡) ,𝜃1]. 𝑚 󳨀→ 1 2 −𝑉𝑘 /2𝜆𝑘 𝑃0 ( 𝑉 )=∏ 𝑒 , ̂ We define the probability (𝐻0)as 𝑘=𝑙 √2𝜋𝜆𝑘 (51) 𝑚 󳨀→ 1 −(𝑉 −𝑠 )2/2𝜆 𝑊 𝑃 ( 𝑉 )=∏ 𝑒 𝑘 𝑘 𝑘 . 𝑃 ⌊𝑉 (𝑡) ∈ ⌋=(𝛼) ;󳨐⇒𝑄 , 1 𝑟 𝐻̂ 0 𝑘=𝑙 √2𝜋𝜆𝑘 0 (59) 𝑊 Theverisimilituderatiocanbewrittenas (𝐻̂ ):𝑃 ⌊𝑉 (𝑡) ∈ ⌋=(1−𝛽);󳨐⇒𝑄 , 1 𝑟 ̂ 𝑑 2 𝐻 󳨀→ 𝑚 𝑉 𝑠 −1/2𝑠 1 Λ(𝑉 )= {∑ 𝑘 𝑘 𝑘 }, exp 𝜆 𝑘=𝑙 𝑘 where (𝑊) is the critical domain in the observable space. Intheend,wecanwritetheequationsasfollows: 󸀠 󳨀→ 󳨀→ 𝑄 =𝑄| 󳨀→ = ∫ 𝑃 ( 𝑉 )[𝑑 𝑉 ], (52) 0 0 𝜋̂( 𝑉 )=1 0 ̂ 𝐻1 𝑊 𝑃𝑟 { }=𝑃𝑟 {𝑉 (𝑡) ∈ }=𝑄0 =𝛼, 󳨀→ 󳨀→ ̂ ̂ 󸀠 𝐻0 𝐻0 𝑄 =𝑄 | 󳨀→ = ∫ 𝑃 ( 𝑉 )[𝑑 𝑉 ]. 𝑑 𝑑 𝜋(̂ 𝑉 )=1 1 (60) 𝐻̂ 𝑊 𝑃 { 1 }=𝑃 {𝑉 (𝑡) ∈ }=𝑄 =1−𝛽. 𝑄󸀠 𝑄󸀠 𝑟 ̂ 𝑟 ̂ 𝑑 Next, 0, 𝑑 will have the following expressions: 𝐻1 𝐻1

+∞ 𝑚 󸀠 𝑚 1 −𝑡2/2 𝛼 In this case, the statistic strategy consists in determining 𝑄 =𝜋 ∫ 𝑒 𝑑𝑡 = ∏ erfc [ ], ∗ 0 𝑘=1 √ √ the optimum critical domain {𝑊 } in the observable space 2𝜋 𝛼/√𝜆𝑘 𝑘=1 𝜆𝑘 so that, if there is any other critical domain, the following +∞ 𝑚 󸀠 𝑚 1 −𝑡2/2 𝛼−𝑠𝑘 relationcanbewritten: 𝑄 =𝜋 ∫ 𝑒 𝑑𝑡 = ∏ erfc [ ], 𝑑 𝑘=1 √ √ 2𝜋 (𝛼−𝑠𝑘)/√𝜆𝑘 𝑘=1 𝜆𝑘 ∫ 𝑃1 [𝑉 (𝑡) ,𝜃1] [𝑑𝑉] ≥ ∫ 𝑃1 [𝑉 (𝑡) ,𝜃1] [𝑑𝑉] . (61) (53) 𝑊∗ 𝑊 where 𝛼 is the significance threshold of statistical strategy. We specify (by estimation) the parameters of probability If we accomplish only one measurement, the signal/noise distribution: ratio can be considered as follows [12]: 𝑉𝑘 𝑉𝑘 =𝐸[ ]=𝜃0, 𝑇 2 0 ̂ 𝑆 1 𝐻0 ( )= [∫ 𝑓 (𝑡) 𝑠 (𝑡) 𝑑𝑡] , (62) 𝑍 𝜆 0 𝑇 𝑉𝑘 𝑉𝑘 =𝐸[ ]=𝑠𝑘 = ∫ 𝑓𝑘 (𝑡) 𝑠 (𝑡) 𝑑𝑡1 =𝜃 . 𝑇 1 ̂ 𝐻1 0 ∫ 𝜑(𝑡1,𝑡2)𝑓(𝑡2)𝑑𝑡2 =𝜆𝑓(𝑡1), (54) 0 ̂ If alternative hypothesis (𝐻1) is not only a simple hypothesis: 𝑛(𝑡 )𝑛(𝑡 ) 𝐸[̂ 1 2 ]=𝜑(𝑡,𝑡 ), 𝐻̂ 1 2 𝑉 = 𝑉 0,1 𝑘 𝑘1 (63) Advances in High Energy Physics 7 but a more complex hypothesis written as Using the following special functions: 𝑥 1 −𝑡2/2 𝑉𝑘 > 𝑉𝑘 or 𝑉𝑘 ≠ 𝑉𝑘 (64) Φ (𝑥) = ∫ 𝑒 𝑑𝑡, 0 0 √2𝜋 −∞ +∞ then there does not always exist a validation test to be the 1 −𝑡2/2 erfc (𝑥) = ∫ 𝑒 𝑑𝑡, most powerful over any other test (so there is no most √2𝜋 𝑥 powerful validation test). If we verify null hypothesis Φ (𝑥) =1−erfc (𝑥) , (73) 1−Φ(𝑥) =Φ(−𝑥) , ̂ (𝐻0):𝑉𝑘 = 𝑉𝑘 (65) 0 Φ (𝑥) =𝛼, against alternative hypothesis 𝑥=𝑢𝛼,

(𝐻̂ ):𝑉 > 𝑉 𝑢𝛼 =𝑢1−𝛼, 1 𝑘 𝑘0 (66) we can calculate for instance then the most powerful test will exist. 𝑉 ̂ 𝑉𝑘 1 𝑘𝑐 2 2 (𝐻 ) 𝑉 𝑐 −(𝑉𝑘−𝑉𝑘 ) /2𝜎 If for the alternative hypothesis 1 there is a value 𝑘1 𝑃 {𝑉 < }=1−𝛼= ∫ 𝑒 0 𝑑𝑉 . 𝑟 𝑘 ̂ √ 2 𝑘 which satisfies the following condition: 𝐻0 2𝜋𝜎 −∞ (74) 𝑉𝑘 > 𝑉𝑘 (𝑠𝑘 > 𝑠𝑘 ) (67) 1 0 0 From (74)itresultsthat 𝑉 − 𝑉 for value {𝑉𝑘 }, then it results that the best test is the one for 𝑘𝑐 𝑘0 1 1−𝛼=Φ[ ] (75) which (𝑉𝑘) values (which determine the critical range) satisfy 𝜎 inequality (the Neyman-Pearson auxiliary theorem) andthenwefind 𝑃(𝑉, 𝑉 ,𝜎2) 𝑘 𝑘1 𝑉 =𝑉 +𝜎𝑢 . >𝜆. 𝑘𝑐 𝑘0 1−𝛼 (76) 2 (68) 𝑃{𝑉𝑘, 𝑉𝑘 ,𝜎 } 0 In similar way, it results that

+∞ For Gaussian noise we have 𝑉𝑘 1 2 2 𝑐 −(𝑉𝑘−𝑉𝑘 ) /2𝜎 𝑃𝑟 {𝑉𝑘 > }= ∫ 𝑒 1 𝑑𝑉𝑘 𝐻̂ √ 2 𝑉 2 1 2𝜋𝜎 𝑘𝑐 𝑃[𝑉𝑘, 𝑉𝑘 ,𝜎 ] Λ[𝑉]= 1 𝑘 2 𝑉 − 𝑉 𝑉 − 𝑉 𝑃[𝑉, 𝑉 ,𝜎 ] 𝑘𝑐 𝑘1 𝑘1 𝑘0 𝑘 𝑘0 =Φ[− ]=Φ[𝑢 + ]. 𝜎 𝛼 𝜎 2 2 𝑉 − 𝑉 𝑉 − 𝑉 𝑘 𝑘 𝑘 𝑘 𝐵𝑉 (77) = (− 1 0 ) (𝑉 1 0 )≈𝐴𝑒 𝑘 , exp 2𝜎2 exp 𝑘 𝜎2 From expressions (76)and(77)weobtain (69) 𝑉 − 𝑉 𝑘1 𝑘0 𝑢𝛼 + =𝑢1−𝛽 (78) From (69)itresultsthatΛ(𝑉𝑘) increases as {𝑉𝑘} increases. 𝜎 {𝑉 } (𝑉 ) Thus,thehighestvaluefor 𝑘 that fulfills68 ( )willbe 𝑘0 which satisfies the equality: or in another form:

𝑉𝑘 = 𝑉𝑘 +𝜎[𝑢1−𝛼 +𝑢1−𝛽]. (79) 󵄨 1 0 Λ(𝑉𝑘)󵄨𝑉 =𝑉 =𝜆. 𝑘 𝑘𝑐 (70) Similarly, we can write the following expressions: By expanding (70)itresultsthat 𝑉 − 𝑉 𝑘𝑐 𝑘0 𝑄0 = erfc [ ]=𝛼, 2 2 2 𝜎 2𝜎 ln 𝜆+[𝑉𝑘 − 𝑉𝑘 ] 𝑉 = 1 0 . (71) 𝑘𝑐 𝑉 − 𝑉 2[𝑉 − 𝑉 ] 𝑘𝑐 𝑘1 𝑘1 𝑘0 𝑄 = [ ]=1−𝛽, 𝑑 erfc 𝜎 (80) ∗ The best critical domain (critical value) {𝑊 } is 𝑉 − 𝑉 𝑉 − 𝑉 𝑘𝑐 𝑘0 𝑘1 𝑘0 𝑄𝑑 = erfc [ − ]=1−𝛽. 𝑊∗ :𝑉 >𝑉 . 𝜎 𝜎 𝑘 𝑘𝑐 (72) 8 Advances in High Energy Physics

From (80) we can determine the signal/noise ratio as 𝑛 󵄨 𝑛 𝑆 def 𝑉𝑘 − 𝑉𝑘 󵄨 1 1 0 󵄨 ( ) = 󵄨 𝑍 𝜎 󵄨 (81) 󵄨𝑉 >𝑉 𝑛2 𝑘1 𝑘0 or written in a different form: 𝑊∗ (𝑉1)1 (𝑉1)2 𝑆 𝑉𝑘 −𝑉𝑘 c 0 = +𝑢 . (82) ∗ 𝑍 𝜎 1−𝛽 Figure 3: Determination of the best critical region (𝑊 ). 𝑉 =0 If 𝑘0 then we have 𝑆 Therefore, for empirical average, the following expressions are =𝑢1−𝛼 +𝑢1−𝛽 =𝑢1−𝑄 +𝑢𝑄 . (83) 𝑍 0 𝑑 obtained: ̂ Let the empiric average of 𝑛 measurements be 𝐻1 𝑉𝑐 𝑃𝑟 { }=𝑄0 =𝑃𝑟 {𝑉𝑛 > } 𝑛 ̂ ̂ 1 𝐻0 𝐻0 𝑉 = ∑𝑉 . 𝑛 𝑛 𝑘 (84) 𝑘=1 =𝛼-significance threshold of statistical test, The statistical hypothesis has the structure as follows: 𝐻̂ 𝑉 𝑃 { 1 }=𝑄 =𝑃 {𝑉 > 𝑐 } ̂ 󵄨 𝑟 ̂ 𝑑 𝑟 𝑛 ̂ 𝐻0 : 𝑉𝑘 = 𝑉0 󵄨 𝐻1 𝐻1 0 󵄨 , 𝐻̂ : 𝑉 = 𝑉 󵄨 (85) 1 𝑘1 1 󵄨 𝜆 ≈𝜎2(𝑘=1,2,3...𝑛) 𝑘 =1−𝛽-power function of test, {𝑉 } where 𝑘 represents the variable of distribution function. 𝐻̂ 𝑉 Now the distribution functions are written as 𝑃 { 0 }=𝑃 {𝑉 > 𝑐 }=1−𝛼, 𝑟 𝐻̂ 𝑟 𝑛 𝐻̂ 𝑉, 𝜎 0 0 𝑃 =𝑃 ( ), 0 0 𝑛, 𝑉 𝐻̂ 𝑉 0 𝑃 { 0 }=𝑃 {𝑉 > 𝑐 }=𝛽. (86) 𝑟 𝐻̂ 𝑟 𝑛 𝐻̂ 𝑉, 𝜎 1 1 𝑃1 =𝑃1 ( ), (92) 𝑛, 𝑉1 2 where 𝑉0, 𝑉1,and𝜎/𝑛 are the parameters for distribution 4.1. Application for a Particular Case with 𝑉0 =0and 𝜎 =0̸ . functions. We consider as known the following expressions: Therefore, we can conclude that the probability equation 𝑉 =0, 𝜎2 =0,̸ is 0 (93) 𝐻̂ +∞ 𝜎 and the parameters 𝛼 and 𝛽 need to be determined. 𝑃 { 1 } =𝑄 = ∫ 𝑃 [𝑉, 𝑉 , ] [𝑑𝑉] =𝛼 𝑟 ̂ 0 0 0 √𝑛 (87) The signal/noise ratio will be calculated as 𝐻0 𝑉𝑐 𝑆 and then =𝑢1−𝛼 +𝑢1−𝛽 (94) 𝜎 𝑍 𝑉 = 𝑉 + 𝑢 , 𝑐 0 √𝑛 1−𝛼 The detection probabilities are (88) ∗ ∗ 𝑄 =𝛼, 𝑊 :𝑉≥𝑉𝑐;𝑉∈𝑊. 0 (95) Also 𝑄𝑑 =1−𝛽. 𝐻̂ +∞ 𝜎 ∗ 1 And then we look for the best characteristic region (𝑊 ): 𝑃𝑟 { }=𝑄𝑑 = ∫ 𝑃1 [𝑉, 𝑉1, ] [𝑑𝑉] =1−𝛽 ̂ 𝑉 √𝑛 𝐻1 𝑐 𝜎 𝑊∗ : 𝑉 > 𝑉 𝑉 > 𝑢 , (89) 𝑛 𝑐 or 𝑛 √𝑛 1−𝛼 (96) and the result is 𝜎 where 𝑉 =𝑉 + 𝑢 . 2 1 0 1−𝛽 (90) 𝑉 =0̸ √𝑛 󵄨 1 (𝑢 +𝑢 ) 𝑛󵄨 =𝜎2 ⋅ 1−𝛼 1−𝛽 . (97) 󵄨 2 󵄨𝑉 =0̸ 𝜈 From (88)and(89)itresultsthat 0 1 𝜎 𝑉1 = 𝑉0 + (𝑢1−𝛼 +𝑢1−𝛽), The graph in Figure 3 indicates that, in case of low √𝑛 amplitude signals detection, more measurements (n-bigger 2 1 (91) values)arenecessaryincomparisonwithhighamplitude 𝑛=𝜎2(𝑢 +𝑢 ) . (𝑛) 1−𝛼 1−𝛽 2 signaldetection,wherethenumberofmeasurements (𝑉1 − 𝑉0) must be low. Advances in High Energy Physics 9

4.2. Algorithm Regarding the Bilateral Test for Validation of andthenitwillresultthat Statistical Hypothesis (Validation of Mean Value for a Given 𝑛 2 2 𝑐=− (𝑉 − 𝑉 ) . Value of Dispersion 𝜎 ). Let us put the matrix in a diagonal ln 2𝜎2 𝑐 0 (108) form so the repartition functions will have the expression: The final result will be 𝑛 2 1 −(𝑉 −𝑉 ) /2𝜆 𝜎 𝑃 = ∏ ⋅𝑒 𝑘 𝑘0 𝑘 , 𝑉 − 𝑉 =±𝑘 ;𝑘=√−2 𝑐. 0 𝑐 0 √𝑛 ln (109) 𝑘=1 √2𝜋 ⋅ 𝜆𝑘 (98) 𝑛 2 The test significance threshold equation will be 1 −(𝑉 −𝑉 ) /2𝜆 𝑃 = ∏ ⋅𝑒 𝑘 𝑘1 𝑘 . 1 √ +∞ 𝛼 𝑘=1 2𝜋 ⋅ 𝜆𝑘 ∫ 𝑃 𝑑𝑉 = 𝜔 𝑘 2 (110) 𝑉𝑐 We make the following hypothesis: because there are two values for 𝑉𝑐 with two equally associ- 2 𝜆𝑘 =𝜎,∀𝑘∈𝑁, ated areas. From (109)wehave 𝑉𝑘 ≅ 𝑉0, (99) 𝜎 0 𝑉 = 𝑉 + 𝑢 𝑐 0 √𝑛 1−𝛼/2 (111) 𝑉 ≅ 𝑉 . 𝑘1 1 andthenresultsthebestcriticaldomain In this case, we have 󵄨 󵄨 󵄨𝑉 − 𝑉 󵄨 ∗ 󵄨 𝑛 0 󵄨 1 2 𝑛 2 (𝑊 ):󵄨 󵄨 >𝑢1−𝛼/2. (112) −(1/2𝜎 )∑𝑘=1 (𝑉𝑘−𝑉0) 󵄨 𝜎/√𝑛 󵄨 𝑃0 = ⋅𝑒 , 󵄨 󵄨 (2𝜋𝜎2)𝑛/2 (100) The statistical strategy structure will be characterized by 2 1 −(1/2𝜎2)∑𝑛 (𝑉 −𝑉 ) 𝑘=1 𝑘 1 󵄨 󵄨 𝑃1 = ⋅𝑒 def 󵄨𝑉 − 𝑉 󵄨 󵄨 2 𝑛/2 ̂ ̂ 󵄨 𝑛 0 󵄨 󵄨 ̂ (2𝜋𝜎 ) 𝑃𝑟 {𝐻1 | 𝐻0} =𝑃𝑟 {󵄨 󵄨 >𝑢1−𝛼/2 󵄨𝐻0 } 󵄨 𝜎/√𝑛 󵄨 or, in general, we define a verisimilitude function for corre- =𝛼=𝑄, spondence: 0 󵄨 𝑃 {𝐻̂ | 𝐻̂ } def=𝑃{𝑉 > 𝑉 󵄨𝐻̂ } 𝑉0, 𝑉1 󳨀→ 𝜇 (101) 𝑟 0 1 𝑟 𝑛 𝑐 󵄨 1 󵄨 󵄨 󵄨𝑉 − 𝑉 󵄨 󵄨 or in the following form: 󵄨 𝑛 0 󵄨 󵄨 ̂ =𝑃𝑟 {󵄨 󵄨 >𝑢1−𝛼/2 󵄨𝐻1 } 𝑛/2 󵄨 𝜎/√𝑛 󵄨 2 1 −(1/2𝜎2)∑𝑛 (𝑉 −𝜇)2 𝑃(𝑉,𝜇,𝜎 )=( ) ⋅𝑒 𝑘=1 𝑘 . (102) 𝑘 2𝜋𝜎2 𝑉1 − 𝑉0 =Φ[𝑢𝛼/2 − ] For 𝜇, the maximum verisimilitude estimation will be 𝜎/√𝑛

𝑛 def 1 𝑉1 − 𝑉0 𝜇̂ = 𝑉 = ∑𝑉 . +Φ[𝑢𝛼/2 + ]=1−𝛽=𝑄𝑑. 𝑛 𝑛 𝑘 (103) 𝜎/√𝑛 𝑘=1 (113) In the following we calculate the verisimilitude functions: The following approximation is considered: 𝑛/2 2 def 1 −(1/2𝜎2)∑𝑛 (𝑉 −𝑉 ) 󵄨 󵄨 𝑃 =( ) ⋅𝑒 𝑘=1 𝑘 𝑛 , 󵄨𝑉 − 𝑉 󵄨 Ω 2 󵄨 1 0 󵄨 2𝜋𝜎 󵄨 󵄨 ≥ 0.5 (114) (104) 󵄨 𝜎/√𝑛 󵄨 𝑛/2 2 def 1 −(1/2𝜎2)∑𝑛 (𝑉 −𝑉 ) . 𝑃 =( ) ⋅𝑒 𝑘=1 𝑘 0 and the result is 𝜔 2𝜋𝜎2 𝑉 − 𝑉 1−𝛽≅Φ[𝑢 + 1 0 ] Also, the verisimilitude ratio is calculated as follows: 𝛼/2 𝜎/√𝑛 (115) 2 def 𝑃𝜔 −(𝑛/2𝜎2)(𝑉 −𝑉 ) 𝑙 = =𝑒 𝑛 0 . (105) and also 𝑃Ω 𝑆 def 𝑉 − 𝑉 { } = 1 0 ≈𝑢 +𝑢 (116) The critical region is given by 𝑍 𝜎/√𝑛 1−𝛽 1−𝛼/2 0<𝑙<𝑐 (106) and finally 2 andthelimitofcriticalregionwillbe 𝜎 2 𝑛≈ ⋅(𝑢 +𝑢 ) . 2 1−𝛽 1−𝛼/2 (117) 𝑙=𝑐 (107) (𝑉1 − 𝑉0) 10 Advances in High Energy Physics

4.3.AlgorithmRegardingBilateralTestforValidationofSta- The verisimilitude ratio will be in the following form: tistical Hypothesis (Validation of Mean Value for an Unknown 2 def 𝑃 1 Value of Dispersion 𝜎 ). Let us consider the following equa- 𝑙 = 𝜔 = . 𝑃 2 2 𝑛/2 tion: Ω 𝑛 𝑛 [∑𝑘=1 (𝑉𝑘 − 𝑉0) /∑𝑘=1 (𝑉𝑘 − 𝑉𝑛) ] 󳨀→ 1 𝑛 (127) 𝑉 = ∑𝑉 . 𝑛 𝑛 𝑘 (118) 𝑘=1 If we define

We define null hypothesis: def 𝑉 − 𝑉 𝑡 = 𝑛 0 , 𝐻̂ :𝑉󳨀→𝑉 √ 𝑛 2 0 0 (119) ∑𝑘=1 (𝑉𝑘 − 𝑉𝑛) /𝑛 (𝑛−1) (128) and alternative hypothesis: 2 ∑𝑛 (𝑉 − 𝑉 ) 2 def 𝑘=1 𝑘 𝑛 ̂ 𝑠 = , 𝐻1 :𝑉󳨀→𝑉1; 𝑉1 ≠ 𝑉0. (120) 𝑛−1

The general form of the verisimilitude function is then we can write

𝑛/2 𝑉𝑛 − 𝑉0 1 −(1/2𝜎2)∑𝑛 (𝑉 −𝜇)2 𝑡= , 𝑃 (𝜇,) 𝜎 = ( ) ⋅𝑒 𝑘=1 𝑘 . (121) (129) 2𝜋𝜎2 𝑠/√𝑛 𝑠 From the equations system: where is the dispersion experimentally determined according to these values. Thus, the verisimilitude ratio gets to the 𝜕 𝑃(𝜇,𝜎) following form: ln =0, 𝜕𝜇 1 𝑛/2 (122) 𝑙=( ) (130) 𝜕 𝑃(𝜇,𝜎) 1+(𝑡2/ (𝑛−1)) ln =0 𝜕𝜎2 and the following limit is verified: the result is −𝑡2/2 𝑛 lim 𝑙=𝑒 . 1 𝑛→∞ (131) 𝜇= ∑𝑉 = 𝑉 , 𝑛 𝑘 𝑛 𝑘=1 The best critical region is given by the following inequality: (123) 𝑛 𝑛 1 1 2 0<𝑙<𝑐. 𝜎2 = ∑(𝑉 −𝜇)2 = ∑(𝑉 − 𝑉 ) . (132) 𝑛 𝑘 𝑛 𝑘 𝑛 𝑘=1 𝑘=1 Therefore it results that 󵄨 󵄨 So (121)becomes 󵄨𝑉 − 𝑉 󵄨 󵄨 𝑛 0 󵄨 󵄨 󵄨 >𝑡𝑐. (133) 𝑛/2 󵄨 𝑠/√𝑛 󵄨 𝑛 𝑃 =[ ] ⋅𝑒−𝑛/2. (124) Ω 𝑛 2 From verisimilitude threshold expression: 2𝜋 ⋅ ∑𝑘=1 (𝑉𝑘 −𝑉𝑛) +∞ 𝛼 𝑉 − 𝑉 𝛼 𝜎2 𝑐 0 Therefore, maximum likelihood estimation for in case of ∫ 𝑃𝜔 ⋅𝑑𝑉𝑘 = ,Φ( ) =1− , (134) 𝑉 2 𝑠/√𝑛 2 null hypothesis (i.e., 𝜇=𝜇0)willbeobtainedfrom(122)and 𝑐 2 (123). The estimated value of dispersion 𝜎̂ will be (in the limit 𝜇=𝑉 it results that case 0) 𝑠 𝑉 = 𝑉 + 𝑢 . 󵄨 1 𝑛 𝑐 𝑠 √𝑛 1−𝛼/2 (135) 2 def 2󵄨 2 𝜎̂ = 𝜎 󵄨 = ∑(𝑉𝑘 −𝜇0) . (125) 󵄨𝜇0=𝑉0 𝑛 𝑘=1 The best critical domains will be determined by the following inequality: Then, by definition it results that 󵄨 󵄨 󵄨𝑉𝑛 − 𝑉0 󵄨 󵄨𝜇0=𝑉0 󵄨 󵄨 >𝑢 (136) 󵄨 󵄨 𝑠/√𝑛 󵄨 1−𝛼/2 𝑃Ω =𝑃󵄨 󵄨 󵄨 󵄨 2 𝑛 2 󵄨𝜎2 → 𝜎̂ =(1/𝑛)𝑘=1 ∑ (𝑉𝑘−𝜇0) so the signal/noise ratio will have the following expression: 𝑛/2 (126) 𝑛 −𝑛/2 = [ ] ⋅𝑒 . 𝑆 def 𝑉1 − 𝑉0 𝑛 2 ( ) =( ). (137) [2𝜋 ⋅ ∑𝑘=1 (𝑉𝑘 − 𝑉0) ] 𝑍 𝑠/√𝑛 Advances in High Energy Physics 11

Consequently, it results that [5] S. Dontu, V.Babin, D. Savastru et al., “Spatial optical solitons in fotonic crystals (1D) with cubic nonlinearity,”in Advanced Laser 󵄨 󵄨 Technologies,vol.66060ofProcceedings of SPIE, p. E6060, 2007. def 󵄨𝑉𝑛 −𝑉0 󵄨 󵄨 𝑃 {𝐻̂ | 𝐻̂ } =𝑃{󵄨 󵄨>𝑢 󵄨𝐻̂ }=𝛼, 𝑟 1 0 𝑟 󵄨 𝑠/√𝑛 󵄨 1−𝛼/2 󵄨 0 [6] A. Wald, Statistical Decision Functions, Chelsea Publishing, 󵄨 󵄨 New York, NY, USA, 2nd edition, 1971.

def 𝑉 − 𝑉 [7]H.L.vanTrees,Detection, Estimation and Modulation Theory, 𝑃 {𝐻̂ | 𝐻̂ } =Φ(𝑢 − 1 0 ) vol. 3, John Wiley & Sons, New York, NY, USA, 2001. 𝑟 1 1 𝛼/2 𝑠/√𝑛 (138) [8]A.J.F.Siegert,“Asystematicapproachtoaclassofproblems 𝑉 − 𝑉 in the theory of noise and other random phenomena,” IRE 1 0 Transactions on Information Theory,vol.3,pp.38–43,1957. +Φ(𝑢𝛼/2 − )=1−𝛽. 𝑠/√𝑛 [9] H. Cramer,´ Mathematical Methods of Statistics, Princeton Uni- versity Press, Princeton, NJ, USA, 1999. 5. Conclusions [10] E. L. Lehmann, Testing Statistical Hypotheses, Springer, New York, NY, USA, 2nd edition, 1997. Our knowledge is achieved by observation and by measure- [11] C. W.Helstrom, Statistical Theory of Signal Detection,Pergamon ments of systems, operations which are affected by errors. The Press, Oxford, UK, 2nd edition, 1968. aim of this paper has been to identify these natural limits [12] P. Rudnick, “A signal-to-noise property of binary decisions,” by the developing of observation and assessment algorithms Nature,vol.193,no.4815,pp.604–605,1962. basedonstatisticalstrategyofcontrolandchecking. [13] B. Mitrica, “Asymmetry of charge ratio for low energetic muons,” AIP Conference Proceedings,vol.972,no.1,pp.500– It is very important to mention that statistical validation 504, 2008. of some communication systems based on control statistical [14] B. Mitrica, I. M. Brancus, H. Rebel et al., “Experimentally strategies points out that the signal/noise ratio is not the guided Monte Carlo calculations of the atmospheric muon and essential parameter in characterising such a system but the neutrino flux,” Nuclear Physics B—Proceedings Supplements,vol. structure of the statistical strategy. In the simplest and most 151, pp. 295–298, 2006. 𝑄 relevant form it contains the false alarm probability 0 [15] B. Mitrica, Studiul dependentei directionale a fluxului de miuoni and detection probability 𝑄𝑑. Therefore a system with high si posibiltati de testare ale modelelor de interactie hadronica signal/noise ratio will not solve the validation (good working [Ph.D. thesis], University of Bucharest, 2010. ofthissystem)fromthepointofviewofmultistochastic [16] G. G. Raffelt, “Neutrinos and the stars,” in Proceedings of the processes that generate noise. International School on AstroParticle Physics/Neutrino Physics Using the algorithms described in the paper an algorithm and Astrophysics, Lake Como, Italy, July-August 2011. based on the bilateral test for description of the unknown [17] W. Winter, “Neutrinos from cosmic accelerators including dispersion can be further developed. magnetic field and flavor effects,” Advances in High Energy A generalized statistical strategy for observations and Physics, vol. 2012, Article ID 586413, 41 pages, 2012. measurements on the nuclear particles is based on these [18] C. Broggini, C. Giunti, and A. Studenikin, “Electromagnetic results, taking into account the particular type of statistics properties of neutrinos,” Advances in High Energy Physics,vol. resulting from the measuring process also. 2012,ArticleID459526,47pages,2012. [19] A. G. Beda, V. B. Brudanin, V. G. Egorov et al., “The results of search for the neutrino magnetic moment in GEMMA Acknowledgments experiment,” Advances in High Energy Physics,vol.2012,Article ID350150,12pages,2012. This work was supported by a grant of the Romanian National [20] B. Mitrica, M. Petcu, A. Saftoiu et al., “Investigation of cosmic Authority for Scientific Research, CNDI-UEFISCDI, Project ray muons with the WILLI detector compared with the predic- no. PN-II-PT-PCCA-2011-3.2-1007 (Contract no. 184/2012) tions of theoretical models and with semi-analytical formulae,” and dedicated in memory of our former colleague Vasile Nuclear Physics B—Proceedings Supplements,vol.196,pp.462– Babin Ph.D. 465, 2009. [21] B. Mitrica, “20 years of cosmic muons research performed in IFIN-HH,” AIP Conference Proceedings,vol.1498,pp.291–303, References 2012. [22] V. E. Hubeny and M. Rangamani, “A holographic view on [1] C. W. Helstrom, “Quantum detection and estimation theory,” physics out of equilibrium,” Advances in High Energy Physics, Journal of Statistical Physics,vol.1,no.2,pp.231–252,1969. vol. 2010, Article ID 297916, 84 pages, 2010. [2]V.I.Vlad,V.Babin,andA.Mocofanescu,“Analyticaltreatment [23] J. 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Research Article Realistic Approach of the Relations of Uncertainty of Heisenberg

Paul E. Sterian

Academic Center for Optical Engineering and Photonics, Faculty of Applied Sciences, University POLITEHNICA of Bucharest, 060042 Bucharest, Romania

Correspondence should be addressed to Paul E. Sterian; [email protected]

Received 10 October 2012; Accepted 24 December 2012

Academic Editor: Bogdan Mitrica

Copyright © 2013 Paul E. Sterian. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Due to the requirements of the principle of causality in the theory of relativity, one cannot make a device for the simultaneous measuring of the canonical conjugate variables in the conjugate Fourier spaces. Instead of admitting that a particle’s position and its conjugate momentum cannot be accurately measured at the same time, we consider the only probabilities which can be determined when working at subatomic level to be valid. On the other hand, based on Schwinger’s action principle and using the quadridimensional form of the unitary transformation generator function of the quantum operators in the paper, the general form of the evolution equation for these operators is established. In the nonrelativistic case one obtains the Heisenberg’s type evolution equations which can be particularized to derive Heisenberg’s uncertainty relations. The analysis of the uncertainty relations as implicit evolution equations allows us to put into evidence the intrinsic nature of the correlation expressed by these equations in straight relations with the measuring process. The independence of the quantisation postulate from the causal evolution postulate of quantum mechanics is also put into discussion.

1. Introduction This principle known as the Heisenberg uncertainty principle can be expressed as follows: A quantum mechanical principle according to Werner Heisenberg as it is shown in his scientific paper [1]whichwas publishedin1927,states,initsmostcommonform,thatitis 1 Δ𝑥Δ𝑝𝑥 ≥ ℎ, (1) not possible to simultaneously determine the position and 2 momentum of a particle: “The more precisely the position is determined, the less precisely the momentum is known where Δ𝑥 is the uncertainty in position, Δ𝑝𝑥 is the uncer- in this instant, and vice versa.” This concept is fundamen- tainty in momentum, and ℎ is the reduced Planck’s constant. tal to understanding quantum mechanics, the science of Heisenberg’s original paper does not attempt to rigorously quantum systems like atoms, electrons, photons, neutrinos, determine the exact quantity on the right side of the inequal- and generally, particles in subatomic physics. It says that ity, but rather uses physical argument to show that the uncer- not all properties of a quantum particle can be measured tainty between conjugate quantum mechanical variables is with unlimited accuracy [2–29]. Until now, this has often ℎ been justified by the explanation that every measurement has approximately [1]. necessarily to disturb the quantum particle thus distorting After Heisenberg, two other scientists, H. P. Robertson the results of any further measurements. This principle has and E. Schrodinger,¨ developed his uncertainty principle. proved to be true concerning the particles, so that even They expanded it in 1930, by adding other pairs of variables modern computers and nuclear power plants have been that cannot be simultaneously known, such as: energy and realized taking into account the uncertainty principle and position, angular position and angular momentum. The other concepts specific to the field of quantum mechanics, uncertainty principle continues to be refined and brought up which became the way we are thinking and working [30–55]. to date. 2 Advances in High Energy Physics

Generally, Heisenberg’s uncertainty principle, states that spaces canonical variables involved in other expressions incompatible dynamic variables in relation to the measuring (2) representing uncertainty relations. For classical dynamic process, satisfy the relations: systems case for the canonical conjugate variables, one can define classical Poisson brackets, while within the context of Δ𝑥 ⋅ Δ𝑝𝑥 ≥ℎ, Δ𝐸⋅Δ𝑡≥ℎ, quantum systems, we get the quantum Poisson brackets. (2) The incompatible quantum observables are correlated Δ𝜑 ⋅ Δ𝐽𝑧 ≥ℎ, Δ𝜙⋅Δ𝑛≥ℎand so on, with Heisenberg’s uncertainty principle, but as we have thus leading to the following statement: shown [4] the proposed new interpretation of this principle in the context of the relativistic causality. Accordingly, we The product of the inaccuracies arising from cannot consider simultaneous measurements of the canonical simultaneous determination of two canonical con- conjugate variables, because these variables correspond to jugatevariablesisoftheorderofmagnitudeof the reciprocal Fourier spaces. The standard experiments, for Planck’s constant. example, the diffraction of the electron by a slit, are not suitable, for the simultaneous measurements of the quantum Theaboverelationscanbewritten,asitisknowninthe particle position and impulse as it is usually accepted because, form of commutation relationships, between corresponding through the measuring apparatus (which realise the Fourier incompatible observables according to the theorem: being transform of the system state function), the information is given two hermitic operators A and B and their commutator propagated at a finite speed. The uncertainty relations can C, one can demonstrate the relationship be understood as statistical correlations between the results 1 of the measurements effected on the dynamic conjugate Δ𝐴 Δ𝐵 ≥ |⟨𝐶⟩| , 2 (3) variables in the reciprocal Fourier spaces. From another point of view, the analytical expressions of where quantum observables can be obtained by replacing the classical canonically conjugate variables within a symmetrised 2 Δ𝐴 = √⟨𝐴2⟩−⟨𝐴⟩ , (4) expression of the classical variable 𝐴, by their corresponding quantum-mechanical operators. In this way the measur- Δ𝐵 = √⟨𝐵2⟩−⟨𝐵⟩2. (5) ing particularities of the fundamental observables 𝑟 and 𝑝 are transferred to more complex observables which can No actual physical measurements can avoid the limitations be reported to the measuring processus, compatible or given by these relationships. incompatible. For the measurement of any group of two or The conclusions drawn from the study of the universality more compatible or incompatible observables, the “laws” of of particle-wave dualism in the context of relativistic causal- the measuring apparatus previously presented in [3, 4]are ity, and other observations resulting from mathematical for- general. In the paper, the author considers the uncertainty malismsofquantumtheoryledtheauthorstoanewapproach relations as implicit evolution equations so the intrinsic of Heisenberg’s uncertainty relationships as they put into nature of the correlations expressed by the uncertainty prin- question the possibility of simultaneous determination in the ciple is shown more precisely. The quantification postulate measurement process of the uncertainties involved by these and the causal evolution postulate are not independent of relationships, showing the incompatibility of “simultaneity” each other, contrary to the different systems of axioms of the with relativistic causality requirements and proposing a quantum mechanics. The principled role of the incompatible reformulation of the principle of uncertainty. observables in the evolution of the quantum systems is more From the classical theory of wave propagation, it is realistically put into evidence by the above interpretation of Δ𝑥 known that the width of a wave packet involves against the uncertainty relations of Heisenberg’s. reciprocal Fourier transform spaces of a pair of signals, an “indeterminacy” relationships of type 2. Fourier Transformers in Δ𝑥 Δ𝑘 ≥ 2𝜋, (6) the Measuring Process Δ𝑘 where representing scattering of wave vectors. Switching, within the measuring process, from the direct Δ𝑡 Similarly, in the case of finite duration disturbances , variable space to the canonical conjugate variable space which one can highlight relationships such as we will be denoted by Fourier space requires a physical data Δ𝑡Δ𝜔 ≥ 2𝜋 processing system. We will illustrate that by the help of a two- (7) dimensional optical Fourier transform. 𝑔(𝑥, 𝑦) 𝑥 against reciprocal Fourier transform spaces of a pair of Let be a function of two independent variables 𝑦 signals, where Δ𝜔 indicating the disturbance spectral content. and ,whichcanbethecoordinatesofapointinaplane.If In quantum theory, relations (5)and(6)canbewritten the following conditions are met: as the first two uncertainty relations (2) for both photons and substantial particles. Fourier transformed reciprocal (i) 𝑔(𝑥, 𝑦) is completely integrated into the infinite plane relationships can be identified, also for signals defined on (𝑥, 𝑦); Advances in High Energy Physics 3

(ii) 𝑔(𝑥, 𝑦) has a finite number of discontinuities and a From the experiments of this type we can conclude that finite number of maxima and minima in any finite there can be no question of simultaneous measurement of rectangle; incompatible observables due to the finite speed of propaga- (iii) 𝑔(𝑥, 𝑦) has no infinite discontinuities, tion of interactions. Let us assume the following hypotheses derived from the then we get the following relations: study presented in the previous paragraphs:

𝐺(𝑓 ,𝑓 ) = 𝐹{𝑔 (𝑥, 𝑦)} (i) canonical conjugate variables, that is, incompatible 𝑥 𝑦 variables belong to reciprocal Fourier spaces; +∞ (ii) Fourier transforms assume the existence of physical = ∬ 𝑔 (𝑥,) 𝑦 exp [−𝑖 (𝜔𝑥𝑥+𝜔𝑦𝑦)] d𝑥 d𝑦, −∞ systems as information processing; (8) (iii) the deduction of uncertainty relations experimentally by using physical systems that perform Fourier trans- respectively, forms to reveal two canonical conjugate spaces and which can thus perform measurements on quantities 𝑔 (𝑥, 𝑦) = 𝐹{𝐺 (𝑓 ,𝑓 )} 𝑥 𝑦 which are incompatible. +∞ Necessary Conclusions. Due to finite speed of propagation = ∬ 𝐺(𝑓𝑥,𝑓𝑦) exp [𝑖 𝑥(𝜔 𝑥+𝜔𝑦𝑦)] d𝑓𝑥 d𝑓𝑦, −∞ of interactions, signal switching within physical system to (9) perform Fourier transform has a finite duration. Therefore, the sizes of the input and output of the system defining the direct and inverse Fourier transforms of the that makes Fourier transforms and conjugates canonical function 𝑔(𝑥,.Thequantities 𝑦) 𝑓𝑥 =𝜔𝑥/2𝜋 and 𝑓𝑦 =𝜔𝑦/2𝜋 variables or its incompatible observables are considered to are spatial frequencies and 𝐺(𝑓𝑥,𝑓𝑦) is the signal spectral perform simultaneous measurements, in the ordinary sense function. of the formulation of Heisenberg’s uncertainty relations. If the functions do not satisfy the conditions of Fourier Reflecting the uncertainty relations, the wave-particle transform, then we get the generalized Fourier transform. dualismstillremainstrue,butitscontentisnotchanging Itisknownthatanopticalsystemsuitableforatwo- the principle of uncertainty with respect to a simultaneous dimensional Fourier transform may be a lens. If the focal measurement. plane 𝑃1 lies above the signal function 𝑔(𝑥,,attheback 𝑦) The cause and the effect cannot be measured simulta- focal plane 𝑃2 of the lens, a Fourier spectrum 𝐺(𝑓𝑥,𝑓𝑦) of the neously as a consequence of the used measurement device signal 𝑔(𝑥, 𝑦) is displayed. In this plane, spatial frequencies (Fourier transformer), through which the signals pass at a aregivenbythefollowingrelations: finite speed. Far from contradicting the principle of causality, uncertainty relations come to confirm it, because if we admit 2𝜋𝑥 2𝜋𝑦 2 2 Einstein relativity principles when analyzing the measure- 𝜔𝑥 =− ,𝜔𝑦 =− , (10) 𝜆𝐹 𝜆𝐹 ment process, one must take into account the finite speed of 𝐹 𝜆 propagation of interactions. where is the focal length of the lens and the wavelength Let us consider, for example, a moving quantum particle, of the radiation used. Optical Fourier transform property of such as electron or photon through a slot machine that a lens can be analyzed using the Huygens-Fresnel diffraction is performing the Fourier transform, due to diffraction formula [10]. phenomena. Signal function at slot plane is the wave function of the particle. Its Fourier transform is pulse wave function in 3. Experimental Setting of Heisenberg space which may be considered a simultaneous determina- Uncertainty Relations tion of the electron coordinate passing through the slot. According to the interpretation presented in this paper, Heisenberg’s uncertainty relations are usually established it results in the impossibility of localizing inside the volume on the basis of the experimental observations. It is well element of the phase space, of a quantum particle at a given known in this regard that Heisenberg imagined an experience time moment, because the measurements of position and of “simultaneous” measuring of the electron position and momentum of a quantum particle cannot be simultaneously momentum by using “ray microscope.” Other examples of made. experimental facts from which analysis suggest that the existence of uncertainty relations is as follows: 4. Uncertainty Relations as Quantum (i) experience concerning diffraction of electrons Evolution Equations through a slit; The canonically conjugate variables being correlated by (ii) experience concerning the deviation of a particle in a uncertainty relations one must pay more attention to the magnetic field; problem of the nature of these correlations. (iii) compton collision processes of particles with a pho- Let 𝑆 be the action-integral operator and 𝜂𝑖,𝜉𝑖,the ton, and so forth. canonically conjugate variables in the quadridimensional 4 Advances in High Energy Physics

Minkovsky space. One considers 𝜂𝑖 =𝑥1,𝑥2,𝑥3,𝑥4 = From the classical point of view, the above equations take the 𝑖𝑐𝑡;𝑖 𝜉 = P𝑖 =𝑚0U𝑖,whereP𝑖 is the 𝑖 component of the 4- following form: impulse [P = P(𝑝𝑟⃗ ,(𝑖/𝑐)E)], U𝑖—the 𝑖 component of the 𝑖 E 𝑝⃗ (𝑥𝑖) 4-velocity, —the relativistic energy, and 𝑟—the relativistic 𝛿𝑄 = [𝑝𝑖,𝑄]𝛿𝑥𝑖, 𝑖=1,2,3, (22) impulse of the system. ℎ According to Schwinger’s action principle, the change of 𝑖 𝛿𝑄(𝑡) = [−𝐻,] 𝑄 𝛿𝑡. the action operator is given by the following expressions: ℎ (23) 𝛿𝑆 =𝐹 −𝐹, 12 2 1 (11) The time-evolution is described as 4 𝛿𝑄 =−𝑄𝛿𝑡̇ (24) 𝐹=𝛿𝑆=∑𝜉𝑖𝜂𝑖. (12) 𝑖=1 and (23)becomes 𝐹 being the generator function of the unitary transformation 𝑖 𝛿𝜂 𝑄̇ = [𝐻,] 𝑄 , which describes the system evolution and the variations 𝑖 ℎ (25) refering to the complete evolution of the system. The operators 𝑄 are changed by unitary infinitesimal which are identical with Heisenberg’s temporal evolution transformations of the form: equation of the operators. Besides, (22) can be understood 󸀠 similarly as “space-evolution” equations of the operators. 𝑈=1+𝑖𝛼𝐹 =1+𝑖𝐹 (13) Let us to consider the particular cases Q =𝑥𝑖;𝑡.The according to the following: result is that (22)and(23) are reduced to the Heisenberg’s uncertainty relations: 𝑄󳨀→𝑄+𝛿𝑄=𝑄+𝑖[𝐹,𝑄] , (14) 𝑖 [𝑝 ,𝑥 ]= 𝛿 , (26) that is, 𝑖 𝑗 ℎ 𝑖𝑗 𝛿𝑄 =𝑖 [𝐹,𝑄] , (15) respectively,

󸀠 𝑖 where 𝛼 is a real parameter and 𝐹 an hermitic operator. [𝐻,] 𝑡 = . ℎ (27) From expression (12), putting 𝛿𝜂𝑖 →𝛿𝜂𝑖/ℎ, ℎ being Planck constant, it results in Equations (26)and(27) can be considered as evolution 𝑖 𝑖 equation with implicit dependence for the fundamental oper- 𝛿𝑄 = [∑ 𝜉 𝛿𝜂 ,𝑄]= [∑ 𝜉 ,𝑄]𝛿𝜂, ℎ 𝑖 𝑖 ℎ 𝑖 𝑖 (16) ators, the evolution of every variable being reported to the coordinate axe which corresponds to this very one. The which represents the general form of the quantum evolution hidden character of the evolution expressed by (26)and(27), equations.Thecompletevariation𝛿𝑄 of the 𝑄 operator can directly put into evidence the intrinsic correlations between be writen under the following form: canonically conjugate variables, with straight implications in (𝜂 ) the measuring process. The intrinsic correlations between 𝛿𝑄 = ∑𝛿𝑄 𝑖 , (17) canonically conjugate variables are understood by the appear- 𝑖 anceofthewavefunctionstothereciprocalFourierspaces so that from (16)and(17), one obtains the evolution equations [3]. These correlations imply the evolution since 𝑝=𝑝(𝑡) and 𝑟=𝑟(𝑡) 𝑝(𝑡) =0̸ 𝑟(𝑡) ≠ 𝑟 depending on the 𝜂𝑖 variables: but so that 0. Therefore, the variables 𝑝𝑖 and 𝑥𝑖 cannot by principle be measured simultaneously. 𝑖 (𝜂𝑖) The time interval of the Fourier transformation process- 𝛿𝑄 = [𝜉𝑖,𝑄] 𝛿𝜂𝑖 (18) ℎ ing by the measuring apparatus to put into evidence the correlated 𝑥-space and 𝑝-space of the quantum system vari- which are of the Heisenberg operator evolution equations ables cannot be avoided. There are these intrinsic correlations type. which determine the imprecisions expressed by uncertainty Accordingly, for different 𝜂𝑖 we obtain the following: relations and the impossibility to localize the quantum system 𝑖 (𝑥𝑖) inside of the elementary cell of the phase space expressed by 𝛿𝑄 = [𝑝𝑟 ,𝑄]𝛿𝑥𝑖,𝑖=1,2,3, (19) Δ𝑝Δ𝑥 =ℎ ℎ 𝑥𝑖 the relation . respectively, 5. Discussions (𝑥 ) 𝑖 𝑖 𝛿𝑄 4 = [ 𝐻, 𝑄] 𝛿 (𝑖𝑐𝑡) , ℎ 𝑐 (20) (a) The temporal evolution equation (25) shows the dependence of 𝑄 on 𝑡 indirectly, via dependence of 𝑄 on 𝐻,whichis or the conjugate variable corresponding to 𝑡, so that the depen- 𝑖 dence of 𝑄 on 𝑡 is an implicit one, as it results from the intrin- 𝛿𝑄(𝑡) = [−𝐻,] 𝑄 𝛿𝑡. ℎ (21) sic correlation between 𝑡 and E.If𝜕𝑄/𝜕𝑡 = 0, 𝑑𝑄/𝑑𝑡 =0 Advances in High Energy Physics 5 only if the observables 𝐻 and 𝑄 are noncorrelated, that is, are statistically correlated, the uncertainties product [𝐻, 𝑄].Inthiscase, =0 𝑄=ct. is a time-conservative being of the order of magnitude of the constant of variable. Planck.” From (22) the result is the dependence of 𝑄 on 𝑥𝑖 (vi) The concordance between uncertainty relations inter- via 𝑝𝑖,whichisthevariablea𝑥𝑖-canonically conjugated. pretations based on that understanding of the mea- Consequently, if 𝜕𝑄/𝜕𝑥𝑖 =0and [𝑝𝑖,𝑄] = 0 (𝑝𝑖 and suring process and the implicit evolution equations 𝑄 are noncorrelated), then 𝑄=ct., which means that derived in this paper is relevant for the coherence of 𝑄 is space conservative. In conclusion, one can observe the theory developed above. the symmetry between temporal development of the system (using 𝐻 operator) and spatial development of the system (vii) The treatise of the uncertainly relations as implicit (using 𝑝 operator). evolution equations allowed us to put into evidence (b) The interpretation of uncertainty Heisenberg’s rela- the intrinsic nature of the correlation expressed by tions (26)and(27) as evolution equations with implicit these equations in straight relations with the measur- dependence connects in some content the quantisation ing process. postulate and the causal evolution postulate of quantum (viii) In the context of the above results, the quantisation mechanics, which appears in this context as being different postulate of quantum mechanics is not indepen- forms of the same evolution principle. dent from the causal evolution postulate, that is, (c) The results can be generalized for the analysis of these two postulates are connected in the axiomatic any group of two canonically conjugate dynamical variables, development of the quantum theory. 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Research Article Simulations of Muon Flux in Slanic Salt Mine

Mehmet Bektasoglu,1 Halil Arslan,1 and Denis Stanca2

1 Department of Physics, Sakarya University, Serdivan, 54187 Sakarya, Turkey 2 Department of Nuclear Physics, Horia Hulubei National Institute for Physics and Nuclear Engineering, P.O. Box MG-06, 077125 Magurele, Romania

Correspondence should be addressed to Mehmet Bektasoglu, [email protected]

Received 16 September 2012; Accepted 5 December 2012

Academic Editor: Bogdan Mitrica

Copyright q 2012 Mehmet Bektasoglu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Geant4 simulation package was used to simulate muon fluxes at different locations, the floor of UNIREA mine and two levels of CANTACUZINO mine, of Slanic Prahova site in Romania. This site is specially important since it is one of the seven sites in Europe that are under consideration of housing large detector components of Large Apparatus studying Grand Unification and Neutrino Astrophysics LAGUNA project. Simulations were performed for vertical muons and for muons ◦ with a zenith angle θ ≤ 60 . Primary muon flux and energies at ground level were obtained from previous measurements. Results of the simulations are in general agreement with previous simulations made using MUSIC simulation program and with the measurements made using a mobile detector.

1. Introduction

Collisions of the primary cosmic rays, mostly protons and alpha particles, with the Earth atmosphere produce secondary cosmic rays; some of which are able to reach the Earth’s surface. Muons interact weakly with the nuclei of the Earth’s atmosphere and experience the relativistic time dilation. As a result, they are the most numerous charged cosmic particles at sea level. Furthermore, they could also be detected underground or underwater thanks to their ability to penetrate the matter in which they propagate. Investigations of muons underground or underwater are important from different aspects. Measurements of muon intensities at various depths, for instance, provide information on the electromagnetic processes that reduce the flux 1. Moreover, there is a direct connection between intensities of underground muons and production of mesons in the stratosphere since temperature changes affect pions and kaons differently 2. A salt mine in Slanic-Prahova, Romania, is one of the underground sites that is eligible for muon measurements. This site is specifically important since it is among the seven 2 Advances in High Energy Physics sites around Europe that are being considered to house large detector components of LAGUNA Large Apparatus studying Grand Unification and Neutrino Astrophysics project 3, 4. The other six locations are Boulby the United Kingdom, Canfranc Spain, Frejus France, Pyhasalmi Finland, Polkowice-Sieroszowice Poland, and Umbria Italy. Three types of detectors, namely, GLACIER with liquid argon, LENA with liquid scintillator, and MEMPHYS with water are considered. Thanks to these large and massive detector elements, LAGUNA is expected to improve our understanding on several issues that are subject of intensive investigations. These issues could be summarized as the proton decay, predicted by Grand Unification Theories aiming at the unification of the fundamental forces of nature, matter-antimatter asymmetry in the universe, and the neutrino physics. Further information on the LAGUNA project could be found, for instance, in 3. Simulation of vertical muon flux underground with water equivalent depth of 600 mwe meter water equivalent, which corresponds to the depth of one of the mines in Slanic site, was previously made by MUSIC MUon SImulation Code5. MUSIC is a simulation tool for three-dimensional simulations of the muon propagation through rock taking into account energy losses of muons by pair production, inelastic scattering, bremsstrahlung, and ionization as well as the angular deflection by multiple scattering. It uses the ground level muon flux obtained from CORSIKA 6.735 COsmic Ray SImulation for KAscade, which is a sophisticated Monte-Carlo code for simulations of the development of extensive air showers EAS in the atmosphere 6see also, for instance, 7 for simulations of atmospheric muon charge ratio at low energies and 8 for atmospheric muon and neutrino fluxes using CORSIKA. Underground muon measurements were performed by different groups. For instance, muon charge ratio measurements using the MINOS Near Detector have recently been performed by Adamson et al. 9. Muon flux measurements have also been previously made by Mitrica et al. 10, 11. The latter measurements were made at three different locations of Slanic site. The measurement locations are IFIN-HH low background radiation lab located in UNIREA salt mine 208 m below the mine entrance and two different levels Level 8 and Level 12, 188 m and 210 m below the entrance, resp. of active CANTACUZINO mine. The measurements in CANTACUZINO mine were made with the detector installed in a van, which could access the measurement locations through a tunnel. UNIREA mine measurements were made by reinstalling the detector components, removed from the van, in IFIN-HH Lab 10. In this work, muon fluxes in the mentioned mines have been obtained using Monte-Carlo simulations, and results have been compared with the measurements 10 made in the mentioned locations.

2. Slanic Salt Mine

◦ ◦ An artistic view of the Romanian salt mine in Slanic-Prahova 45.23 N, 25.94 E is given in Figure 1. The entrance of the mine is 408 m above sea level. The salt ore is made of around 500 m thick, a few kilometers long, and wide homogenous matrix consisting of salt NaCl > 98% and diﬀerent impurities <2%12. One of these mines, CANTACUZINO, is still active. However, UNIREA, which is the largest mine at the site, is now open for touristic visits. This mine has corridors with stable salt “walls” that have been shaped after extraction of salt over years. Its features can be summarized as follow see, for instance, 10.

◦ i The temperature is about 12 C independent of the conditions outside. ii The humidity is around 65%. Advances in High Energy Physics 3

CANTACUZINO

UNIREA

Proposed excavation for LAGUNA

Figure 1: An artistic representation of the salt mine in Slanic, Romania color online.

iii The ﬂoor is 208 m below the ground and has an area of 70 000 m2. iv 2.9 million m3 volume of salt has been excavated. v The walls’ heights are between 52 m and 57 m. vi The corridors’ widths are between 32 m and 36 m. vii The mine could be accessed via two elevators. viii There exist phone, internet connection, cafeteria, and so forth.

A schematic drawing of UNIREA mine is illustrated in Figure 2 where the gray and white regions represent the salt walls and corridors, respectively. Horia Hulubei National Institute for Physics and Nuclear Engineering IFIN-HH of Romania constructed and commissioned a laboratory 13 in UNIREA mine for low background measurements in 2006. The laboratory is represented with a red rectangle color online and labeled as μBqlab in Figure 2. Part of the muon ﬂux measurements by Mitrica et al. 10 was performed in this laboratory. The locations of the elevator and the cafeteria are also shown in the ﬁgure.

3. Monte-Carlo Simulations

In this study Geant4 for geometry and tracking package, release 4.9.3.p01, is used to get muon fluxes at different locations of Slanic site. Geant4, whose codes are written in C computer language, is an object-oriented toolkit to simulate the passage of particles through matter 14. It is being extensively used in different fields of applications, such as high energy, nuclear, accelerator, and medical physics. It has recently been used in cosmic muon studies to investigate effects of the Earth’s electric and magnetic fields on cosmic muons 15,the azimuthal angle dependence of the low energy ones <1GeV16, and the zenith angle dependence of cosmic-ray muons at sea level 17. A total of six simulation runs, three for nearly vertical muons with the zenith angle ◦ ◦ θ ≤ 10 and three for muons with θ ≤ 60 , were performed separately for UNIREA 4 Advances in High Energy Physics

Cafeteria

Elevator

IFIN-HH lab

Figure 2: Schematic drawing of UNIREA mine with the low background radiation laboratory, elevator, and cafeteria indicated. The frame represents part of the mine selected for the simulation color online.

and two different depths of CANTACUZINO mine. For vertical muons the medium of CANTACUZINO mine, as a first order approximation, was represented by a 210 m thick, 350 m long, and wide solid box made of NaCl impurities of <2% were not included in the simulations. UNIREA mine was simulated as a salt box with the same surface dimensions but with 208 m thickness taking into account tens of meters wide and high corridors. A Geant4 representation of the mine is given in Figure 3, which was produced by selecting part of the mine where the low background radiation laboratory is located interior part ◦ of the frame in Figure 2. Flux simulations of muons with θ ≤ 60 were made in order to compare the simulations with the measurements 10, 18. In this part of the three runs the salt medium was extended in length and width, such a way that muons arriving in larger angles are accepted. For each run of the simulations, a total of 1 million positively and negatively charged muons with energies above 100 GeV were distributed randomly from the ground level taking into account the muon charge ratio of ∼1.3 at sea level see, e.g., 19. The threshold energy of 100 GeV is selected in order to increase the statistics by considering only the muons with enough energy that are able to penetrate ∼210 m of salt. Energy and fluxes of the muons injected have been taken from the sea level measurements by Rastin 20. Underground muon fluxes have been simulated using the standard electromagnetic EM package for electromagnetic interactions and LHEP, for hadronic interactions. Geant4 EM package, including processes such as ionization, bremsstrahlung, multiple scattering, ± Compton and Rayleigh scattering, and photo-electric effect, handles basic processes for e , ± photon, μ , and hadrons. LHEP combines both the high- and low-energy parameterized models that describe inelastic interactions for all hadrons 21. − Energies of muons both μ and μ reaching different levels of CANTACUZINO mine and the floor of UNIREA mine were recorded during each simulation run, and fluxes were obtained for each case. Results are given in the following section. Advances in High Energy Physics 5

Figure 3: A Geant4 representation of a part of UNIREA mine with the low background radiation laboratory of IFIN-HH shown with a black box color online.

Nearly vertical µ ﬂux at CANTACUZINO mine 10−3 ) 1 − ) c

GeV/ −4 ( 10 1 − s 1 − sr 2 −

m −5

( 10

Muon ﬂux 10−6 0 50 100 150 200 250 300 350 400 Muon momentum (GeV/c)

Level 8 (−188 m) Level 12 (−210 m)

◦ Figure 4: Flux of nearly vertical muons θ ≤ 10 at two diﬀerent levels of CANTACUZINO mine.

4. Results and Discussion

In the present work, Geant4 simulations were performed for UNIREA and CANTACUZINO mine for nearly vertical muons as the ﬁrst step. Selection of vertical muons was done by ◦ distributing the primary muons within the zenith angle of 10 and accepting the secondary ones reaching the locations of interest within the same zenith angle range. Flux distributions obtained from these simulations are given in Figures 4 and 5. 6 Advances in High Energy Physics

Nearly vertical µ ﬂux at UNIREA mine 10−3 ) 1 − ) c GeV/ ( 10−4 1 − s 1 − sr 2 −

m −5 ( 10 Muon ﬂux 10−6 0 50 100 150 200 250 300 350 400 450 Muon momentum (GeV/c)

◦ Figure 5: Flux of nearly vertical muons θ ≤ 10 at UNIREA mine.

Table 1: Measurement and simulation results of underground muon fluxes at different locations of Slanic site. Muon flux Muon flux Location Depth − − − − m 2 s 1 m 2 s 1 mine below the ground measurements simulations UNIREA −208 m 0.18 ± 0.01 0.14 ± 0.02 CANTACUZINO −188 m 0.19 ± 0.02 0.15 ± 0.02 CANTACUZINO −210 m 0.09 ± 0.01 0.10 ± 0.02

It should be noted that the vertical muon flux for CANTACUZINO mine Figure 4 obtained using Geant4 simulation is consistent with the flux obtained using MUSIC 5 given in 10. This, to some extent, confirms validity of the simulations performed for this study. One can observe a peak appearing at 15 GeV/c for muons reaching Level 8 −188 m of CANTACUZINO mine solid diamonds in Figure 4. The flux distribution for muons reaching Level 12 −210 m of the same mine empty diamonds in Figure 4, on the other hand, does not show a peak due to the selected threshold of 100 GeV. The reason for that behavior is that muons have to penetrate an additional volume of 22 thick salt to reach −210 m. At higher momenta above ∼350 GeV/c, the two distributions start to get closer to each other. In Figure 5, vertical muon flux in UNIREA mine is illustrated. It is seen from the figure that a clear peak arises at ∼30 GeV/c. The distribution is similar to that of CANTACUZINO mine at level 8 except for a shift of ∼20 GeV/c in the peak position resulting in more lower energy muons in UNIREA. Similar behavior of these distributions could be attributed to the fact that they have similar water equivalent depths 10. In order to compare the simulations with measurements made by Mitrica et al. 10, simulations were rerun after extending the surface area, where the primary muons are ◦ distributed, such a way that muons with θ ≤ 60 are accepted. Results are given in Table 1. It can be seen that the simulation results, within statistical error, are in good agreement with the measurements especially for CANTACUZINO mine. For UNIREA mine, simulation slightly underestimates the muon flux, which could be the result of neglecting the additional gaps above the mine see Figure 1 in the simulations. A reason for the source of overall Advances in High Energy Physics 7 discrepancy could be that the primary muon flux at the ground was assumed to be isotropic for high-energy muons of interest.

5. Conclusions

Vertical muon fluxes for different locations, at the floor of UNIREA mine and at two levels of CANTACUZINO mine, of Slanic-Prahova have been obtained using Geant4 simulation package. Primary muons with energies above 100 GeV were distributed at the ground level ◦ within 10 . While the muon flux distributions of CANTACUZINO Level 8 and UNIREA show a peak at muon momenta of 15 GeV/c and ∼30 GeV/c, respectively, no peak appears at the distribution of CANTACUZINO mine Level 12, which is due to the selection of threshold energy of 100 GeV. Simulation for Level 8 of CANTACUZINO mine 188 m below ground is consistent with the one previously made using MUSIC. ◦ Muon flux simulations were also performed for muons with θ ≤ 60 for the same locations, and the results were compared with the ones obtained from the measurements. A good agreement, within statistical uncertainty, is observed between the simulations and the measurements. It should be noted that the overburden mainly composed of soil over the salt is not taken into account in the present study since its effect is expected to be small, if not zero. Further simulations with a more detailed description of the mines, together with the soil overburden taken into account, and with a more realistic selection of the nonvertical primary muon fluxes at the ground are expected to yield much satisfactory results in comparison with the measurements.

Acknowledgments

The numerical calculations reported in this paper were performed at TUBITAK ULAKBIM and High Performance and Grid Computing Center TR-Grid e-Infrastructure.Oneofthe authors D. Stanca would like to thank the Romanian Authority for Scientiﬁc Research for the support on the project: Parteneriate 194/2012-CORONA and PN 09 37 01 05.

References

1 P. K. F. Grieder, Cosmic Rays at Earth: Researcher’S Reference Manual and Data Book, Elsevier, Amsterdam, The Netherlands, 2001. 2 E. W. Grashorn, J. K. de Jong, M. C. Goodman et al., “The atmospheric charged kaon/pion ratio using seasonal variation methods,” Astroparticle Physics, vol. 33, no. 3, pp. 140–145, 2010. 3 D. Autiero, J. Ayst¨ o,¨ A. Badertscher et al., “Large underground, liquid based detectors for astroparticle physics in Europe: scientiﬁc case and prospects,” Journal of Cosmology and Astroparticle Physics, vol. 11, article 011, 2007. 4 A. Rubbia, “The Laguna design study-towards giant liquid based underground detectors for neutrino physics and astrophysics and proton decay searches,” Acta Physica Polonica B, vol. 41, no. 7, pp. 1727– 1732, 2010. 5 V. A. Kudryavtsev, “Muon simulation codes MUSIC and MUSUN for underground physics,” Computer Physics Communications, vol. 180, no. 3, pp. 339–346, 2009. 6 D. Heck, J. Knapp, J. N. Capdevielle, G. Schatz, and T. Thouw, “CORSIKA: a monte carlo code to simulate extensive air showers,” Forschungszentrum Karlsruhe Report FZKA 6019, 1998. 7 B. Mitrica, “Asymmetry of charge ratio for low energetic muons,” in Proceedings of the Carpathian Summer School of Physics, vol. 972 of AIP Conference Proceedings, pp. 500–504, 2007. 8 J. Wentz, I. M. Brancus, A. Bercuci et al., “Simulation of atmospheric muon and neutrino ﬂuxes with CORSIKA,” Physical Review D, vol. 67, no. 7, Article ID 073020, 2003. 8 Advances in High Energy Physics

9 P. Adamson, C. Andreopoulos, D. J. Auty et al., “Measurement of the underground atmospheric muon charge ratio using the MINOS Near Detector,” Physical Review D, vol. 83, Article ID 032011, 10 pages, 2011. 10 B. Mitrica, R. Margineanu, S. Stoica et al., “A mobile detector for measurements of the atmospheric muon flux in underground sites,” Nuclear Instruments and Methods in Physics Research A, vol. 654, pp. 176–183, 2011. 11 B. Mitrica, M. Petcu, I. Brancus et al., “Measurements of the atmospheric muon flux in the underground of slanic prahova salt mine,” U.P.B. Scientific Bulletin Series A, vol. 73, no. 3, pp. 203– 212, 2011. 12 C. Cristache, C. A. Simion, R. M. Margineanu et al., “Epithermal neutrons activation analysis, radiochemical and radiometric investigations of evaporitic deposits of Slanic-Prahova Romania salt mine,” Radiochimica Acta, vol. 97, no. 6, pp. 333–337, 2009. 13 R. Margineanu, C. Simion, S. Bercea et al., “The Slanic-Prahova ROMANIA underground low- background radiation laboratory,” Applied Radiation and Isotopes, vol. 66, no. 10, pp. 1501–1506, 2008. 14 S. Agostinelli, J. Allison, K. Amako et al., “Geant4a simulation toolkit,” Nuclear Instruments and Methods in Physics Research A, vol. 506, no. 3, pp. 250–303, 2003. 15 M. Bektasoglu and H. Arslan, “Estimation of the effects of the Earth’s electric and magnetic fields on cosmic muons at sea level by Geant4,” Journal of Atmospheric and Solar-Terrestrial Physics, vol. 74, pp. 212–216, 2012. 16 H. Arslan and M. Bektasoglu, “Azimuthal angular dependence study of the atmospheric muon charge ratio at sea level using Geant4,” Journal of Physics G, vol. 39, no. 5, Article ID 055201, 2012. 17 M. Bektasoglu and H. Arslan, “Investigation of the zenith angle dependence of cosmic-ray muons at sea level,” Pramana-Journal of Physics. In press. 18 B. Mitrica, “20 years of cosmic muons research performed in IFIN-HH,” in Proceedings of the Carpathian Summer School of Physics, vol. 1498 of AIP Conference Proceedings, pp. 291–303, 2012. 19 S. Haino, T. Sanuki, K. Abe et al., “Measurements of primary and primary and atmospheric cosmic- ray spectra with the BESS-TeV spectrometer,” Physics Letters B, vol. 594, pp. 35–46, 2004. 20 B. C. Rastin, “An accurate measurement of the sea-level muon spectrum within the range 4 to 3000 GeV/c,” Journal of Physics G, vol. 10, no. 11, pp. 1609–1628, 1984. 21 Geant4 Collaboration, “Geant4 Physics Lists,” 2012, http://geant4.cern.ch/support/proc mod cata- log/physics lists/physicsLists.shtml. Hindawi Publishing Corporation Advances in High Energy Physics Volume 2012, Article ID 274614, 15 pages doi:10.1155/2012/274614

Research Article Status and New Data of the Geochemical Determination of the pp-Neutrino Flux by LOREX

M. K. Pavicevi´ c,´ 1 F. Bosch,2 G. Amthauer,1 I. Anicin,ˇ 3 B. Boev,4 W. Bruchle,¨ 5 V. Cvetkovic,´ 6 Z. Djurciˇ c,´ 7 W. F. Henning,8 R. Jelenkovic,´ 6 V. Pejovic,´ 3 and A. Weiss9

1 Division of Material Sciences and Physics, Department of Mineralogy, University of Salzburg, Hellbrunner Street 34, 5020 Salzburg, Austria 2 GSI Helmholtzzentrum fur¨ Schwerionenforschung, Planck Straße 1, 64291 Darmstadt, Germany 3 Institute of Physics, University of Belgrade, Pregrevica 118, 11000 Belgrade, Serbia 4 Faculty of Mining and Geology, Goce Delcevˇ University of Stip,ˇ Goce Delcevˇ 89, 92000 Stip,ˇ Macedonia 5 GSI Helmholtzzentrum fur¨ Schwerionenforschung, Planck Straße. 1, 64291 Darmstadt, Germany 6 Faculty of Mining and Geology, University of Belgrade,− Dusinaˇ 7/II, 11000 Belgrade, Serbia 7 Physics Division, Argonne National Laboratory (ANL), 9700 South Cass Avenue, Argonne, IL 60439, USA 8 Physics Department E12, Technical University of Munich, James-Franck Street, 85748 Garching, Germany 9 Max-Planck Institute for Astrophysics, Karl-Schwarzschild Street 1, 85741 Garching, Germany

Correspondence should be addressed to M. K. Pavicevi´ c,´ [email protected]

Received 21 August 2012; Revised 19 October 2012; Accepted 2 November 2012

Academic Editor: Bogdan Mitrica

Copyright q 2012 M. K. Pavicevi´ c´ et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

LOREX LORandite EXperiment addresses the determination of the solar pp neutrino flux 205 ν → 205 − during the last four million years by exploiting the reaction Tl e Pb e with an incomparably low-energy threshold of 50 keV for the capture of solar neutrinos. The ratio of 205Pb/205Tl atoms in the Tl-bearing mineral lorandite provides, if corrected for the cosmic-ray induced background, the product of the flux of solar neutrinos and their capture probability by 205Tl, averaged over the age of lorandite. To get the mean solar neutrino flux itself, four problems have to be addressed: 1 the geological age of lorandite, 2 the amount of background cosmic- ray-induced 205Pb atoms which strongly depends on the erosion rate of the lorandite-bearing rocks, 3 the capture probability of solar neutrinos by 205Tl and 4 the extraction of lorandite and the appropriate technique to “count” the small number of 205Pb atoms in relation to the number of 205Tl atoms. This paper summarizes the status of items 1 age and 3 neutrino capture probability and presents in detail the progress achieved most recently concerning the items 2 background/erosion and 4 “counting” of 205Pb atoms in lorandite. 2 Advances in High Energy Physics

1. Introduction

The determination of the long-time average of the solar neutrino ﬂux Φν with the thallium- bearing mineral lorandite, TlAsS2, from the mine of Allchar, Macedonia, is based on the neutrino capture reaction proposed by Freedman et al., 1976 1:

205 ν −→ 205 − Tl e Pb e 1.1

The average ﬂux Φν over the exposure time a age of lorandite since its mineralization follows from the common activation equation:

−1 −1 −1 Φν N T − Bσε λ 1 − exp−λa , 1.2 where N is the total number of 205Tl atoms, T the total number of 205Pb atoms, B the number of 205Pb atoms induced by background reactions mainly 205Tl μp,n 205Pb, σ the solar neutrino capture cross-section of 205Tl, ε the overall detection eﬃciency, λ the decay constant of 205Pb and a the geological age of lorandite i.e., the age of mineralization. The neutrino capture reaction:

205s ν E ≥ −→ 205 ∗ Tl e νe 50 keV Pb e 1.3

E ≥ exploits the by far lowest threshold of νe 50 keV for solar neutrinos. The last step and the central problem of LOREX is the quantitative determination of 205Pb atoms in lorandite. This renders finally the mean solar neutrino flux, that is, the mean luminosity of the sun during the last 4.31 million years, which is the geological age a of lorandite from Allchar, as given by Neubauer et al. 2. Before entering the final phase of the experiment, four problems must be reliably addressed; however,

1 the age a of lorandite has to be known precisely: age of lorandite,

2 the background of 205Pb atoms produced by cosmic radiation mainly μp,n- reactions and by natural radioactivity must be determined quantitatively. In this context the knowledge of the erosion rate of the overburden rocks during the existence of lorandite is of utmost importance: background and erosion,

3 the ratio 205Pb/205Tl provides only the product of solar neutrino flux and neutrino capture probability into different nuclear states of 205Pb. However, the capture of ∗ neutrinos should populate predominantly the first excited state at E 2.3keV. Hence, to get the neutrino flux itself, one has to determine the capture probability into this low-lying state of 205Pb: neutrino capture probability into the 2.3keV state of 205Pb,

4 how can the expected ultra-low abundance of 205Pb be reliably measured: detection of 205Pb. Advances in High Energy Physics 3

2. Main Directions of Present and Future Investigations 2.1. Age of Lorandite

The age of the Tl mineralization is an essential parameter of the experiment, as it equals the integration time of mineral lorandite as the geochemical pp-solar neutrino detector. As it turned out, another important prerequisite for the realization of LOREX is that the ore deposit has to provide for more than two lorandite-rich ore bodies, located at significantly different depths. Geological research demonstrated that lorandite in sufficient quantities occurs in the Allchar Sb-As-Tl-Au deposit located in FYR Macedonia at the north-western margins of the Kozufˇ Mountains, close to the border between FYR Macedonia and Greece. The mine contains the world’s largest known concentrations of thallium-bearing minerals and, in particular, the mineral lorandite. The polychronous and polygenetic Sb-As-Tl-Au Allchar deposit was formed by complex physicochemical processes occurring in a heterogeneous geological environment. The deposit originated through polyphase interactions of hydrothermal fluids and the surrounding magmatic, sedimentary, and metamorphic rocks. The genesis of ore mineralization is genetically related to the products of Pliocene magmatic activity. The spatial location of the mineralization was controlled by magmatic, structural, and lithological factors as suggested by Jankovic´ and Jelenkovic´ 4. The Allchar deposit comprises several ore bodies of various shapes, textural and structural characteristics, and associations of elements. Thallium mineralization has been proved in two locations, that is, two ore bodies: Crven Dol and Centralni Deo ore bodies, situated in the northern and central part of the Allchar deposit, respectively, Figure 1. Troesch and Frantz determined the geological age of Tl mineralization in Crven Dol Figure 1a as 4.22 ± 0.07 Ma, using sanidine from adit number 21 5. This determination was obtained by isochrone 40Ar/39Ar five-degree measurement of argon content with the derivation 2σ of the first phase and 1σ of other four phases. During the final stages of volcanic activity in the Allchar area occurred hydrothermal alteration of the wall rocks, and this can be considered as the period of initial deposition of ore minerals in this area. The age of K-feldspars alkali feldspar has a general formula: , K Na AlSi3O8, but varies in crystal structure depending on the temperature it formed at; the formula actually is a blend ranging from pure sodium albite to pure potassium end-member orthoclase, microcline, or sanidine in an altered zone at the Rudina locality is 4.31 ± 0.02 Ma according to Neubauer et al. 2, which documents the beginning of intensive alteration and deposition of thallium mineralization. The close spatial association of mineralization and hydrothermally altered rocks is found by a drill-core B-2 Figure 1b of the Rio Tinto company in 1999 at the Rudina locality, which is geologically connected with the ore body Centralni Deo. These drill cores revealed the presence of As-, Sb-, and S-mineralization and strongly altered rocks at depth intervals 30–60 m and 160–280 m, respectively, from Rio Tinto Co. 3.

2.2. Background Reactions and Cosmic Ray Contribution

In the case of LOREX more than 30 processes have been identiﬁed and analyzed which potentially contribute to the ”background” of 205Pb. After careful evaluation only four processes turned out to potentially have nonnegligible contributions:

1 the 205Tlμp, n205Pb reaction: contribution of fast muons, 4 Advances in High Energy Physics

1000 1000

d2 = 205 m

d1 = 178 m

850 d1 = 28 m d = 55 m 850

2 (m) (m) Present surface

800 800

Lorandite Rocks Eroded layer

a Crven Dol, Adit P-21

d4 = 420 m

d3 = 385 m B 900 Present surface 2 900 B3 (m) (m) 140 m 103 m = = 4 3 850 d d 850

Lorandite Rocks Eroded layer

b Centralni Deo, Adit 823

Figure 1: Geological cross-section of the ore body Crven Dol a and Centralni Deo b of the Allchar ore deposit together with the presumably eroded layer.

2 the 205Tlμp, n205Pb reaction: contribution of stopped muons, 3 the 204Pbn, γ205Pb and 206Pbn, 2n205Pb reactions, 4 205Pb mobilized from the environment of lorandite.

Figure 2 shows present estimates of diﬀerent contributions to the production of 205Pb in lorandite on the basis of the erosion rate 70 m/Ma and 130 m/Ma, traces of U and Th Advances in High Energy Physics 5

Table 1: Cosmic-ray contributed Nμ− and total number Nt of 205Pb atoms per 10 kg of lorandite from diﬀerent depths, known to contain signiﬁcant quantities of lorandite.

N 205 N 205 Paleo-depth Pb fast muons Pb total Depth of Erosion d × 4 × 4 N 205 N 205 p of 10 10 Pb ν Pb fast muons location rate − − location at. 10 kg 1 at. 10 kg 1 % % m m/Ma mwe lorandite lorandite d 1 28 70 455 93.8 115.8 19.0 81.0 d 2 55 70 525 56.9 78.9 27.9 72.1 d 3 103 130 980 18.6 40.6 54.2 45.8 d ∗ 4max 140 130 1070 13.0 35.0 62.8 37.2 ∗ Drillings of Rio Tinto Exploration Ltd. 3see Figure 1b.

in lorandite and surrounding rocks by Pavicevi´ c´ 6, and the method by Heisinger and coworkers 7 as a function of the paleodepth dp of the deposit. To determine the erosion rate in Allchar we applied terrestrial in situ cosmogenic nuclides including both radioactive 10Be and 26Al and stable 3He and 21Ne nuclides in different minerals and compared the obtained data with the results of geomorphologic analysis. 26Al concentrations of 16 samples have 1σ uncertainties of 26–58% and yield maximum erosion rates from ∼70 m/Ma to ∼600 m/Ma at different locations. The noble gas analyses included measurements of 3He in one diopside sample and 21Ne in quartz from five different locations and in one sanidine sample, revealing erosion rates between ∼20 m/Ma and ∼70 m/Ma, with asymmetric 1σ uncertainties between 10 and 200%. The 10Be measurements revealed unrealistically high values and had to be omitted from interpretation. Both the combined 21Ne-26Al data and the geological information indicate that a simple steady-state erosion history is not applicable to the Allchar area. Rather, long periods of burial ∼500 ka–3 Ma by volcaniclastic material and, possibly, glacier ice have interrupted the times of exposure and erosion. Nevertheless, it is remarkable that 85% of all erosion rate values determined from different cosmogenic nuclides 3He, 21Ne, 26Al in various monitor minerals at various locations, as well as the results of geomorphologic analysis, yield consistent results in the range from ∼20 to ∼90 m/Ma. We argue that the 26Al concentrations most likely reflect the erosion rate during the last, postburial period ∼100 ka. For the two most important Allchar locations with lorandite ore bodies Crven Dol and Centralni Deo we propose the erosion rates of ∼70 m/Ma and ∼130 m/Ma, respectively, according to Pavicevi´ cetal.´ 8.The paleodepths for the four confirmed ore-bodies with significant quantity of lorandite are found from their present-day depths and the estimated thickness of eroded layers at corresponding locations Figure 1 and Table 1. Table 1 also lists the final estimates of concentrations of 205Pb atoms per 10 kg lorandite at different depths; the concentration due to the cosmic-ray fast muons, the concentration due to pp-neutrino captures, and the total concentration. For the shallowest d ∼ d location 1 the neutrino contribution amounts to 20%, while for the deepest one 4 it amounts to ∼63%. As seen in Figure 2, concentrations of 205Pb in samples from different depths reflect— due to the muon contribution which is depth dependent—both the present-day depth of the sample as well as the erosion history of the overburden layers. Curves that correspond to different average erosion rates form a family of exponentials Anicinˇ et al. 10 and experimental determination of 205Pb concentrations in samples from a number of different depths allow for the simultaneous determination of both the muon contribution and 6 Advances in High Energy Physics

103

(NPb205)total −70 m/Ma

102 (NPb205)total −130 m/Ma per gram of lorandite d = 455 205 1

(N 205) d2 = 525 d = 980 101 Pb ν 3 (NPb205)fast muons atoms of Pb N r

n d4 = 1070

100 4 6 8 10 12 14 16 Depth of deposit (102 mwe)

Figure 2: Estimate of the present amount of 205Pb in lorandite due to solar neutrinos and to background 6 reactions in the last 4.31 · 10 years as a function of the paleodepth dp of lorandite. The values are calculated by Pejovic´ by adopting the value of 0.55 μb for the neutrino capture cross-section for 205Tl from Hartman et al. 9, the contents of U and Th in lorandite and surrounding rocks are from Pavicevi´ c´ 6 and the method of Heisinger et al. 7. n: contributions due to lead mobilized from the rock walls. r: 205 contributions from natural radioactivity. N Pb fast muons: contribution due to reactions induced by fast 205 205 cosmic muons. NPb ν:numberofPb due to solar neutrino capture, for a capture rate of 146 SNU − 1SNU 10 36 captures/target atoms · sec, obtained after correcting the original 260 SNU value for 205 neutrino ﬂavour-oscillations. N Pb total: the sum of the neutrino contribution and of all background contributions.

the erosion history of the deposit. The contribution due to the 205Pb mobilized from the surrounding rock at the time of lorandite mineralization, marked by “n”, and that due to natural radioactivity in lorandite and in the surrounding rocks, marked by “r”, contribute together by less than 4% to the total concentration U and Th concentrations are low: marble, dolomite, and quartz latite have contents of U in the range of 0.054–0.45 ppm and Th of 0.061–0.66 ppm, while the mean concentrations in lorandite amount to 0.12 ppm for U and 0.022 ppm for Th, respectively, as given by Pavicevi´ c´ 6. Estimate of contribution of “n,” that is, mobilised 205Pb from surrounding rocks at the time of the formation of the Tl-mineralization age of lorandite and the natural radioactivity contribution “r,” as consequence trace concentrations of U and Th amount to less than 4% see Figure 2. The low contribution of “n” is consequence of the very low concentration of U and Th in rocks: marble, dolomite, and Qz-rhyolite, which have the content of U 0.054–0.45 ppm and Th 0.061–0.66 ppm Pavicevi´ c´ 6. The contribution of natural radioactivity “r” that is predominantly caused by U and Th in lorandite is low due to low concentrations of these elements in lorandite: U 0.12 ppm and Th 0.022 ppm Advances in High Energy Physics 7

Pavicevi´ c´ 6. All background components not speciﬁc to lorandite not originating from thallium were estimated to amounts of between 3 and 15 SNU Neumaier et al. 11 and can experimentally be determined by measuring the 205Pb contents in monitoring minerals realgar As2S2 and orpiment As2S3 . 205 205 From the data for N Pb ν and N Pb fast muons shown in Table 1 we estimated by a Monte Carlo simulation the mean neutrino ﬂux Φν 1.2 during the geological age a of lorandite as

10 −2 −1 Φν 3.41 ± .4410 m sec 2.1

by using the following parameters see 1.2:

N 1.25 · 1025 2.5 · 1023 atoms of 205Tl. 2.2

This number corresponds to 10 kg of lorandite, collected at a suﬃciently deep location, for the background B to be acceptable, namely, at a paleo-depth of dp 980 m, where the calculated background B of 205Pb atoms amounts to about 46%, see third row of Table 1

− − σ 4.3 · 10 45 2.15 · 10 46 cm2, a 1.26 · 1014 1.26 · 1012 s, 2.3 − − − λ 1.48 · 10 15 7.4 · 10 17 s 1, − − ε 1 · 10 3 1 · 10 4 .

Whereas the geological age a of lorandite and the decay constant λ of 205Pb are by now satisfactorily well known, the solar neutrino capture cross-section σ of 205Tl is experimentally unknown. The value assumed in 2.3 is not more than the best educated guess, based on previous estimates of Bahcall and other theorists Bahcall 12, Wapstra and Audi 13, Braun and Talmi 14, Freedman and Nolte 15, ana Ogawa and Arita 16. How the nuclear matrix element for the dominant neutrino capture channel into the first excited state of ∗ 205PbE 2.3keV can be experimentally determined will be outlined in the next Section 2.3. Likewise, the total detection efficiency ε assumed in 2.3 is only a optimistic guess. It is obvious that one of the most demanding problems of LOREX is the measurement of the extremely low concentrations of 205Pb in potentially available samples of a generally very scarce material. Methods that might be suited to this difficult task are discussed in Section 2.4. 8 Advances in High Energy Physics

2.3. Determination of the Neutrino Capture Probability into the 2.3 keV State of 205Pb

From the relative abundance of 205Pb with respect to 205Tl, even corrected for all background eﬀects, one can extract only the time-integrated product of solar neutrino ﬂux and the neutrino- π capture probability, leading from the nuclear ground state of 205Tl I 1/2 to individual ∗ excited nuclear states of 205Pb , according to

205 . . ν E ≥ −→ 205 ∗ − Tl g s e νe 52 keV Pb e 2.4

E with an energy threshold at νe 52 keV, much lower than the corresponding thresholds of all other radio- or geochemical experiments which are either already performed e.g., GALLEX or proposed. The solar pp-neutrinos with a maximum energy of 422 keV can be π − ∗ π − captured only into the ground state I 5/2 ,theﬁrstE 2.3keV,I 1/2 ,and the second excited state E∗ 263 keV, Iπ 3/2− of 205Pb. It is obvious from the well- known systematic of beta decay that the capture probability into the 2.3 keV state ΔI 0, parity change should be by far larger than the capture into the ground state ΔI 2 as well as into the second excited state with ΔI 1 Behrens and Jaenecke 17. The nuclear matrix element for the transition to the 2.3 keV state in 205Pb is not known. There is one—and only one—possibility Kienle 18 to determine experimentally this unknown nuclear matrix β element, namely, by measuring the bound-state beta decay b decay of bare or hydrogen- like 205Tl81 into hydrogen-like helium-like 205Pb81 , according to

205 81 205 81∗ ∗ − −→ E . νe , Tl Pb 2 3keV eb bar 2.5 where a neutron of the 205Tl atomic nucleus transmutes to a proton, and where a mono- ν chromatic electron-antineutrino e bar is being created together with an electron that e− 205 81 remains bound b in an inner shell mainly K or L-shell of the daughter ion Pb .The Q value of this decay amounts to only 52 keV. Since the nuclear parts of neutrino capture β and of b decay are identical, a measurement of the bound state beta-decay probability of bare or hydrogen-like 205Tl provides the unknown nuclear matrix element log ft value for the transition ∗ to the ﬁrst excited state of 205Pb at E 2.3keV. Bound-state beta decay probabilities with comparable small Q values have been measured at the Experimental Storage Ring ESR of GSI in two pioneering experiments, for the examples of bare 163Dy → hydrogen-like 163Ho Jung et al. 20,andofbare 187 Re → hydrogen-like 187Os Bosch et al. 21,andofbare207Tl → hydrogen-like 207Pb β Ohtsubo et al. 22 . The well-developed technique of detecting b decay, as exploited in these experiments, is ”Schottky lifetime spectrometry” Litvinov et al. 23, where the signals of the stored and electron-cooled parent- and daughter ions, induced on pick-up plates, are steadily recorded, yielding their revolution frequencies which are unambiguously correlated to their corresponding mass-to-charge ratios. From these ”Schottky lines,” the numbers of both parent and daughter ions are recorded as a function of time, yielding β the b decay probability and, thus, the nuclear matrix element log ft value searched for. However, the revolution frequencies of parent and daughter ions could not be resolved in these experiments due to the very small Q values involved. Therefore, a special technique was applied, namely, the removal of the single bound electron of the daughter ions by means of an internal gas jet acting for a short time. Advances in High Energy Physics 9

205Tl81+ 1/2+ g.s.

βb Qβb (K)=31.1 keV

T1/2(βb) ≈ 120 d (?)

1/2− 2.3 keV

205Pb0 g.s.

6 EC T1/2(EC)=17.3(4) · 10 a

QEC = 50.5(5) keV

205Tl0 1/2+ g.s.

Figure 3: The neutral 205Tl0 atom is stable with respect to β− decay into the continuum since the Q value 81 forthisdecayisnegative,Qβ− −QEC −50.5 keV. However, for bare 205Tl or hydrogen-like 205Tl ions bound-state β decay becomes allowed, where the created electron remains bound in the K-shell of the 205 81 Q Q daughter ion Pb . Due to the “saved” K-shell binding energy, the value for this decay βb K gets positive. Both, the capture of solar pp-neutrinos and the bound-state beta decay populate predominantly − the ﬁrst exited state 1/2 of the 205Pb nucleus at 2.3 keV and share the same nuclear matrix element for this − transition. Therefore, the measurement of the bound-state β decay probability of bare or hydrogen-like 205Tl ions provides the unknown capture probability of the solar pp-neutrinos by the 205Tl atoms. Based on β− T β 205 the log ft values of comparable decays, the bound-beta half-life 1/2 b of bare Tl ions was estimated by Takahashi and Yokoi 19 to about 120 d. Since this extrapolated value has to be regarded as uncertain within at least a factor of three, only the measurement of the bound-beta half-life can provide a safe number with a reliable error margin for the capture probability of solar pp-neutrinos by 205Tl.

β 205 For the corresponding experiment concerning the b decay of bare Tl see Figure 3 with a comparable small Q value, exactly the same detection technique as in the two successful experiments mentioned above has been proposed. However, there were—and still are—serious and too expensive safety restrictions for the use of Tl in an ion source due to its toxicity, which prevented the realisation of this experiment over the last 18 years. Nonetheless, since this proposal remained all the time on the list of high-priority experiments, we were encouraged to search for another way of its realisation. We proposed as the ”new technique” getting bare 205Tl ions their indirect production by in-ﬂight fragmentation of a primary 206Pb beam in the fragment separator FRS together with their subsequent injection into the experimental storage ring ESR. The decisive point is that at least 106 bare 205Tl β ions have to be provided and stored, in order to obtain a minimum number of a few 100 b β 205 decays within storage times of a couple of hours the b half-life of bare Tl is estimated to 120 days Takahashi and Yokoi 19. By two major achievements of the last years this indispensable number of at least 106 stored bare 205Tl ions can now be reached at high conﬁdence see Figure 4.

1 By a signiﬁcant improvement of the output of the lead ion source and the reduction of beam losses, a number of 2 · 109 206Pb ions could be delivered safely to the FRS already in two experiments. Based on the known cross-section for in-ﬂight fragmentation and the known distribution of atomic charge states, this would yield a number of about 105 bare 205Tl ions per injection into the ESR. 10 Advances in High Energy Physics

Production Experimental target Fragment separator storage ring

From SIS

Figure 4: Part of the accelerator facility of GSI, relevant for the proposed measurement of the bound-beta half-life of bare 205Tl81 ions. A beam of 206Pb ions, accelerated in the synchrotron SIS to an energy of some 100 A MeV, hits the production target Be of the fragment separator FRS, where a plenty of highly-charged ions will be generated by nuclear reactions. With the aid of an appropriate setting of the FRS magnets and by exploiting the Z-dependent stopping power in a degrader placed in the symmetry point of the FRS black triangle,onlybare205Tl81 ions can pass through small slits at the end of the FRS. Those ions will be stored in the experimental storage ring ESR and accumulated by repeated injections until a number of at least 106 ions will be reached. After the application of electron cooling, the 205Tl81 ions are circulating in the ring for a couple of hours, where a few of them will decay to hydrogen-like 205Pb by bound-state β decay.

2 By the combination of stochastic cooling and the storage of the injected ions at inner orbits several subsequent injections 10 ···30 can be applied without any losses of the already stored ions rf stacking of fragments. This technique has been successfully applied in several experiments within the last years.

Due to these important steps the reach of 106 stored and cooled bare 205Tl ions is β feasible. Therefore, this new procedure for the determination of the b decay probability of bare 205Tl—and, therewith, of the solar neutrino capture cross-section by 205Tl—has been approved in June 2010 by the international experimental board of GSI ESR-proposal 100. Six days of beam time and the highest priority ”A” were assigned. A copy of this decision is attached in the supplement of this proposal. The experiment is now in the procedure of scheduling. Its realisation within the next 18 months is reliable, taking into account the ”waiting list” for high-priority experiments at the FRS-ESR facility.

2.4. Extraction and Detection of Ultra-Low Amounts of 205Pb in Lorandite

One of the key requirements of the geophysical LOREX project is the ultra-sensitive, quantitative detection of the neutrino-induced trace amounts of 205Pb present in lorandite. . . × 5 205 For 10 kg lorandite TlAsS2 one estimates about 3 5–11 6 10 atoms of Pb depending on the depth at Allchar at which the respective lorandite sample is mined. This implies a necessary separation factor of about 1020 between 205Pb and 205Tl 70% isotopic abundance. Separation factors of this extreme magnitude are perhaps directly achievable for very short- lived radioisotopes through the measurement of their decay radiation Low Level Counting, LCC. For 205Pb, with a half-life of about 17 million years and in view of the diﬃculty to detect electron capture decay, this is impossible. For the LOREX, therefore, the direct detection and counting of the 205Pb atoms was proposed, either with mass-spectrometric methods or with measurements of characteristic atomic transition radiation. The intrinsic limitation of these methods to small sample sizes is substantially helped with an initial chemical Pb-Tl separation, which has been established to provide a separation factor of 1013 Pavicevi´ c´ and Bruechle 24. For Allchar lorandite the Pb content has been found to be about 1.5 ppm Pavicevi´ c´ 6. Thus, after the initial chemical Advances in High Energy Physics 11

− Pb-Tl separation, a 20 mg Pb sample with a 205Pb/Pb-ratio of ∼10 15 will be obtained. The sample will also contain a residual amount of ∼1012 Tl atoms. The methods that appear suitable, in principle, for the detection of 205Pb at trace amount levels under consideration here are low-energy mass spectrometry specifically ICP- MS, i.e., inductively coupled plasma mass spectrometry, high-energy mass spectrometry i.e., AMS, accelerator mass spectrometry, and laser-induced atomic spectroscopy. The latter includes in particular resonance ionization mass spectrometry RIMS and the recently developed atom trap trace analysis ATTA. Quality criteria in each case are the separation factors for Pb/Tl and 205Pb/Pb and the overall detection efficiency. The latter is critical for a relevant statistical accuracy of the measured 205Pb concentration. In summary, the unambiguous detection of the 205Pb atoms with statistical uncertainty of less than 10%, − requires a method that provides fully resolved separation of 205Pb from 205Tl at the 10 7 level, − and 205Pb from other lead isotopes at the 10 15 level, and detection efficiency for 205Pb atoms − − of preferably 10 2 but at a minimum of 10 3. High-energy AMS relies on the acceleration of ions to energies where molecules are fully destroyed through breakup in stripper foils, the differential energy loss provides chemical element identification of the remaining ions, and powerful ion-beam detectors could be taken from heavy-ion nuclear physics research. Trace concentrations have been reliably − measured for low-mass radioisotopes A<40 down to values of 10 16. However, for heavier nuclei the nuclear-charge separation is less pronounced at the typical heavy-ion accelerator because of increased energy-loss straggling and decreasing relative nuclear charge resolution. Earlier experiments of 205Pb/205Tl separation at about 6 MeV per nucleon beam energy Ernst et al. 25; Henning and Schuell 26 have produced separation factors of 102 to 103 between 205Pb and 205Tl, by far not sufficient for the 107 factor described above. In addition, the − overall efficiency in these studies was found to be less than 10 6, and in the most optimistic − extrapolations it was difficult to see how this could be brought to values better than 10 4. A novel variant of AMS was then proposed, based on the recent developments of Schottky mass spectroscopy in a high-energy ion storage ring, following the acceleration of ions to several hundreds of GeV per nucleon energies and full stripping Radon et al. 27. The heavy-ion storage-cooler ring ESR at the GSI Helmholtz Zentrum in Darmstadt, Germany, is uniquely suited for providing a clear-cut solution of the “isobar problem” being such a serious obstacle for tandems. After acceleration in a high-energy synchrotron all atomic species can be fully ionized, and transferred to the ESR where they will be electron- cooled, affecting a common sharp velocity for all stored ions. In this case, the revolution frequency in the ESR depends only on the mass-to-charge m/q ratio of the ions which is—for fully stripped atoms—equal to m/Z. Therefore, isobars of different nuclear charge Z appear at widely separated revolution frequencies and are easily resolved. One also gets rid of any isobaric molecular contamination, which often represents the most serious obstacle for tandem-based AMS. Moreover, the ESR provides the ultimate detection limit for heavy Z>45,highly charged ions: even one single stored and electron-cooled ion can be unambiguously detected see Figure 5. The high resolving power and ultimate detection sensitivity of the ESR enabled “Schottky mass spectrometry SMS” that delivered new and precise atomic masses for more than 180 nuclides Litvinov et al. 23. Related studies on other heavy-mass radioisotopes have demonstrated the needed separation factor, but the overall efficiency − cannot be brought above 10 4 for a heavy ion around mass 200 due to ion source efficiencies, the need for multiple stripping, and the general transmission losses experienced in the chain of accelerators to reach the required high energies. A variant we shall consider now is to 12 Advances in High Energy Physics

0.7 8 74 754 keV

W 0.65 143mSm62+ 143g 62+

171 Sm 0.6 ) 7 0.55 (1 particle) (1 particle) a.u. ( 0.5

+ 0.45

6 73 + 72 Ta 0.4 Intensity 168 Hf ) + 0.35 71 5 166 m/∆m ≈ 700000

a.u. 0.3 Hf ( + 33800 33900 34000 34100 34200 34300 34400 34500 75 164 Frequency (Hz) Re 4 + + 89 173 71 + + + + 73 Intensity 74 Tm Lu 76 71 + W W 159 70 164 + 3 + Os + Lu + 168 71 66 170 + 72 Yb + + 72 + 175 163 + 68 Er + 69 71 67 70 Ta + + Ho 161 + 67 Hf 68 Er 68 158 78 66 Er Hf Yb 166 Lu 152

2 165 + Ho + 157 Pt + Tm 154 183 159 + + + Dy + Tm 161 62 60 + 75 + 154 180 65 + 64 + 64 63 156 72 + + + 152 157 59 + 64 65 Sm Re Nd 65 55 Tb 53 Tb Ta Dy 62 Gd I Pr Tb 172 1 138 m,g Gd Cs Dy 147 165 m,g 141 145 Eu 122 138 149 143 147 127 150 150 143 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 Frequency (Hz)

Mass known

Mass unknown

Figure 5: Schottky spectra versus the down-scaled revolution frequencies of stored and cooled nuclei, circulating in the experimental storage ring. Each of the lines shows a diﬀerent nuclear species. Since for cooled ions a one-to-one correspondence exists between their revolution frequency and their mass- to-charge ratio, those spectra provide a highly precise mass spectroscopy. The inset shows the Schottky signals of two Sm62 ions, one of them in the nuclear ground state at the higher frequency, the other one in a metastable state at an excitation energy of 754 keV. This demonstrates convincingly the capability of the ESR to detect—with ultimate sensitivity—one single stored and cooled highly-charged ion together with its accurate mass determination Figure by courtesy of Litvinov et al. 23.

inject a lower charge state into the synchrotron accelerator and then to strip at the injection into the storage ring with very high efficiency. This eliminates, in effect, one stripping stage with a resulting broad charge state distribution and thus increases efficiency. Estimated to be − around 10 4 or better, the exact value needs to be experimentally determined. So there has been considerable progress in this “storage ring variant” of AMS, but the overall detection efficiency that can be finally reached finally is still unknown. Over the past decades, several methods of trace analysis based on laser spectroscopic techniques were proposed and very successfully developed. The high degree of selectivity obtained by these methods is a result of resonant laser-atom interaction. Atoms of different elements interact resonantly with light at significantly different frequencies owing to differences in their atomic structure. Atoms of different isotopes of the same element exhibit isotope shifts, a small change in their resonance frequencies caused by the variation in the nuclear mass and charge radius. By tuning the laser frequencies precisely onto the resonance frequencies of a particular isotope, one can selectively excite, ionize, or manipulate the atoms of this isotope while having a much smaller effect on the other isotopes and elements. Advances in High Energy Physics 13

At the moment the recently developed method of trace analysis with an atom trap appears, with some caveats, a very promising approach. Atom trap trace analysis ATTA is a laser-based atom counting method originally developed at Argonne National Laboratory Chen et al. 28. Its apparatus consists of lasers and vacuum systems of tabletop size. At its center is a magnetooptical trap, a MOT Raab et al. 29. The MOT captures atoms of the desired isotope by using laser beams. When the laser frequency is tuned to within a few natural line widths on the low-frequency side of the resonance of the targeted isotope, only atoms of this particular isotope are trapped. Atoms of other isotopes are either deflected before reaching the trap or allowed to pass through the trap without being captured. The detection method e.g., a sensitive CCD camera takes full advantage of the high selectivity of photon burst spectroscopy. A single atom can be trapped and observed for 100 ms or longer, during which 106 fluorescence photons can be induced and as many as 104 photons can be detected. These advantages allow single atoms to be counted with a high signal-to-noise ratio, and, since the selectivity depends exponentially on the number of photons detected in a burst, they also ensure a superb selectivity. Indeed ATTA is immune to contamination from other isotopes, elements, or molecules. For the present proposal we suggest to focus on the Schottky scan developments at the GSI- Darmstadt ESR heavy-ion storage ring. The crucial question that has to be answered in test and pilot experiments is whether or not an overall detection efficiency including all − steps from the ion source to the storage ring of 10 3 or better see the reasoning above for the 205Pb ions can be achieved. In parallel we will carefully observe the progress and the developments in ATTA technology with regard to trace analysis of lead isotopes. The sensitivity improvements are key to sample size. The present proposal to obtain the order of 10 kg lorandite from the Allchahar mine is close to the needed sample size that current trace technologies require. But it is not quite there yet. Any further improvements in the detection techniques, which we believe will occur, have the potential of adding the necessary safety margins. However, this requires serious development and study. Any progress made though might not only benefit the present 205Pb proposal but radioisotope trace analysis in general.

3. Summary

It has been shown that the first two of the four major problems of LOREX, as addressed at the beginning of this work, namely, the age of lorandite and the background-induced amount of 205Pb, have been meanwhile successfully addressed and are near to a final conclusion. In particular, the determination of the erosion rate by cosmogenic nuclides was decisive for getting a first but reliable estimate for paleo-depth and, therefore for the amount of background. Furthermore, it has been demonstrated how the measurement of the bound- beta decay probability of bare 205Tl can provide the unknown neutrino capture probability into the first excited state of 205Pb. The corresponding experiment has been accepted for being performed at the GSI Helmholtzentrum. Finally it has been shown how the small amount of 205Pb atoms to be expected could be determined by the Schottky noise technique at the ion storage ring of GSI which provides single-ion detection sensitivity. Taking into account the present-day state-of-the-art of all the techniques needed to solve the four problems of LOREX, we conclude that it is realistic to expect the first result for the solar pp neutrino flux averaged over the last 4.2 million years in a foreseeable future. This number will have most probably still a large error margin in the order of 50% or even more, at the 68% CL. We expect, however, that this accuracy could be improved with time, and that it might approach a level of ≤30% as discussed by Pavicevi´ cetal.´ 30. 14 Advances in High Energy Physics

Acknowledgment

The authors thank the FWF - Wien for supporting this project by grant P 20594.

References

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Research Article Exclusive Reconstruction of B-Decays with Missing Neutrals

M. Dima

Department of Computational Physics, Horia Hulubei National Institute of Physics and Nuclear Engineering, Atomistilor Street 407, P.O. Box MG-6, 76900 Bucharest, Romania

Correspondence should be addressed to M. Dima, [email protected]

Received 6 September 2012; Revised 21 October 2012; Accepted 23 November 2012

Academic Editor: Bogdan Mitrica

Copyright q 2012 M. Dima. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Often decay channels that are of theoretical interest cannot be reconstructed exclusively due to missing neutrals such as neutrinos, or due to single-track vertices. This situation appears both in underground astrophysics experiments as well as in conventional accelerator experiments. A method to “recover” such missing particles from their kinematics and reconstruct “exclusively” the modes would beneﬁt both domains in a number of ways. The main idea is to combine 4- momentum conservations in vertices with available geometric information in the event. The paper 0 − − − − 0 gives details of such methods on the Bs → Ds K , Ds → K K π π prototype decay, which also encounters 2-fold ambiguities in its solutions. Such ambiguities can be lifted and the paper shows how, while also addressing the potential the method has in physics analyses and detector studies.

1. Introduction

The kinematics of decay modes with a missing particle, usually an elusive neutrino, are of interest in both underground astrophysics experiments as well as in conventional accelerator experiments. Exclusive reconstruction in today’s new generation experiments is important for precision physics, performant background rejections needed in rare decays, and so forth. Some modes that are of considerable theoretical interest, from the experimental point of view, pose inherent diﬃculties with missing neutrals and single-track vertices. While such is not an impossible situation since the vertex must be somewhere on the track, the precise location eludes in general the reconstruction of the mode. Nonetheless, in certain cases, information from the rest of the event provides this capability—in general in the form of 4-momentum conservation in subsequent vertices. Work on recovery using dynamic information has been explored before 1, 2, not necessarily in association with vertexing. Code addressing 2 Advances in High Energy Physics

K+ − π0 K π−

− Ds

Location from 4-momentum conservation

K+ 0 Bs

0 − − − 0 Figure 1: Topology of the mode considered in the absence of magnetic ﬁeld: Bs → Ds K K π π K . The line Q is the perpendicular from the D-vertex onto the kaon track.

such methods stems from the days of the CLEO collaboration, KWFIT 3, 4 and of BaBar Collaboration, KinFitter 5. In underground experiments the geometric equivalent to accelerator B-physics programs are strange-particle decays 6, 7, where kinematic imprecisions associated with the missing neutrino and a traditional lack of some form of vertexing have prevented exclusive reconstruction of the modes. At the new underground astrophysics experiments such as LAGUNA 8–12 tracking-vertexing facilities are being discussed in some of the studies. The methods studied could in principle be applied for all “stealth” particles neutrino, π0, other neutrals decaying further downstream. The objective in such cases is to recover if possible exclusively the event, by combining conservation equations and geometric aspects in the decays. The case made in this paper is for tracking-vertexing assemblies in underground astrophysics experiments and for more precise vertexing in accelerator-based experiments. 0 − − − − 0 Consider the prototype mode Bs → Ds K , Ds → K K π π , which is of interest γ π0 for CKM measurement, however, with a somewhat fair branching ratio. With in the final state the branching ratio is roughly equal to that without the π0 13, thus putting the two together essentially doubles the statistics. Reconstruction of the π0 would in principle be possible in the calorimeter, however, with less resolution than using tracking. Fortunately there is sufficient information in the event for reconstructing the mode without explicit calorimeter information on the π0—in principle with better resolution also. This information is from 4-momentum conservation in the B-andD-vertices. A particular 2- fold ambiguity from the quadratic equations arises in this and other modes. It is important to be able to lift this ambiguity without imposing cuts which due to detector resolution can eliminate signal. Figure 1 shows the topology of the event in the absence of magnetic field— such as for the LHCb experiment at the LHC. A small track bending over the vertexing region O can also be included, in the form of an III helical correction, giving a solution also for other detectors with full-strength magnetic field in the vertexing region. Vertexing methods reject reasonably well QCD backgrounds originating at the interaction point IP, with some resolution there around; however, other B-modes can Advances in High Energy Physics 3 constitute significant backgrounds. One such mode is the sister mode with pion in the B- vertex, roughly 4-5 times more abundant. Kinematically and topologically similar modes B0 B0 from d also exist—the latter roughly 3 times more abundant than s . Although there B0 is no exact replica of the mode in d version, there are many modes with nonnegligible branching ratios that “losing” one track can mimic this mode. Due to the similarities in topology displaced vertices and kinematics B-masses, center of mass decay energies,the method cannot distinguish between such cases—not with current detector resolution. The only remaining solution is performant Particle ID, making sure that the B-vertex track is B0 B0 a kaon d being less “kaon-productive” than s and that there are two kaons present in ff B0 the D-vertex. All other kinematic parameters o er little protection against d modes—due to the high boost factors, mass similarities, and center of mass decay energies. A pleiad of such parameters has been studied: the discriminant of the second order equation, pointback, reconstructed invariant masses, angles between track-combinations or decay-planes, 2-3 parameters combinations of the aforementioned, and so forth. For all the detector resolution was insufficient to tell apart the current mode from its sister mode best achievable ca. 41% B0 rejection , or from other d originating modes ca. 45% rejection .

2. Dynamic Vertexing

The 4-momentum conservations in the B-andD-vertices are 2 2 2 2 EK ED MB pD pK 2pDpK , 2.1 2 2 2 2 ED − Ev mπ pD pv − 2pDpv , where v refers to the “virtual” particle having 4-momentum equal to the sum of the charged tracks in the D-vertex. These can be rewritten as

2 2 2 MK MD − MB pDpK EKED, 2 2.2 2 2 2 MD Mv − mπ pDpv − EvED. 2

Since pB pD pK, the three vectors lie in the same plane. Also, the B-vertex is on the kaon track, hence pD λQ μpk, the two constants λ and μ being determined from 2.1 as linear functions of ED with some coeﬃcients:

λ αED β, 2.3 μ aED b.

2 2 2 2 However, pD ED − MD λQ μpK , resulting in a second order equation in ED: 2 2 2 2 2 ED − MD ED αQ apK ED · 2 αQ apK βQ bpK βQ bpK . 2.4

For convenience Q has the direction of Q in the ﬁgure and the absolute value of 1 GeV/c. 4 Advances in High Energy Physics

The ambiguity raised by the second order equation is solved in favor of the “”sign. What actually happens is that βQ bpk is rather small and the equation looks like 2 2 2 2 ED − MD χ ED 2χE D . 2.5

The solution with “−” sign is therefore negative in value, hence unphysical. Once ED is known, the coeﬃcients λ and μ are known and so are pD and pB. Having the D-vertex and −pD pointing back at the kaon track, a B-vertex can be now inferred. The problem is formulated as follows: the B-vertex is a point inside the 1σK kaon track error-tube with the property that aiming along the pD direction, the D-vertex is missed by about 1σD, while aiming along the −pB direction, the IP is missed by about 1σIP.The r − λ n n p /p r kaon track is parametrised as 0K K K where K K K, 0K, some origin on the track, and λK, a running parameter describing the track. Therefore, if B is the B-vertex, the above requirements translate into σ −r λ n B 1 kaon track tube, K,from 0K K K , 2 D-vertex ± σD,fromB λDpD, 3 IP ± σIP,fromB λBpB.

This implies minimising the above 3 constraints simultaneously: B λ n − r σ−2 B λ n − r K K 0K K K K 0K −2 B λDpD − vDσD B λDpD − vD 2.6 −2 B λBpB − vIPσIP B λBpB − vIP with respect to the three running parameters λK units m, λD,andλB both in units of m/GeV/c and to B. Annulling the respective derivatives: B − r σ−2n 0K K K λK , −2 nK σK nK − B − vD σ 2 nD D λD , 2.7 −2 nD σD nD −2 B − vIP σIP nB λB . −2 nB σIP nB

Minimising with respect to the B-vertex B, the following is obtained:

− |n n |σ−2 1 −2 x x x B σx − q 2.8 1 −2 xK,D,B nx|σx |nx Advances in High Energy Physics 5 with |n n |σ−2 −2 x x x q σx − |vx. 1 −2 2.9 xK,D,B nx| σx |nx

For the kaon track error tube an extended acception of error ellipsoid was used: one with infinite long-axis. In the case of a round cross-section equal axes the error- ellipsoid operator reduces to the perpendicular to track projector. Therefore in q only the r perpendicular to track error of 0K will contribute to the B-vertex error. Similarly, for spherical error-ellipsoids, the D-vertex and the IP would contribute only with their respective errors perpendicular to nD and nB. This is not exactly the case, both ellipsoids being elongated, the IP along z and the D-vertex along its flight direction. This extra elongation simply translates into the addition of a parallel projector along said directions to the respective error-ellipsoid operators. For the D-vertex the elongation being exactly along nD and greater than the spherical part of the operator, the combined effect in q is the same as having only the spherical part. For the IP the elongation is along z, which is not nB,but almost. So again, to first approximation, only the waist of the IP will play a determinant part in the B-vertex errors. The IP being very accurate waist-wise for the LHCb-IP: σxy 20 μm versus σz 60 μm 14, the main contribution will come from the D-vertex—set by smearing to a typical resolution of this detector 15. The code was tested using a PYTHIA simulation of the LHC environment for the LHCb experiment LHC energy bb events, “HardQCD:gg2bbbar”, for which the tracks were smeared both in momentum value and direction like a needle deviating in direction within an error-tube. The momentum value smearing was chosen such as to give 2-body mass resolutions as those reported by this experiment in literature 16, 17ca. 12 MeV/c2, while the error-tube diameter ca. 15 μm was chosen such as to give the vertex locator resolutions reported in the literature 17ca. 150 μm longitudinally and 25 μm transversally. Once the particle tracks and vertices are obtained in a form simulating detector response, they are fed to the code for reconstruction. Figure 2 shows the reconstructed B-vertex resolution in terms τ d M /cp of proper time, determined from proper flight B B. The physically relevant directions are parallel to flight direction and transverse to this. The method uses 3 constraints combined, hence a rudimentary approximation is to allot a gaussian in the resolution fit for each. The top part of the figure shows the residuals with respect to flight-direction which is almost z-aligned, fitted with 3 Gaussians. The combined resolution is on the order of 32 fs. The bottom part shows residuals transverse to the flight direction approximately the xy-plane fitted with 3 half-Gaussians centered at zero, resolution on the order of 5.4 fs. It is evident that the resolution is dominated by the boost direction flight direction elongated error-ellipsoid. This is to be expected due to the high boosts, where the shallow opening angles among tracks translate pixel detector errors into large longitudinal ones. The obtained resolution is similar to usual resolutions in B-reconstructions achieved in 4 track decays 1840 fs. The obvious advantage here is that although particles are missing, their kinematics helps “recover” them as if they were present and this is an exclusive reconstruction. The method can also be used for detector studies, such as calibrating Particle ID, or calorimetry, in the lepton electron/muon sector. This implies in general using semileptonic modes. Although the traditional leptonic decay of J/ψ is standard, it yields two hard tracks, quite close to each other which in the electron case makes difficult estimating the individual 6 Advances in High Energy Physics

103 Longitudinal

102

−200 −150 −100 −50 0 50 100 150 200 Proper time resolution (fs)

a 104 Transversal 103

102

1 0 5 10 15 20 25 30 35 40 45 50 Proper time resolution (fs)

Figure 2: Residuals of the reconstructed B-vertex with respect to the Monte Carlo position: a projected onto the B-flight direction, b transverse to the B-flight direction. The dimensions are proper time in fs. Three Gaussians were used in the fits in the case of the transverse centered at zero, the global resolutions being ca. 32 fs longitudinally and 5.4 fs transversally—details are in the text. radiative losses. Also Particle ID performs lesser on tracks very close to one another, the real performance used in B-physics being actually better. Therefore, the larger variety given by semileptonic modes would be preferable, if only a pure enough betterthanParticleIDmiss- B0 → D∗− K−π −ν ID rates sample could be selected. Consider, for instance, the mode d l l ππ−π.TheB-vertex provides 3 “clean” pion tracks useful for Particle-ID studies in the hadron sector. The D-vertex would also be good, if only labels could be attached to the tracks. Owing to the large mass difference between kaon/pion and electron, the equations would prevent a vertexable solution if the masses were wrongly attached. However, in the case l μ, the pion and lepton tracks are similar in mass. Still, they are quite different in dynamics, − one coming from a lepton line, united to the baryon half of the reaction via a W , while the other from a continuous quark line. The imbalance in this case would come from the different M momentum properties putting the wrong momentum in lνl , for instance, versus other dynamic quantities in the reaction. In this sense the method can act as a track-labeler in the D-vertex, offering a quite clean sample of B-origin leptons for Particle-ID studies—which is rare. A study was performed for kaon/pion separation power of the method. The mode with no π0 in the final state was chosen. Of the existing tracks in the D-vertex one was purposely reported “lost” to the program and its mass fed to the code. If the kaon track is reported “lost,” but pion mass is given for it to the code, the inner kinematics of the reactions will work out wrong, further influencing the highly nonlinear vertexing procedure described aforehand. The vertexing produces now new momenta for all particles implied and an invariant mass can be recomputed for the “lost” particle’s mass different, but close, to the one inputted. This mass error versus pointback is a criterion that gives a ca. 45% kaon-pion separation. As Advances in High Energy Physics 7

−M pointed above, for leptons additional handles due to inner dynamics exist i.e., lνl and so the rejection power should be better especially for the electron, where the mass is also much lighter.

3. Conclusions

The method aims to recover modes otherwise nonusable, with missing neutrals lost neutrino,orlessprecisecalorimetry. This is very important to both underground based experiments as well as accelerator-based experiments, where background rejection or measurement precision depends on the exclusive reconstruction of the event. The paper lifts the two-fold ambiguity arising in the second order equation involved, which otherwise relied on other criteria pointback for instance which cut on signal. The potential of the method for Particle-ID source studies lepton sector is also discussed. The methods studied could in principle be applied for all “stealth” particles neutrino, π0, other neutrals decaying further downstream. Plans for extending the method could involve these options together with the Particle-ID studies.

Acknowledgment

This work was supported by a Grant of the Romanian National Authority for Scientiﬁc Research, CNCS-UEFISCDI, Project no. PN-II-ID-PCE-2011-3-0323.

References

1 V. I. Goldansky, P. Yu. Nikitin, and I. L. Rozental, Kinematic Methods in High-Energy Physics, vol. 2 of Scientiﬁc Reviews Supplement Series, Physics, Harwood, Chur, Switzerland, 1989. 2 N. I. Starkov and V. A. Ryabov, “Kinematic methods for analysis of neutrino interactions in calorimetric detectors,” Bulletin of the Lebedev Physics Institute, vol. 2000N12, pp. 1–6, 2000, Sbornik Kratkie Soobshcheniya Po Fisike, vol. 2000N12, pp.3–8, 2000. 3 P. Avery, CSN 98-355 Data Analysis & Kinematic Fitting with KWFIT, 1998. 4 P. Avery, Kinematic Fitting Algorithms and Lessons Learned from KWFIT Padua, Computing in High Energy and Nuclear Physics, 2000. 5 BaBar KinFitter, BAD #1061. 6 B. Mitrica, “Asymmetry of charge ratio for low energetic muons,” AIP Conference Proceedings, vol. 972, pp. 500–504, 2007. 7 P. Schreiner and M. Goodman, in Proceedings of the 30th International Cosmic Ray Conference (ICRC ’05), vol. 9, p. 97, Pune, India, 2005. 8 A. Rubbia, “The LAGUNA design study—towards giant liquid based underground detectors for neutrino physics and astrophysics and proton decay searches,” Acta Physica Polonica B, vol. 41, p. 1727, 2010. 9 D. Autiero, J. Ayst¨ o,¨ A. Badertscher et al., “Large underground, liquid based detectors for astroparticle physics in Europe: scientiﬁc case and prospects,” Journal of Cosmology and Astroparticle Physics, vol. 11, Article ID 011, 2007. 10 L. Mosca, “Possibilities for the LAGUNA projects at the frejus´ site,” AIP Conference Proceedings, vol. 1304, pp. 303–311, 2010. 11 LAGUNA FP7 Design Study, Grant Agreement No. 212343. 12 LAGUNA-LBNO FP7 Design Study, Grant Agreement No. 284518. 13 C. Amsler, M. Doser, M. Antonelli et al., “Review of particle physics,” Physics Letters B, vol. 667, pp. 1–6, 2008. 8 Advances in High Energy Physics

14 “LHCb Trigger System,” Nuclear Physics B—Proceedings Supplements, vol. 156, supplement 1, p. 135, 2006. 0 15 P. Spradlin, G. Wilkinson, and F. Xinga, “A study of tagged D0 → hh decays for D0 − D mixing measurements,” LHCb-2007-049 Report. 16 S. Borghi, M. Gersabeck, C. Parkes et al., “First spatial alignment of the LHCb VELO and analysis of beam absorber collision data,” Nuclear Instruments and Methods in Physics Research A, vol. 618, no. 1–3, pp. 108–120, 2010. 17 A. Augusto Alves, L. M. Andrade Filho, A. F. Barbosa et al., “The LHCb Detector at the LHC,” Journal of Instrumentation, vol. 3, p. S08005, 2008. B0 ﬀ J/ψf 18 R. Aaij, C. Abellan Beteta, A. Adametz et al., “Measurement of the s E ective Lifetime in the 0 ﬁnal state,” Physical Review Letters, vol. 109, Article ID 152002, 8 pages, 2012. Hindawi Publishing Corporation Advances in High Energy Physics Volume 2012, Article ID 801982, 10 pages doi:10.1155/2012/801982

Research Article Perspectives on Entangled Nuclear Particle Pairs Generation and Manipulation in Quantum Communication and Cryptography Systems

Octavian Danil˘ a,˘ Paul E. Sterian, and Andreea Rodica Sterian

Academic Center of Optical Engineering and Photonics, Polytechnic University of Bucharest, 313 Spl. Independentei, 060042 Bucharest, Romania

Correspondence should be addressed to Andreea Rodica Sterian, [email protected]

Received 30 September 2012; Accepted 29 October 2012

Academic Editor: Bogdan Mitrica

Copyright q 2012 Octavian Danil˘ a˘ et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Entanglement between two quantum elements is a phenomenon which presents a broad application spectrum, being used largely in quantum cryptography schemes and in physical characterisation of the universe. Commonly known entangled states have been obtained with photons and electrons, but other quantum elements such as quarks, leptons, and neutrinos have shown their informational potential. In this paper, we present the perspective of exploiting the phenomenon of entanglement that appears in nuclear particle interactions as a resource for quantum key distribution protocols.

1. Introduction

Quantum entanglement has long been proven to be the most resourceful method of achieving feasible, high fidelity quantum key distribution over growing distances 1–6. Exploiting entanglement can be done using multiple observables, giving experiments a practical versatility. Polarization entangled states 7, while being very easily obtainable, are very hard to manipulate as they propagate through different media such as optical fibers. On the other hand, time-bin entanglement is harder to obtain, but manipulation requirements, such as temperature, polarization, and propagation velocity, are easier to fulfill. Quantum key distribution 8, 9 schemes that have been applied to regular qubits may be applied to qubits that result from nuclear interactions. The conventional method of achieving quantum key distribution is generating quantum elements photons and manipulating them as such as to obtain the desired states on which quantum key distribution operates. To this extent, quantum key distribution can be obtained using either single or entangled states, and due 2 Advances in High Energy Physics to the nature of the two, there have been devised two different protocols that extract the information from the generated states. The first protocol 8, created by Charles Bennett and Gilles Brassard—BB84 employed singular photonic states, with no coherence between their informational values. The information-carrying observable was the polarization of the photon, on which the two participants carry out local operations, that is, rotations in the analysis vector bases and classical communication in which the two participants communicate a part of their informational operators either the values obtained or the analysis bases in which the single states are detected. The second protocol 9, elaborated by Artur Ekert—Ek91, is derived from the BB84 protocol but differs from it in an essential manner: it employs bidimensional, maximally entangled states, also called Bell states. The usage of entangled states has major advantages, and the source that supplies the participants need not be a part of the particular setup of the transmitter. Thus, participants can share random keys supplied by a dedicated encryption server. Any quantum key distribution protocol makes interceptor detection possible, by verification of the qubit error rate that any foreign measurement induces onto the states prepared by the two participants. The qubit error rate is calculated either by direct verification of the raw keys obtained after single state communication or by carrying out standard Bell measurements, in order to establish entanglement quality after key communication. Optimal attacks 9 which are the most efficient in the present days induce an error rate of approximately 15%. Thus if after key distribution the two participants have two keys that differ with more than 15%, they drop the conversation on the count that an interceptor was found on the channel. In practical setups, entangled states are considered to be favorable to single states, simply by not requiring any participant to employ costly equipment on this setup. A big disadvantage, however, is that because of the no-cloning theorem, the created entangled states cannot be reproduced. While entanglement does not decay naturally, depolarization and thermal interaction are liable to destroy the created state over long communication distances. Secure quantum key distribution was achieved over a distance of several kilometers in a single-mode optical fiber 10–12, and although promising, long- distance communication may just be too much for conventional photon pair entangled state communications. To overcome this obstacle, one may consider using other information carriers that have better propagation performances than photons. The best candidate for this task is the neutrino, known for the fact that it travels through any medium without any absorption, making long-distance communication a very feasible idea. The goal of this paper is to highlight the perspective of using entangled nuclear pairs in quantum key distribution protocols. The paper is structured as follows. Section 2 covers the theoretical background of entangled states and quantum key distribution protocols, Section 3 presents the experimental setup for entangled photon pairs, and Section 4 treats the perspective of employing nuclear particles as entangled states. Finally, conclusions are drawn in Section 5.

2. Theoretical Background

The quantum description of nature has been developed as a consequence of Gedanken experiments 13, which revealed that quantum elements exhibit a dual behaviour of particle and wave, which can be projected into the desired state depending on the type of measurement carried out. The main advantage of quantum states is that for any orthogonal basis |0 and |1, all quantum states can be described as a superposition of the two, Advances in High Energy Physics 3 as |ψ α|0 β|1. The probability amplitudes α and β satisfy the relation |α|2 |β|2 1— the normalization equation. In the bidimensional case, representation of the compound state is written as |ϕ |ψ⊗|ψ |ψψ. Any compound state that can be factorized into the compounds is called a separable state. However, some physical interactions between quantum elements yield states of the form 7

± ψ α|01 ± β|10, 2.1 ± φ α|00 ± β|11, which cannot be decomposed into their compounds. These are formally deﬁned as entangled states. Correlations between the states hold for any distance between the quantum elements, and√ for their entire lifetime should no external destructive interaction occur. For α β 1/ 2, maximally entangled or Bell states can be obtained. Discerning between separable and entangled states is an important prerequisite for applications. The most general method employed is the veriﬁcation of Bell’s inequality 10, 11. It has been shown that all separable states respect the relation

Ea, b Eb, c Ec, d − Ed, a < 2 2.2 with Ex, y being the experiment of measuring the informational values of two systems given by variables x and y,withresultsEx, y±1. Entangled states violate this inequality, yielding √ Ea, b Eb, c Ec, d − Ed, a 2 2 2.3 for maximally entangled or Bell states. Quantum key distribution protocols use quantum states in order to produce naturally and purely random keys that can further be applied into cryptographic schemes such as the Vernam protocol. In addition to this, any eavesdropper that listens in on the communication will leave a trace in the transmitted keys in the form of qubit error rate, should this rate be greater than 15%. As seen in Figure 1, the Ekert protocol consists of an entangled photon pair source that sends maximally entangled states to both participants called Alice and Bob. ◦ ◦ They choose to analyse the incoming photons on three conventional angles—22.5 ,45,and ◦ ◦ ◦ ◦ ◦ 67.5 . Alice uses 22.5 and 45 , while Bob uses 45 and 67.5 . The common polarization angle is set to detect the raw key that will be used for encryption, while the other two angles are used for verification of Bell’s inequality. Depending on the type of entangled states the source supplies, Alice and Bob will ideally obtain either identical or complementary raw keys. The ◦ quality of entanglement can be calculated by randomly selecting states measured on the 22.5 ◦ and 67.5 analysis angles and calculating the Bell inequality. Eavesdropping on the protocol induces a degradation of entanglement, up to a point that the conversation is dropped. Generation of entangled states is achieved through different methods for different quantum elements. In the case of photons, generation of polarization-entangled photons is achieved either by spontaneous parametric downconversion SPDC, which occurs in second-order nonlinear optical media, or by quantum dot experiments. In the case of SPDC, 4 Advances in High Energy Physics

EPR source Quantum channel Quantum channel

◦ ◦ 90 67.5◦ 90 67.5◦ 45◦ 45◦ Classical channel Detection Detection 22.5◦ 22.5◦

◦ 0 Alice Eve Bob 0◦

Figure 1: Scheme of the Ek91 protocol. one pump photon instantly converts into two polarization entangled photons that respect the energy and momentum conservation laws 14, 15:

ωp ωs ωi, 2.4 kp ks ki, where indices p, s,andi denote the pump, signal, and idler photons. Efficiency of entangled − − state generation ranges from 10 12 to 10 7, which leads to a good entangled photon pair rate for pump powers of hundreds of milliwatts. Naturally, the conservation laws hold for fixed frequencies that are almost impossible to maintain constant. This effect is called phase matching. In some nonlinear optical media, the nonlinear optical susceptibility has its sign changed in some regions, which leads to the creation of a locally characteristic wavenumber K that fulfills the relation:

kp ks ki K. 2.5

Thus, as seen in Figure 2, depending on constructive parameters, the desired phase matching considerations can be achieved.

3. Entangled Photon Pair Source Experiment

Having all the previous considerations, entangled photon pair sources that offer up to 1100 pairs/s have been constructed 16–22, with competitive operational parameters. Raw and net visibilities of 97% and 99.5%, respectively, have been obtained, with a Bell parameter of 2.8. The full source setup is illustrated in Figure 3. The layout of the source consists of a 2-Watt Ti : Sa laser pumping a 3.5 cm long, periodically poled lithium niobate waveguide with a 6 μm − poling period, obtaining a type II entangled photon pair with 10 9 efficiency. The generated pair was then transmitted through standard telecom fiber devices to the detection module, where two ultramodern InGaAs avalanche photodiodes, running in gated mode, register the coincidences 23–26. Advances in High Energy Physics 5

Standard + k k waveguide U = ct. + − + − + −−+ −−+ + + − + 1 2 −

k3 Periodically polarized Electrode k2 waveguide Normal deﬀ k1 Inversed deﬀ Tunable K

a b

Figure 2: Entangled photon pair generation devices: a periodically poled waveguide structure; b phase matching and quasiphase matching for waveguides.

SB HWP PBS APD Alice HB-PMF

PPLN/W DWDM Laser ITU 46 DWDM CC

ITU 47

HWP PBS APD Bob Pumping Generation Manipulation Detection

Figure 3: Layout of the source.

In order to successfully transmit the generated entangled state, the signal and idler photons have to be identical for any other measurement except polarization; otherwise the state is inherently destroyed. Manipulation of the photons has been carried out by means of spectral and temporal overlapping. Spectrum overlapping has been achieved by ◦ stabilizing the waveguide temperature up to 0.1 C. The spectrums have been filtered using two adjacently centered ITU channels dense width division multiplexers, that ensure that, if a photon is detected in one filter window, the other one is sure to be found in the complementary one. Thus, deterministic postselection of photons has been obtained as is shown in Figure 4a. Temporal overlapping has been obtained by employing a simple high-birefringence polarization maintaining optical fiber that is used to compensate for the delay between the two different velocities of the photons in the waveguide. This solution is illustrated in Figures 4b and 4c. The detection modules are standard Bell measurement arrangements that consist of a half waveplate, a polarized beam splitter and an avalanche photodiode at each side, and a Soleil Babinet phase compensator placed at one of the two modules. The two photodiodes operate in gated mode, in order to minimize dark counts as follows: when Alice’s photodiode records a photon, it commands Bob’s photodiode to open, over a series of electronic equipment. Bob’s side has a delay line after the polarized beam splitter long enough that the photon that propagates through it spends just as much time needed for the open command signal to reach Bob’s photodiode. The Bell measurements conducted are carried out by forcing Alice to fix her analysis basis and then varying the analysis angle on Bob’s side. 6 Advances in High Energy Physics

ITU 47 ITU 46 150 0.8 nm 0.8 nm 140 100 130 120 110 80 100 90 60 80 70 60 Coincidence 40 50 40 20 30 20 Kilo-coincidences per 2 s Kilo-coincidences per 2 10 0 0 1536 1537 1538 1539 1540 1541 1542 1543 4.1 4.15 4.2 4.25 4.3 4.35 λ (nm) Position (mm)

H Min V Max

a b 500 450 400 350 300 250 200

Coincidence 150 100 50 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Position (mm)

6 m Panda (Thorlabs) Without Panda Noise

Figure 4: Temporal compensation of the photons: a spectrum of the two polarizations with the two ﬁlter ITU windows; b delay induced by the waveguide anisotropy; c delays compensated by 6 metres of polarization maintaining ﬁber.

The measurements were carried out for four ﬁxed analysis bases, the source yielding very good operational parameters as we show in Figure 5.

4. Entanglement with Nuclear Particles

The success of entangled photon quantum key distribution schemes gave way to the perspective of employing other elements as information bearers 17. Nuclear particles, neutrinos in particular, have little absorption in any media, thus being able to propagate through any environment, at great distances. Other particles, such as muons and leptons, present Advances in High Energy Physics 7

15000

10000

5000 Coincidences per 5 seconds

0 0 102030405060708090100 HWP angle (deg)

Alice at {H} {A} {V} Noise {D}

Figure 5: Bell state measurement results.

p′

ντ

− k τ 1 k2 νμ p e−

νe

νμ

Figure 6: Tau lepton decay process.

almost the same absorption pattern through media. Entangled neutrino states can be generated as a result of the decay interaction:

− − τ −→ ντ νμ e νμ νe. 4.1

k k As shown in Figure 6, the two ﬁnal antineutrinos symbolized by 3 and 4 have almost parallel momenta and thus the same helicity. This makes the total spin wavefunction of the interaction a symmetrical one. The antisymmetric nature of fermions implies that the ﬂavor 8 Advances in High Energy Physics wavefunction should be antisymmetric. The wavefunction of the two emitted neutrinos will have the form

1 ψ √ νeνμ − νμνe 4.2 2 for which we have the corresponding Bell inequality P tl νμ, A S 1 P∞, A − Pt ν , A P t ν , ∞ − P t ν ,t ν Pt ν ,t ν l2 e l1 μ l1 μ r1 e l2 e r1 e

≤ 1, 4.3

A t ν t t Pt, ∞ where denotes r2 μ, li ,and ri are the evolving times on left and right sides. symbolizes the case where all three-flavor triggers on the right side are countered. In this case, the neutrino flavors play the role of polarizations, while the time variation plays the role of angles between them in photon experiments 21, 22, 27. Further studies showed that there exists a natural quantum key distribution protocol for entangled neutrinos, should the distances of the four detectors from the source be identical. The entangled state makes coincidence counting at Alice and Bob’s side be either AB {νe,νμ} or AB {νμ,νe}. If an eavesdropper makes a measurement on Alice and Bob’s neutrinos and resends the states, the ensemble state becomes a product state of |ψ |νeνμ or |ψ |νμνe. In order not to be detected, the eavesdropper must be located at the point where the same flavor countings of A1B1 and A2B2 are both zero. Thus, as long as the detection distance of the eavesdropper is smaller than the one considered above, it cannot obtain any information without being detected. This is an equivalent property to that of the conventional quantum key distribution protocols such as BB84 or Ek91. Apart from the tau lepton decay process, neutrinos can be generated from the muon decay process, described by

− − μ −→ e νe νμ,μ−→ e νe νμ. 4.4

The measured observable in detection modules is the muon ratio, and it is known that the cosmic muon flux and the muon charge ratio are closely linked to the neutrino flux. At lower energies, the trajectories of the muons are influenced by earth’s magnetic field. Thus measuring the charge ratio, one obtains quantitative information on the neutrino flux. From the detection point of view, nuclear particles require a significantly larger and more complex detection apparatus. If, for photons, commercially available Peltier effect cooled InGaAs avalanche photodiodes were sufficient to achieve a good key rate, neutrino detection is carried out inductively, by detecting the flavor of muons and recording the decay times stopped in the detector. Separation of the positive and negative muons, prior to decay observations, is made using magnetic spectrometers. One such detector, containing 20 modules, each of 1 m2 surface, each composed of an active layer, a 3 cm thick scintillator, wavelength filters, and photocathodes compose the WILLI detection stage 18–20. This stage has been improved with a rotational module, by removing the lead layers. The mechanical Advances in High Energy Physics 9 frame of the rotor makes the detector able to move both in azimuth and zenith. Minimizing the dark counts can be achieved by using the modules in anticoincidence. The extended air shower miniarray EAS is part of the detection system and is in − charge of measuring the muon charge ratio μ /μ produced by the interaction of a primary cosmic ray with the atmosphere. It consists of twelve detection stations placed at about 50 m from the main detector. Each station consists of four scintillator plates, read twofold by a PMT through a wavelength shifter. The electronic scheme behind the detector array is composed of a threshold discriminator, set at −50 mV, providing as output a logical signal which is passed through an FPGA circuit. From the FPGA, each two signals are passed through an OR logical gate and then multiplexed selectively. The resulting signal is then fed to a TDC and QDC acquisition setup. The usual running time of the detector, however, ranges from tenths to hundreds of days, in order to have a statistically correct interpretation of the acquisition data.

5. Conclusions

Summing up all the ideas described in the previous sections, the perspective of successfully extending technologies used in photonic quantum cryptography protocols to nuclear particles becomes an imminent reality with the discovery of usable nuclear entangled states. The nuclear equivalent of spontaneous downconversion can be used to generate flavor- entangled neutrino states, which exhibit extraordinary propagation properties through all media, and thereby overcoming the long-distance-entangled state degradation obstacle. Furthermore, since there is a clear link between neutrinos and other nuclear particles such as muons, one can establish an observable detection link between the two nuclear fluxes. The link consists of a direct proportionality between the muon charge ratio and the neutrino- entangled state, and it can be exploited in a quantitative matter to establish a raw key rate. Experimental data obtained from setups confirm the feasibility of the theoretical issues and expand the application range of quantum key distribution to the nuclear field.

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