De/Dx Studies with and E Tracks of the ALICE GEM IROC Prototype / De/Dx

Technische Universität München Fakultät für Physik

Abschlussarbeit im Bachelorstudiengang Physik

dE/dx studies with π and e tracks of the ALICE GEM IROC prototype dE/dx Untersuchungen mit π und e Spuren am ALICE GEM IROC Prototypen

Paul Philipp Gadow

Monday 26th August, 2013 Erstgutachter (Themensteller): Prof. L. Fabbietti Zweitgutachter: Prof. L. Oberauer

Betreuer: Sverre Dørheim

Bachelor-Kolloquium: 27.08.2013 Abstract

A time projection chamber (TPC) is a large volume tracking detector measuring coordinates in space and specific energy loss along trajectories of charged particles, even in high-multiplicity events. TPCs have been successfully used in several experiments including ALICE at CERN. The charge amplification is conventionally accomplished by multi-wire proportional chambers (MWPCs), which require gating grids to prevent ions from drifting back into the drift volume and from distorting the drift field, thus limiting the trigger rate to (1 kHz). The use of Gas Electron Mul- O tiplier (GEM) for gas amplification in TPCs has been introduced as an alternative and was successfully implemented in the FOPI experiment at FAIR, Darmstadt [10]. The GEM’s intrinsic ion-backflow suppression presents an oppurtunity to run the detector without gating, allowing higher trigger rates as have been already achieved at the LHC after the upgrade. This thesis investigates the charged-particle identification capabilities of an Inner Readout Chamber (IROC) prototype of the ALICE TPC equipped with a stack of three GEMs by the means of specific energy loss (dE/dx) measurements. The prototype has been tested at the T10 beam line at Proton Synchrotron (PS) at CERN, using beams consisting predominantly of electrons and pions at momenta of 1 GeV/c up to 6 GeV/c, varied over different runs. Energy loss spectra are obtained from reconstructed particle tracks by the method of the truncated mean. From the spectra the relative energy resolutions are extracted and used to extract the separation power between pions and electrons at fixed momenta The energy resolution of the ALICE IROC prototype for different HV settings was in the interval 9 % to 11 % for electrons and in the interval 11 % to 14 % for pions at a beam momentum of 1 GeV/c The results for the separation power between electrons and pions were spread around 4 σ for a beam momentum of 1 GeV/c and around 3 σ for a beam momentum of 2 GeV/c. The obtained values for electrons at 1 GeV and the separation power agree with a previous analysis of the data by Jens Wiechula and Martin Ljunggren [36].

iii

Contents

1 Introduction ...... 1 1.1 The ALICE Experiment ...... 1 1.2 The ALICE-Time Projection Chamber ...... 3 1.3 Analysis of the data sample by University of Tübingen ...... 7

2 Foundations ...... 11 2.1 Particle identiﬁcation ...... 11 2.2 Energy loss of charged particles in matter ...... 12

3 Experimental Techniques and Methods ...... 17 3.1 The ALICE IROC-Prototype ...... 17 3.2 Data Sample ...... 21 3.3 The TPC Reconstruction Chain ...... 24 3.4 Extraction of Speciﬁc Energy Loss Data ...... 30

4 Results and Discussion ...... 33 4.1 Data Selection ...... 33 4.2 Track Reconstruction ...... 36 4.3 Energy Loss Spectra ...... 44 4.4 Comparision of the data with the PAI model predicion ...... 49 4.5 Results and comparision with the Tübingen analysis ...... 50

5 Conclusions and Outlook ...... 55

A List of runs during beam time ...... 57

B Results of the analysis for higher beam momenta ...... 61

C Acknowledgements ...... 65

Bibliography ...... 67

Chapter 1 Introduction

1.1 The ALICE Experiment

The ALICE detector [5], shown in figure 1.1, investigates collision of heavy lead ions (82Pb). In 2010 and 2011 ALICE was operated at a center of mass (cms) energy of 1 √s = 2.76 TeV/nucleon with an integrated luminosity of Lint = 0.16 nb− [36]. The collisions happen in the radial center of the detector. In these collisions a fireball of very high temperature can form due to the high center of mass energy, where a quark-gluon-plasma is created, in which the constituents of the nuclei - quarks and gluons - behave as free particles. The plasma expands adiabatically and cools to a temperature of 2 1012 K, where quarks und gluons recombine to hadronic matter. × The mesons and baryons created in this hadronization process exit the fireball and can be measured in the detectors. A challenge for the detectors is the high track multiplicity. In simulations of Pb-Pb-collisions up to 20 000 tracks in the TPC were predicted [5]. By measuring the collision temperature and the distribution of the created hadrons and comparing them to those of plasma free proton-proton collisions conclusions on the quark-gluon-plasma’s properties can be made.

1.1.1 Physics campaign in the ALICE experiment The long-term goal of ALICE is the precise characterization of the quark-gluon- plasma [31]. The quark-gluon-plasma is assumed to be the state of matter which predominantely existed in the ﬁrst picoseconds to 10 microseconds of the electro- weak phase transition in the big bang model. By determination of its properties, including critical temperature, degrees of freedom, speed of sound and transport co- eﬃcients, a better understanding of quantum chromodynamics as a multi-particle theory can be achieved. Experiments like ALICE contribute towards the characterization of strongly interacting matter at high temperatures by studying rare probes, their collective properties and their hadronization.

1 Chapter 1 Introduction

1.1.2 Upgrade Strategy for ALICE at High Rate To investigate the questions concerned with the quark gluon plasma, the experimental approach taken by ALICE is to increase the collision frequency of 8 kHz to 50 kHz 1 for lead collisions and to increase the integrated luminosity to Lint = 10 nb− [31]. To run a near minimum bias mode, the Inner Tracking System will be rebuilt and the ALICE detectors will be modified to provide a fully pipelined readout, implying a major upgrade of the data acquisition and trigger system to build on ALICE’s capabilities of excellent tracking in a most high multiplicity environment and particle identification over a large range of transverse momenta. The operation of the TPC at a rate of 50 kHz cannot be accomplished with an active ion gating scheme as it has been used until now to prevent the backflow of ions in the drift region of the TPC and therefore prevent distortions of the drift field. With the current setup the TPC cannot be triggered at rates exceeding 3.5 kHz [31]. Therefore the replacement of the existing MWPC-based readout chambers by a multiple-stage GEM stack was proposed. GEMs have proven their reliability in high-rate applications, provide intrinsic supression of ion-backflow and allow the TPC to operate continuously in an ungated readout mode.

Figure 1.1: Artistic view of the ALICE detector indicating the position of the TPC [5]

2 1.2 The ALICE-Time Projection Chamber

1.2 The ALICE-Time Projection Chamber

A Time Projection Chamber (TPC) [32] is an advanced particle detector, which has been successfully used in various particle physics experiments such as PEP-4 [3], ALEPH [9], DELPHI [18], NA49 [2], FOPI [16], STAR [8] [1] and ALICE [5]. Usually a TPC consists of a large cylindrical volume centered around the interaction vertex, which is inside of a solenoid magnetic field and filled with gas. The TPC is the main component of the ALICE detector and is able to determine tracks, measure the particle’s momentum, determine vertices and identify particles by analyzing the particle’s energy loss. A TPC makes use of ideas from MWPC detectors and drift chambers and is essentially a large gas-filled cylinder [28]. Due to its size the ALICE TPC is separated in two parts by a high voltage electrode at the center. A uniform electric field along the beam axis is created by the application of voltage between the endcaps of the cylinder and the electrode. A magnetic field parallel to the beam is applied for measuring the particles momentum and to reduce the transverse diffusion of drifting particles in addition. Since the electric field has to be highly homogenous to obtain a good spatial resolution, a so-called ”field cage” consisting of a series of field strips surrounds the cylindrical volume and divides the potential from the cathode stepwise down to the anode, so that distortions of the drift field are minimized. The active volume of the ALICE-TPC is 88 m3 and consists of a cylinder which spans 500 cm along the beam pipe and extends from 85 cm to 250 cm in radial di- mension [5]. The cylindrical field cage is filled with a Ne/CO2 (90/10) gas mixture with 100 ppm H2O, less than 1 ppm O2 and less than 10 ppm of other gases, but also other gas mixtures were tested [36]. In the center of the chamber one can find the drift electrode, which is held at a potential of 100 kV. The end plates consist of 18 sectors each covering 20◦ in azimuthal angle, where multiwire proportional chambers (MWPCs) are seated on top of cathode readout pads. They are shown in figure 1.2 together with the coordinate systems of ALICE. The trapezoidal detector elements in radial distance of 84.4 cm to 132 cm to the center of the cylinder are called In- ner Readout Chambers (IROC), whereas the detector elements in radial distance of 134.6 cm to 246.6 cm are called Outer Readout Chambers (OROC). The detector covers almost a full solid angle of 4π. The ALICE TPC’s spatial resolution is 300 µm and its dE/dx-resolution is 5 7%. The potential applied to the drift cathode results − in a constant drift field of 400 V/cm throughout the detector volume [22]. Using the gas mixture of Ne/CO2 (90/10) the maximum drift time is 88 µs . The MWPCs provide a gain of around 7 103 [5]. × 1.2.1 Principles of Operation of the ALICE GEM-TPC While in the traditional TPC the ends of the cylinder are covered by a sector array of proportional anode wires to cause gas amplification of the primary ionization

3 Chapter 1 Introduction

Figure 1.2: IROCs (blue) and OROCs on an endcap, shown together with the ALICE coordinate systems. charge carriers, in the ALICE GEM-TPC GEMs take the role of the anode wires. After the gas amplification the charge carriers induce a signal on the readout pads behind the amplification stage. In contrast to MWPCs, electrons instead of ions induce the signal in a GEM-TPC, resulting in a much faster signal with different polarity, which is of advantage in a high multiplicity environment to prevent pileup. As the cylinder is centered on the interaction point of a collider, particles emanating from this point pass through the gas filled chamber, ionize the gas molecules and produce ions and free electrons, which drift towards the endcaps (in case of the ions to the drift electrode). This process is illustrated in figure 1.3. When the electrons reach the end caps, they are accelerated by the electric field of the anode wires of the MWPC and produce an electron avalanche by ionizing additional gas molecules during the acceleration. The coordinate, where the primary electron was created by the ionizing particle, can be calculated from the signals induced on a plane of cathode pads below the anode wires. The projection of the space point on the pad plane is given by the center of gravity of the amount of charge induced on the pads. The third coordinate along the cylinder axis is given by the drift time of the electrons produced by the ionizing particle. While operating a MWPC TPC, space charge accumulates in the drift volume due to positive ions drifting back towards the central cathode and distorts the drift field. In MWPC TPCs this is prevented by placing a gating grid just before the anode wires, so positive ions are captured at this grid and inhibited from entering the drift volume. In high multiplicity experiments with high trigger rates however, a gating grid cannot be used, since the gating only works for trigger

4 Chapter 1 Introduction — The time projection chamber

A Time Projection Chamber (TPC) [NM78] allows three-dimensional measurements of particles traversing a gas volume. TPCs have been and currently are successfully employed in many experiments such as PEP-4 [M+83], ALEPH [A+91], DELPHI [B+89], NA49 [Wen98, A+99b], STAR [A+99a, A+03] or ALICE [A+10]. Ionizing particles create electrons by ionizing gas atoms in a large cylindrical formed volume. The gas volume usually covers the full 4p solid angle around the interaction point. The electrons are separated from the remaining gas ion by an electric field. The electrons then drift toward the amplification unit at the end cap of the gas volume where they are multiplied in a gas ionization process. A strong magnetic field parallel to the drift direction reduces the transverse diffusion. Figure 1.1 shows a schematic view of a TPC. Usually, Multiwire Proportional Chambers (MWPCs) are used as amplification unit. But Gas Electron Multipliers (GEMs) [Sau97] seem1.2 to beThe an even ALICE-Time better alternative, Projection because they Chamber intrinsically deter ions created in the amplification process from drifting back into the drift volume. Once in the drift volume, ions stay relatively long there compared to electrons, because

Figure 1.1: Schematic view of a GEM-based TPC. Figure 1.3: Schematic ﬁgure of a GEM-based TPC [17]

rates up to (1 kHz). GEMs with their intrinsic ion-backﬂow supression present a O 1 possible choice to overcome the necessity of a gating grid in a TPC.

1.2.2 Gas electron multipliers for gas ampliﬁcation F. Sauli presented GEMs as a possible device for charge multiplication [35]. GEMs are a composite grid of two metal layers separated by a thin insulator. control density of GEM wires convenience, efficiency GEM GEM with charging avalanche the Fig. drift the lower comparable avoid 532 a regions Using GEM amplification Fig. 10 MWPC, The 5.9 The . the cm2 central 3. 2. MWPC GEM region, . a keV electrode, is electrode at detector. Schematics discharge mesh a Computed channels test . the thin can MWPC and of collimated schematically up positive . field grid “Fe for drift multiplying assembly channels a be to . on printed problems. in gaps, drift takes the lines is . easily transfer the the Due X-ray of the has a electric problems of and along installed . volume potentials; MWPC drift GEM the contrary, have X-ray intrinsic place; a . center; to been circuit used reduces disentangled. multiply, source test . regular shown the voltage. plane field the of been at . replacing is modified, source, chamber to electrons focusing at was charge ground . added. great board in central can spread F. demonstrate plotted. this defines has image the . in process the For Sauli operated depending . drift Fig. the been outer care used one allows multiplying holding . potential, For is ionization effect replacing due released field distortions I the operation . into 3. cathode obtained; for Nucl. has used; most of edges. . A to sensitive the the to with of and lines, . standard, collection the been on diffusion. Instr. of the and maintain measurements. channel. . to in operation one of produced through Above 5 of the this potentials. verify the to field, a the X avoiding to taken and cathode +v ‘VC ‘VC the volume standard 5 values study, anode easily upper 10 Only high A Meth. cm2 two and full For the the the the of to in X in Phys. the together corresponding creased. MWPC characteristics they any to cess, distribution ceeds Increasing at kV), Keeping recorded tion good the potentials rate according flatness tolerant varying transferred influence voltages mesh from (- intensity of channels, charges variations active measured independently can MSGC, results gain covered maximum affected these absence identical gain of Due In To The be 104), Res. charge, 8 - detector envisage detector consequence 90-10, capability,

Figure 4.1: Electron microscope photograph of a GEM foil. The length scaleaffect is indicated at the bottom. Figure 1.5: Computed implying the choice loss the 140 tested order adjusting keV obtained the rates. investigate to area; uniformity A exhibit the of about with to is the by in of At keeping the collimated sticking with on the for negative the direct 386 across drift by to in in

V electric ﬁeld in the mul- X-rays charge, other the measurements variation recorded

Figure 1.4: Close up view ofthe a GEM under an elec- set - mechanical used charging-up charging drift Coupled allowed upper is to is the experimental either the very with - detector rate the photons the the displacing V,,, (1997) the implies to and drift a 3 argon-dimethylether drift not before region V,,, at the the grid; avoid component. full the the pre-amplification mm’. MWPC drift for

charge tiplying hole [35] direct voltage to

tronMWPC microscope [36] V,,, high gain to capability drift possible a without transferred moderately of voltage from to at affected velocity, detector further, GEM well 8 and the efficiency 531-534 at all pre-amplification = MWPC voltage it to up of use has a the properties: keV that response converting breakdown; into In the dipole a 50 = electrode spectrum; measurements pre-amplification imperfections detector. can is collection of a transferred the pre-amplification a processes itself. 0; from known order ?4% a been mesh, above were needs. the high-rate beam insulator V, pre-amplification, on necessity moderate the remarkably generator; the Fig. gain by the a also collimated has diffusion of providing field potential. a gain of charge quenched standard GEM exposed insulator; to the - channels. of realized which it pre-amplified signal 4 from GEM been at there transfer space-charge - in be characteristics, the 500 reductions be is regions inside discharges shows of the 10’ fixed in pre-amplification from (DME) detector, convenient the conductivity surfaces in exploited energy is of the described factors and and a to the exposed the equals is detector begins to may counts includes source similar constant, 55Fe a progressively generator. The MWPC at the potential in factor of gas using the no structure the factor The - increasing have Lorentz moderate GEM irradiated defects in constant the this 2000 channels, difference resolution

implying 5 pulse drift however close spectrum induced mixtures; such are preliminary the charge within the mrne2 first to dominated across conditions to to ionization to only around excessive around here. case, has although mesh volume. possible material without propor- V. operate appear, (- with region; control is a direct. height angles in as to GEM rates been This little high very gain total pro- The s-l, area - one ex- the ten the the the the the in- by be of in 6, 6, is at a a 1

Figure 4.2: Garﬁeld / Magboltz simulation of charge dynamics of two arriving electrons in a GEM hole [Bohmer:2012wd]. Electron paths are shown as light lines, ion paths as dark lines. Spots mark places where ionization processes have occurred. The paths have been projected on the cross section plane.

25 Chapter 1 Introduction

Typically, a GEM consists of a 50 µm thin Kapton foil clad with a 5 µm thin layer of copper on both sides, etched with a regular matrix of open channels in a photo- lithographic process. In this way a dense (104 holes/cm2), regular pattern of holes is formed, which can be seen in figure 1.4. Due to the etching process, the holes have a double conical shape with an inner diameter of 50 µm, an outer diameter of 70 µm and a pitch of 140 µm. A GEM foil with the electrodes kept at a suitable potential difference (typically 200 - 400 V) can amplify the charge drifting through the holes by multiplication of the electrons [36]. Since the field lines are focused in the holes, as can be seen in figure 1.5, the resulting fields in the GEM holes are very high ( (50 kV/cm)), so the electrons O are accelerated in the holes and ionize gas atoms. The created electrons and ions are accelerated as well, thus creating an avalanche. Multiple GEM foils assembled in a stack in the same gas volume allow even larger effective amplification factors in a succession of steps. The electrons created in a hole are extracted to the next amplification stage, whereas the ions follow the field lines either on the cathode-side of a GEM foil, where they recombine, or go back to the drift volume of the detector. The process of avalanche formation and the principle of ion-backflow are depicted in figure5.1 1.6. Sources and Suppression of Space Charge

Incoming Backdrifting ion primary electrons Low drift field Low drift field

High High extraction field Secondary ions extraction field

(a) (b)

FigureFigure 1.6 5.2:: Working Working principle principle of a of GEM: a GEM: a) Incoming Incoming primary primary electrons electrons follow are the fieldguided lines along of the lowthe drift field field lines into of the the hole, low where drift the field acceleration into the of the hole, high where electric fieldavalanches causes avalanche of electron-ion multiplication pairs are of electron-ion generated pairs.(a). The b) The asymmetric small mobility field of theconfiguration ions together of with low an drift asymmetric field and field higher configuration extraction prevent field together the backflow with of the ions insmall the drift ion mobility volume [17]. lead to ecient back-flow suppression (b).

energy to ionize another atom. An avalanche of secondary electron-ion pairs 6is produced. This is the principle of gas amplification. The field strength is maximal inside the holes, especially at the rim resulting from the double- conical cross-section of the hole structure. Here, most of the electron-ion pairs are created (Fig. 5.2(a)). The e↵ect of intrinsic ion back-flow suppression is imaged in Fig. 5.2: The field lines of the drift field are squeezed through the holes in the GEM foil, guiding the incoming primary ionization electrons into the hole. The charge avalanches are generated primarily at the edges of the holes, where the field strength reaches the highest values. The small mobility of the ions and smaller di↵usion of the ions compared to electrons prevents them from drifting into the hole’s center, and they are consequently eciently collected on the GEM’s surface. This mechanism prevents them from reaching the drift volume again. The electrons, on the other hand, reach the extraction region below the GEM in great number. Both e↵ects are enhanced by the asymmetric field configuration (Fig. 5.2(b)). Multiple GEMs can be mounted in series and thus combined to a so- 4 called GEM-stack, further increasing both the e↵ective total gain (Ge↵ 10 ) and the ion back-flow suppression. In the panda TPC three GEMs will⇠ be combined in such a stack.

55 1.3 Analysis of the data sample by University of Tübingen

GEMs have been successfully employed in GEM-based tracking detectors, used in the COMPASS experiment at CERN [26]. GEMs have been successfully used for gas ampliﬁction in the FOPI TPC [10], in LHCb [20] and TOTEM [37].

1.3 Analysis of the data sample by University of Tübingen

An analysis of the data sample was done by Jens Wiechula, University of Tübingen, and Martin Ljunggren, Lund University, in order to evaluate the dE/dx measurement capabilities of the IROC prototype [36]. The methods used and the results shall be reviewed and briefly discussed. The data obtained by means discussed in chapter 3 consisted of signals with amplitude, time and pad ID. Only samples within a time interval 1 µs to 4 µs were accepted. Gain equalization was realized by using the electron tracks and normal- izing the maximum charge for each pad to the median, thus producing a gain map for each run. The maps for all runs were averaged resulting in a map used for gain corrections. Because sector gaps were still visible in the gain map, the rows 9, 17, 25, 32, 39, 45, 51 and 57 of the readout pad were excluded from the analysis. Since the front-end cables of the first two pad rows were mapped wrong, the gain correction algorithm was only sufficient for 46 pad rows to which the analysis was confined. A simple clustering was applied on the signals by looking for local maxima of the amplitude on pads and combining the pad with the maximum amplitude in the center with the 8 adjacent pads (or less in corners) and if those also had a signal with their neighbours to a cluster. To be considered a local maximum, the amplitude of the pad had to exceed 4 ADC counts and in addition 2 samples above the threshold were required. The position of the cluster was obtained by a center of gravity method by calculating the amplitude weighted average in pad and time direction. A track finder combined the clusters to tracks. A track is supposed to have at least 10 clusters and can have up to 3 gaps between clusters. The track finder starts with the cluster in the last pad row and associates clusters of the next row to a track, using a search road of 3 pads and 3 time bins. The track finder is iterated until all clusters are processed, then two linear fits are applied to the clusters associated to a track, one in pad and row, the other one in time and row. For the dE/dx measurements only single-track events were accepted, with an additional cut on the number of clusters in a track n > 32 (except for a gain scaling of 100 and the transfer field 2 < 400 V/cm). In order to distinguish between electron and pion tracks, electrons were selected using the signal of a Čherenkov counter, which had to exceed a threshold of 400, respectively events below a treshold of 150 were regarded as pions. To symmetrize the energy loss distributions, a truncated mean method was used, which selected the interval of 5 75% of the samples. With gain −

7 Chapter 1 Introduction

correction about 0.5% better resolution was achieved. No corrections for pressure and temperature variations were applied. The results of the analysis for different setups, which are discussed in chapter 3, are shown in figures 1.8 and 1.7. The seperation power defined in chapter 2 provides a measure for the particle identification capabilities of a detector, which is better for lower beam momenta and higher gas amplification. In Monte Carlo simulations of a dE/dx spectrum for 1 GeV/c pions using information from all 63 rows of the padplane resulted in a relative resolution of 9.0% [36]. The measured resolutions for electrons move between 9 % to 11 %, whereas the measured resolutions for pions move between 10 % to 12 %. The disagreement with the simulation results from the reduced number of rows used in the analysis. ] σ 7 1GeV (neg.) 2GeV (neg.) 6

4 separation [

π 3

e/ 2

0 100 102 104 106 108 100 102 104 106 108 7 3GeV (neg.) 6GeV (pos.) 6 5

4 3 2 1 0 100 102 104 106 108 100 102 104 106 108 IBF gain [%]

Figure 5.39: Separation power between pions end electrons with 1 6 GeV/c momentum measured for Figure 1.7: diSeparation↵erent HV settings. power between pions end electrons with 1 GeV/c to 6 GeV/c momentum measured for diﬀerent HV settings [36].

1524 simulation, for all 63 rows the resolution is 9%. This indicates room for improvements 1525 in the analysis of the test beam results.

1526 Detector stability

1527 During the PS test beam a total of 8 HV trips occurred, most probably triggered by 1528 discharges in the GEM foils. No increase of the current in any of the HV channels was 1529 recorded before the trips. 1530 All trips occurred while running the detector with ion backflow settings (see Table 5.8). 1531 After the first trips (#1–3 in Table 5.8)atthehighestgainsinionbackflowconfiguration, 1532 the measurements were carried at lower gains for the rest of the test beam. A few more 1533 trips occurred at these lower gains. The trips might be related with the absolute voltage 1534 on the GEM1 top electrode (UGEM1T). The value of UGEM1T for any of the ion backflow 1535 configuration is always higher than the corresponding value for even the highest standard 1536 settings. In addition, this electrode’s HV channel showed overcurrent status after the 8 1537 trip. Since the gain across this GEM was always rather low, the quality of the foil is 1538 suspected to lead to instabilities.

1539 5.2.7 Operation during the LHC p–Pb period

1540 Prototype in ALICE cavern

1541 The second in-beam operation with the GEM IROC prototype was performed at the 1542 ALICE cavern during the 2013 LHC p–Pb period at ps =3.5TeV. The goal of the 1543 experiment was to evaluate the stability of the detector operation under LHC conditions. 1544 The prototype was installed underneath the LHC beam pipe (see Fig. 5.41), 10 m from ⇠

95 1.3 Analysis of the data sample by University of Tübingen

14 - tf2: 200 - [%]

〉 1GeV e tf2: 400 1GeV π x 13 tf2: 600

/d tf2: 800

E Std (gain/69%*100%)

d 12 〈 )/

x 11 /d E 10 (d σ 9 100 102 104 106 108 100 102 104 106 108 14 2GeV e- 2GeV π- 13

9 100 102 104 106 108 100 102 104 106 108 14 3GeV e- 3GeV π- 13

9 100 102 104 106 108 100 102 104 106 108 14 6GeV e+ 6GeV π+ 13

9 100 102 104 106 108 100 102 104 106 108 IBF gain [%]

Figure 5.38: The relative dE/dx resolution measured for di↵erent HV settings for electrons and pions Figure 1.8: Thewith relative momentum dE/dx ranging resolution from 1 to 6 measured GeV/c. Only for 46 pad diﬀerent rows are HV used settings for the analysis. for electrons and pions with momentum ranging from 1 GeV/ c to 6 GeV/ c by the Tübingen dE/dx analysis [36].

Chapter 2 Foundations

2.1 Particle identiﬁcation

Particle identiﬁcation (PID) is fundamental to particle physics experiments [29]. Some strategies and methods used in the analysis of the GEM IROC test run at the PS will be brieﬂy discussed. Measuring a particle’s momentum and velocity simultaneously allows determination of its mass, since the momentum of a relativistic particle is given by p = mcβγ and its velocity by v = cβ, so its mass can be obtained by means of p m = . (2.1) cβγ

The mass resolution is given by

dm 2 dp 2 dβ 2 = + γ2 . (2.2) m p β The particle’s momentum can be determined by its curvature in a magnetic ﬁeld, while its velocity can be obtained by measurements of its emitted Čherenkov radiation, energy loss due to ionization (dE/dx), Time of Flight (TOF) and emission of transition radiation, the latter two not being discussed in this context. In addition to PID by mass determination, information can be obtained by the characteristic signa- tures particles leave in the detector caused by particle families’ diﬀerent interactions with matter.

2.1.1 Energy resolution and separation power The energy registered in a detector is subject to ﬂuctuations. For instance, radiation quanta of a single ﬁxed energy will be spread out over more than just one channel in the detector. The energy resolution is a measure for the capability of a detector to distinguish between two peaks in an energy spectrum. For a Gaussian distribution describing the energy deposit in the detector with mean µ and standard deviation

11 Chapter 2 Foundations

σ, the relative energy resolution is defined as σ(dE/dx) rel. res. = . (2.3) dE/dx h i The separation power for two particles A and B with the same momentum, but different masses is defined as

µA µB nσE = A − B . (2.4) (σE + σE )/2 2.2 Energy loss of charged particles in matter

When a particle passes through matter, it loses part of its kinetic energy due to inelastic Coulomb collisions with atomic electrons of the material. The atoms of the material are excited or even ionized, if the energy transfer exceeds the ionization energy of the particular atom. The average energy loss per unit path length dE/dx h i cannot be measured directly, however assuming a linear correlation between the ionization of the medium and the energy loss of the particle, it can be measured in terms of the average number of electron/ion pairs n , that are produced while the h i particle passes through a medium of length x, provided the average energy W spent for the creation of one electron-ion pair is known: dE n W = h i . (2.5) dx x Typical values of W for relativistic particles passing through a gas lie around 30 eV and can be assumed as constant factors [33]. The total energy loss of a heavy, charged particle with respect to a given diﬀerential cross section dσ(E)/dE is given by

Emax dE dσ = N E0 dE0, (2.6) dx dE0 Z0 where N denotes the volume density of electrons in the traversed region. The mean energy loss per unit length of a particle passing through matter was derived in a perturbative calculation by Bethe [12], assuming energy transfer by soft and hard collisions. It extends only to energies, above which atomic eﬀects are not important. The mean energy loss of a moderately relativistic particle can be described by

2 4 2 2 2 dE 4π z e N 1 2mc β γ Tmax δ = ln β2 , (2.7) − dx (4πε )2 mc2β2 2 I2 − − 2 0

12 2.2 Energy loss of charged particles in matter with ze the charge of the particle, N the electron density of the medium, m the electron mass, Tmax the maximum kinetic energy transmitted in a collision to an atomic4 electron,30. PassageI mean of excitation particles through energy matter of the medium and δ the density eﬀect correction. The stopping power dE/dx for positive muons in copper is shown in of interest (dE/dx, X0, etc.)varysmoothlywithcompositionwhenthereisnoh i ﬁgure 2.1.density dependence.

Fig. 30.1: Stopping power (= dE/dx )forpositivemuonsincopperasa Figure 2.1function: Stopping of βγ = powerp/Mc over for nine positive!− orders muons of# magnitude in copper. in momentum Solid curves (12 orders indicate of the total stoppingmagnitude power, in kinetic vertical energy). bands Solid indicate curves indicate boundaries the total between stopping power. different Data approxi- below the break at βγ 0.1aretakenfromICRU49[4],anddataathigher mationsenergies made to are calculate from Ref.the 5.≈ Vertical stopping bands power indicate [11]. boundariesbetweendifferent approximations discussed in the text. The short dotted lineslabeled“µ− ” illustrate It shouldthe “Barkas be noted effect,” that the equationdependence (2.7) of stopping does power not depend on projectile on chargethe particle’s at very mass, however,low at energies fixedmomentum [6]. p = βγmc = const, βγ depends on m. For the energy loss E per traveled distance x measured with sufficiently precise resolution, this 30.2.2. Stopping power at intermediate energies : allows theThe separation mean rate of of energydifferent loss particles by moderately with relativistic the same char measuredged heavy particles,momentum. M1/δx,iswell-describedbythe“Bethe”equation, dE Z 1 1 2m c2β2γ2T δ(βγ) 2.2.1 Distribution= ofKz a2 chargedln particle’se max energyβ2 loss . (30.4) − dx A β2 2 I2 − − 2 ! " # $ Since theIt describesenergy loss the meanof a charged rate of energy particle loss is in a the statistical region 0.1 process,< βγ < the1000 distribution F (x, ∆)forof intermediate- the energyZ lossmaterials∆ per with length anx accuracyof the particle’sof a few %. path With∼ through the∼ symbol the medium, 1 2 commonlydefinitions known and as values ’straggling given in function’, Table 30.1, the is of units great are MeV interest. g− cm The.Atthelower two most promi- nent methods to determine it are theJune 18, Laplace 2012 16:19 transformation method [27] and the convolution method [14]. Typical for energy loss distributions is their assymetric shape, which is shown in figure 2.2. The long tail towards high energy deposits comes from single collisions

13 Chapter 2 Foundations

with large energy transfer. Therefore one can not simply calculate the mean of the distribution to obtain the most probable value, but has to apply for instance the ARTICLEmethod IN PRESS of the truncated mean, where only a certain percentage of the energy loss 158 H. Bichsel / Nuclear Instruments and Methodssamples in Physics is evaluated Research in Acalculating 562 (2006) the 154–197 mean.

1. Introduction 0.6

1.1. General concepts

0.4 The concept dE=dx [1] representing the mean rate of energy loss in an absorber (Section 3.3) is used inappro- w )(1/keV)

priately in the description of the physics of most high ∆ energy particle detectors. Consider Fig. 1 which gives the f( 0.2 <∆> probability density function (pdf) f D for energy losses D 1 ð Þ of particles with bg 3:6 traversing x 12 mm of Ar gas. ∆p ¼ ¼ The most probable energy loss Dp and the width w of f D ð Þ are more representative of f D than the mean energy loss 0.0 ð Þ 12345 D x dE=dx. Details are given in Section 5.1, in h i ¼ ∆ (keV) particular it will be seen that Dp=x depends on x. Fig. 1. The straggling function f D for particles with bg 3:6 traversing Correspondingly, the energy loss quantities ( C and s)Figure 2.2: Straggling function F (x,ð ∆)Þ for particles traversing¼ 1.2 cm Ar gas with h i 1.2 cm of Ar gas is given by the solid line. It extends beyond per unit length derived for tracks depend on track lengthβγ = 3.6 as obtained2 2 2 with the PAI model (solid line). The original Landau function Emax 2 mc b g 13 MeV. The original Landau function [2,3] is given is represented by the dotted¼ line. The most probable energy loss ∆p, the mean energy (see Table 5). by the dotted line. Parameters describing f D are the most probable loss ∆ and the full-width-half-maximum W areð shownÞ as describing parameters of The functions f D customarily are called ‘‘straggling energy loss Dp x; bg , i.e. the position of the maximum of the straggling ð Þ functions’’ [4] or stragglingð Þ spectra, except in high energythe distributionfunction, at [13]. 1371 eV, and the full-width-at-half-maximum (FWHM) physics where they are called ‘‘Landau functions’’ in a w x; bg 1463 eV. The mean energy loss is D 3044 eV. Bothð calculationsÞ¼ of the energy loss distributionh i ¼ are determined by the electron generic sense. Here, ‘‘Landau function’’ is used only to density N and the cross section dσ/dE. The question remaining is how to model this designate the function described in Ref. [2] and shown incross section. Quantum mechanical models describing even shell excitations exist, Fig. 1 by the dotted line. For very thin absorbers the energythe most common is the Photo Absorption Ionization (PAI) model [6]. loss spectra are more complex. An example for particles 100 2 GeV protons 1 m Si with bg 2:1 traversing x 1 mm of Si is given in Fig. 22.2.2 Photo Absorption Ionization model! (PAI) (also see¼ Appendix G). Such¼ spectra have been described 80 Considering fast charged particles losing their energy in a number of independent soft earlier [5] and have been measured [6]. Structures of thiscollisions with the medium’s bound electrons in a semiclassical treatment, Allison and type are also observed in measurements of stragglingCobb (1980)) 60 [6] derive the mean energy loss per unit length due to the longitudinal ∆ effects on resonant yields of nuclear reactions, called the f( ‘‘Lewis effect’’ [7]. 40 This study describes the theory of the electronic interactions of fast charged particles with matter. Collision 20 and energy loss cross-sections are derived and straggling functions and their properties are calculated. The use of 0 these functions for tracking and for particle identification14 0 50 100 150 200 250 300 (PID) in time projection chambers, TPC, or silicon vertex ∆(eV) trackers, SVT, is described. The aim is to achieve an uncertainty of 1% or less in the calculations. Fig. 2. Straggling in 1 mm of Si, compared to the Landau function. The Bethe–Bloch mean energy loss is D 400 eV. The trajectory of a fast particle through an absorber is h i ¼ called a track with length t. It is subdivided into segments of length x. One method of PID consists of measuring the ionization by a particle in several thin detectors and either replaced by most probable values and full-width-at-half- its energy [8,9] or its momentum [10,11]. Much of the past maximum (FWHM). work on PID [12,13] has been based on empirical The main concern here is with TPCs, but the term information without consideration of problems that will ‘‘detector’’ will be used to indicate that the principles be described here. described also apply to other systems, e.g. SVTs and thin Various analytic expressions have been used to describe absorbers in general. An extensive review of the use of Si and correlate experimental data. In particular, straggling detectors can be found in Ref. [14]. functions have been approximated by Gaussians, and mean In any detector there are several stages which lead from values and variances of straggling functions have been used the interactions of fast charged particles in the detector to a for the data analysis. Such data are given for calculated digital output signal used for tracking and PID [15]. The straggling functions in Sections 3–5. It will be seen that first stage is the energy loss D in segments due to the mean values and variances for segments of tracks should be interactions of the particles with the matter in the detector. For small detector volumes, called pixels or cells [16], the next stage is the determination of the energy D deposited in 1The charge of the particles is assumed to be z 1e throughout and it the volume V under observation. The third stage is the ¼Æ is usually not included in the equations. conversion of D into ionization J which is defined as the 2.2 Energy loss of charged particles in matter component of the electric field of the fast moving, charged particle

dE ∞ e2 Nc = dω σ (ω) ln[(1 β2ε )2 + β4ε2]1/2 (2.8) dx − β2c2π Z γ − 1 2 Z0 ε1 + ω β2 arg 1 ε β2 + iε β2 (2.9) − 2 − 1 2 ε | | ω 2 2 Nc 2mβ c 1 σγ(ω0) + σ (ω) ln + dω0 , (2.10) Z γ ¯hω ω Z  Z0  with the medium’s dielectric constant ε = ε1 + iε2 expressed in terms of the gen- eralized oscillator strength, the energy transfer ¯hω and the photoabsorption cross section σγ = Zωε2/Nc√ε1. Where the expression for the mean energy loss in 2.7 is derived in a perturbative calculation, in the PAI model it is derived from the electric field at the position of the charged particle and the energy loss is described as the effect of this electric field doing work on the particle. Interpreting equation in terms of the number of discrete collisions with energy transfer ¯hω and comparing with

dE ∞ dσ = NE ¯hdω, (2.11) dx − dE Z0 one obtains the desired diﬀerential cross section as predicted by the PAI model

dσ α σγ(E) 1/2 = ln (1 β2ε )2 + β4ε2 − (2.12) dE β2π EZ − 1 2

α 1 2 ε1 2 2 + β arg 1 ε1β + iε2β (2.13) β2π N¯hc − ε 2 − | | E 2 2 α σγ(E) 2mc β α 1 σγ(E0) + ln + dE. (2.14) β2π EZ E β2π E2 Z Z0

The ﬁrst and the third term describe the energy loss by ionization, whereas the second term describes the energy loss by radiation. The last term describes the energy loss by ionization, for high energy transfers it becomes the dominant term and approaches the Rutherford cross section. The PAI model predicts a speciﬁc energy resolution in terms of FWHM1 (%) for argon of

0.43 0.32 R(n, ∆x, P ) = 96 n− (∆xP )− , (2.15) · 1full width half maximum

15 Chapter 2 Foundations where n denotes the number of dE/dx samples, ∆x the sample size in cm and P the pressure in atm. The exponent 0.43 was chosen instead of the original 0.46, − − which was calculated for a maximum likelihood analysis, to represent the truncated mean analysis which was applied in this analysis [38]. The prediction for argon in equation (2.15) can be extrapolated for a Ne/CO2 (90/10) gas mixture with ionization potential I and mean number of electrons per 0.32 ν ν/I − molecule by multiplication with the factor νAr/IAr . With the parameters listed in table 2.1, one obtains the factor 1.28. Assuming a Gaussian distribution, the relative resolution of distribution is rel. res. = (8 ln 2) 0.5 R(n, ∆x, P ). · − · The relative resolution predicted by the PAI model for Ne/CO2 (90/10) is

0.43 0.32 rel. res. (n, ∆x, P ) = 52 n− (∆x P )− . (2.16) · ·

Table 2.1: Ionization potentials and number of electrons/molecule for Ar and Ne/CO2 (90/10) mean ionization energy Ar IAr 26.4 eV [15] number of electrons/atom Ar νAr 18 mean ionization energy Ne/CO2 I 35.2 eV [17] mean number of electrons/molecule Ne/CO2 ν 11.2

2.2.3 Čherenkov detectors With the emission of Čherenkov radiation, a threshold velocity of a particle can be measured. When a charged particle passes through a medium of refractive index n 1 with a velocity βc > n greater than the local phase velocity of light in the medium, it emits Čherenkov radiation. The angle θC in which Čherenkov radiation is emitted, relative to the particle’s direction, is given by 1 cos θ = . (2.17) C βn

Since for fixed momentum p0 = βγmc the velocity of particles varies for particles with different masses, Čherenkov counters can be used to provide information for the identification of particles.

16 Chapter 3 Experimental Techniques and Methods

3.1 The ALICE IROC-Prototype

To demonstrate that the MWPC readout of the TPC can be replaced with GEM foils, a full size IROC prototype was built based on a spare MWPC-IROC of the ALICE TPC with the wire grids replaced by GEM foils [36]. The prototype is a trapezoidal-shape chamber, that is 497 mm long and between 292 and 467 mm wide. It consists of 4 components, which are shown in ﬁgure 3.1: GEM stack, pad plane, insulation plate and an aluminium frame. Below the GEM stack responsible for gas ampliﬁcation, there is a pad plane with 5504 4 mm 7.5 mm pads, made of a multi- × layer Printed Circuit Board (PCB). A 3 mm Stesalit insulation plate separates the pad plane from the aluminium frame.

Figure 3.1: Exploded view of the mounted IROC prototype with triple GEM stack, pad plane and IROC aluminium frame and GEM stack mounted on aluminium frame [36].

17 Chapter 3 Experimental Techniques and Methods

GEM foils

The GEM foils used in the prototype were manufactured at CERN using a single mask etching technique, which is less precise than the double-mask process but un- avoidable due to the large size of the foils [36]. The nominal diameters of the GEM holes are 50 µm for the inner hole and 80 µm for the outer hole, while the pitch between holes is 140 µm. An optical quality check conﬁrmed the hole size to be 40 µm to 50 µm and 70 µm to 80 µm respectively [36]. The top side of a trapezoidal foil is segmented into 18 individually powered sectors with an inter sector spacing of 400 µm, which corresponds to the thickness of the spacer grid. Between the edges of the sector and the active area there is an additional 100 µm of copper to account for misalignments and to avoid holes directly at sector borders. The bottom side of a foil is unsegmented and can be directly connected to the High Voltage (HV) supply, whereas the top side is powered in parallel via loading resistors soldered directly on the foil between HV distribution path and the sectors. The mechanically stretched foils are glued on 2 mm ﬁberglass (G10) frames which contain a 400 µm spacer grid aligned with the sector boundaries to keep the GEM foils at a 2 mm distance. An additional frame is glued between the bottom GEM foil and the padplane increasing the induction gap to 4 mm. The GEM foils are mounted in the stack with the unsectored side of the GEM foils facing the padplane.

Padplane

The padplane consists of a multi-layer PCB, where 5504 pads are ordered in 63 rows with 68 to 108 pads per row. Because of the trapezoidal shape, the pad’s geometry varies from rectangular pads in the center of the padplane to tetragons resembling parallelograms near the borders of the pad plane, as can be seen in ﬁgure 3.2. The position of the p-th pad in row r with Nr pads in the row is calculated in the local coordinate system of ALICE with the interaction point in the center of the ALICE TPC as the origin:

x(r, p) = (852.25 + 7.5r) mm y(r, p) = (4p + 2 2N ) mm. (3.1) − r

Test box with field cage The chamber was mounted in the test box depicted in figure 3.3, which contained a drift electrode made of 50 µm aluminized mylar foil and a rectangular field cage consisting of 8 field-defining strips with 15 mm pitch and total dimensions of 57 cm 61 cm. Between each of the strips a 1 MΩ resistor was placed. The last strip × of the field cage was positioned 1 mm below the level of the first GEM foil in the stack and can be adjusted to match the drift field at the top electrode of the first

18 3.1 The ALICE IROC-Prototype

Figure 3.2: View of the pad plane

GEM by applying a voltage. The last strip is grounded by a 3.3 MΩ resistor. As can be seen in ﬁgure 3.4, the drift distance from the cathode to the ﬁrst GEM is 10.6 cm. Mylar windows were machined in the walls of the test box for beam and radioactive source measurements.

19 Chapter 23 TheExperimental IROC-detector Techniques prototype and Methods

FigureFigure 3.3: 2.5 Test: Picture box with of the mounted IROC ALICE mounted IROC-prototype to the test box. [36]

Table 2.1 lists all materials built into the detector that will be in the beam line and thus absorbing energy.

Function Material Thickness Detector window Aluminized Mylar 50µm Detector gas Ne/CO2 5cm Fieldstrip Aluminzed Mylar 25µm Active Volume Ne/CO2 63.5cm Figure 3.4: CrossFieldstrip section of the test Aluminzed box with Mylar mounted 25 IROCµm prototype and field cage. The positions of the first foil in the GEM-stack, as well as the positions of the Detector gas Ne/CO2 5cm padplane and ofDetector the top of Window the aluminium Aluminized frame Mylar(alubody) 50 areµm marked with red lines and labeled. The drift distance is 106 mm [36]. Table 2.1: Di↵erent materials in the detector. High Voltage supply and settings The prototype is powered using an ISEG HPn300 30 kV module for the cathode voltage and an ISEG EHS 860n 8-channel 6 kV module for the 3 GEM foils and the last strip of the field cage. The prototype was operated at different HV settings: Standard settings: The standard voltage settings are the ones typically ap- • plied in triple-GEM detectors, allowing the highest amplification to take place in the first GEM in order to provide maximum stability against discharges. The settings were inherited from the COMPASS experiment, but due to the

1020 3.2 Data Sample

usage of a Ne-CO2 (90/10) gas mixture in the prototype instead of Ar-CO2 (70/30) as in the COMPASS experiment, all voltages in the GEM stack were scaled down by a factor of 69, 70, 71, 72, 73(%).

Ion Backflow (IBF) settings: These field configurations are aimed at the • minimization of backdrifting ions in the drift region, since the charge amplification by avalanche formation happens mainly in the third GEM for these settings. The GEM voltages can be scaled to vary the total gain by a factor of 100, 103, 105, 107(%). Furthermore the electric field between second and third GEM (Transfer Field 2) could be set to the values 200 V/cm, 400 V/cm, 600 V/cm and 800 V/cm. In contrast to standard settings, IBF settings may cause stability issues resulting in trips in the detector.

The standard drift ﬁeld of the ALICE TPC of 400 V/cm was used for the prototype with the potential on the last strip of the ﬁeld cage being kept at the same level as the top electrode of the top GEM foil’s potential. The HV settings for the prototype are shown in table 3.1 .

standard settings IBF settings drift ﬁeld 0.4 kV/cm 0.4 kV/cm

∆UGEM1 400 V 225 V TF1 3.73 kV/cm 3.8 kV/cm

∆UGEM1 365 V 235 V TF2 3.73 kV/cm 0.2 kV/cm adjustable

∆UGEM1 320 V 285 V induction ﬁeld 3.73 kV/cm 3.8 kV/cm

Table 3.1: Voltage settings for the ALICE IROC prototype

3.2 Data Sample

3.2.1 Experimental set-up The GEM IROC prototype was placed in the T10 beam line at Proton Synchrotron (PS) at CERN in the PS East Area experimental hall. The T10 beam is a secondary beam delivering secondary particles like electrons and pions and is derived from + + the 24 GeV/c primary PS beam. The test beam delivered either e and π or e− and π− with momentum ranging from 1 GeV to 6 GeV. The GEMs were powered

21 Test beam-time at PS EastChapter Area 3 Experimental – T10 Techniques and Methods

FigureP. Gasik 3.5: (TUExperimental Munich) set-up forALICE dE/dx TPC performance Upgrade measurements4XII2012 of the ALICE 22/32 IROC prototype at PS East Area T10 beamline [36]. with standard and IBF optimized voltage settings for each type of beam. The drift velocity of the Ne/CO2 (90/10) gas mixture in this configuration is 2.73 cm/µs. With a sampling frequency of 20 MHz the time invervall between two samples is 50 ns. A sample corresponds to a drift length of 1.365 mm [36]. The experimental setup is shown in figure 3.5. Two scintillation detectors were used for beam definition. A beam Čherenkov counter and a Pb-glass calorimeter were used as a reference during the test beam to provide PID capabilities, since no identification was possible with the IROC due to the absence of a magnetic field. The beam Čherenkov counter was installed in front of the prototype. It consisted of an aluminium tube with a diameter of 20 cm, that was filled with nitrogen at atmo- spheric pressure and was equipped with UV sensitive photomultipliers. The Pb-glass calorimeter was installed behind the prototype for additional electron/pion separation and to give additional information on particles passing the prototype. Since part of the electrons gave a significantly smaller signal in the Pb-glass calorimeter only the information of the Čherenkov counter was used for particle identification. The smaller signal in the Pb-glass calorimeter arose from misalignment of this detector to the rest of the set-up. The prototype was equipped with 10 EUDET Front End Cards (FEC) [24] corresponding to about 1200 channels [36]. The card included a PCA 16 programmable

22 3.2 Data Sample charge preamplifier, the digitization and signal processing was done with an ALTRO chip. The FECs were reading out signals from 16 to 18 pads on all 63 padrows of the padplane, corresponding to a width of the readout region of 6 cm to 7 cm, which is depicted in figure 4.1 [36]. The shaping time of the system was 120 ns, with a sampling frequency of 20 MHz this corresponds to 2.4 samples. The system had an RMS noise of around 600 electrons. The zero supression threshold was 2 ADC counts corresponding to about 1200 electrons with a conversion gain of 12 mV/fC [36]. The FECs were read out using the readout system currently used in the ALICE detector with two ALICE TPC readout control units sending the acquired data to a local data concentrator PC, which contained the recieving ReadOut Reciever Card and runs the ALICE data acquisition software DATE. A local trigger unit and a busy box handled the corresponding trigger logic. Data transfer and trigger communication were based on optical links. The readout of beam detectors, scintillators, Čherenkov counter and Pb-glass calorimeter was done via a classic CAMAC system into a PC running a LabView acquisition system. A busy logic implemented in the CAMAC system was responsible for synchronizing the events. Subsequently the data streams were merged into a single data file based on the proper synchronization of the trigger and an event tag [36]. The average data acquisition rate was 500 events/spill for a beam intensity of about 2000 particles/spill [36].

23 Chapter 3 Experimental Techniques and Methods

3.3 The TPC Reconstruction Chain

In this section the steps of the track feature extraction from signals of the ADCs connected to the single pads to tracks of particles traversing the TPC will be presented. The reconstruction of particle tracks is done in context of the software framework fopiroot, which was written and implemented in the C++ programming language. fopiroot is based on the FairRoot [4] package developed at GSI, Germany, which is an extension of the ROOT framework developed at CERN [19]. The reconstruction is done by tasks that can conveniently be run from macros. The reconstruction chain is shown in ﬁgure 3.6.

Figure 3.6: Structure of the reconstruction chain

3.3.1 Pulse Shape Analysis The Pulse Shape Analysis (PSA) is the ﬁrst algorithm that processes data from single readout pads. It combines consecutive data samples to a pad hit and assigns

24 3.3 The TPC Reconstruction Chain it a time and an amplitude. The PSA searches the samples for local minima, local valleys or samples below a certain threshold, where it divides samples into pulses. Such a pulse is processed and assigned an amplitude A, which is deﬁned by the sum of all amplitudes of the samples in the pulse and a time, to be stored as a pad hit:

Apad hit = Asample tpad hit = tmax tshaping. (3.2) i − Xi The identification number of the pad (pad ID) is also stored with the pad hit to determine the position of the pad in the detector and obtain spatial informations for clustering finding. The time determination can be accomplished in different ways. The simplest way is to define the time of the pad hit t by the time of the sample with the maximum amplitude, shifted backwards in time by the peaking-time of the signal shaper tshaping = 120 ns. Another method called constant fraction discriminator which is used in the electromagnetic calorimeter trigger of the COMPASS [21] was also implemented. The algorithm calculates the difference between a pulse and a

40 amplitude (ADC counts) 20

-20

-40

-60 22 24 26 28 30 32 time (samples)

Figure 3.7: Constant Fraction Discriminator (CFD): The original signal is shown in blue crosses, the delayed signal in pink crosses and the difference between both signals in yellow. The time of the pad hit assigned by the CFD is shown by a red line, which is obtained by subtracting a calibration constant from the time, where the difference between delayed signal and signal crosses the abscissa axis. delayed and amplified version of the pulse. To obtain the time of the pulse, the point where the linear interpolation of the difference between pulse and amplified pulse crosses the axis is calculated. From this point a calibration constant is subtracted and this value is assigned as the time of the pulse.

25 Chapter 3 Experimental Techniques and Methods

3.3.2 Cluster Finding The Cluster Finder [34] takes the pad hits and combines hits that are likely to correspond to a common primary ionization to a cluster. Locally adjacent hits are grouped into a cluster, based on the information provided in a pad plane which represents the spatial distribution of the pads in the x- and y-plane. The time signal of a pad hit corresponds to the z-coordinate of the signal. First the algorithm sorts all pad hits in a certain timeslice by decreasing amplitude. Starting with the pad hit with the highest amplitude, it loops over pad hits and checks each pad hit against all clusters created until then. The cluster ﬁnder combines adjacent pads only, if the pad hits come from the same pad or neighbour a pad of any unsplit pad hit already in the cluster and if in addition the processed pad hit is within a certain time slice of the center of gravity in the cluster. If no matching cluster is found, a new cluster is created from the pad hit. If a pad hit matches more than one cluster, its amplitude is split between the matching clusters. From the pad hits assigned to a cluster the amplitude of that cluster is calculated by the sum of its pad hit amplitudes. The cluster is assigned a position by a weighted mean method:

pad hits xpad hit Apad hit xCl = · . (3.3) P pad hits Apad hit

The quantity σ = (σx, σy, σz) describesP the cluster’s spatial error. It is estimated from the standard deviation of the signal positions weighted with the cluster’s amplitude ACl. By dividing the variance by the amplitude, which is proportional to the number of ionization electrons, the reduction of the statistical ﬂuctuations from electron drift is taken into account1. An arbitrary factor C was introduced to scale the errors to an appropriate size. The variance and σi is calculated as

1 2 Vari = Apad hit(xpad hit,i xCl,i) (3.4) ACl − pad hit X C σi = Vari. (3.5) ACl · p For clusters consisting of one hit, σ is calculated as

C di σi = , (3.6) ACl · r12 where dx and dy denote the length and wide of a pad and dz the jitter in z. A two dimensional clustering in padrows and time has been implemented by restricting the q 1 Vari The error should then be calculated as σi = C · . However in the code it was implemented ACl as written in the text. Since the arbitrary factor C introduces a large systematic uncertainty this problem is estimated to have a minor eﬀect. The algorithm should be revised.

26 3.3 The TPC Reconstruction Chain existing clustering algorithm to search for adjacent pad hits only in the same padrow and in time.

Figure 3.8: Illustration of the 3D cluster ﬁnding algorithm working on event 15 in run 681, pad hits (shown as cylinders) are grouped as clusters (shown as spheres). A cylinder’s radius is proportional to the digi amplitudes in a logarithmic scaling.

3.3.3 Pattern Recognition In order to reconstruct the trajectories of particles passing through the detector, a Pattern Recognition algorithm has to group clusters, which originate from a single physical track. Usually in a particle physics experiment, the pattern to be recognized are helices, assuming helical trajectories of charged particles in a homogenous magnetic field. For this analysis however, due to the absence of a magnetic field, the pattern to be recognized are straight lines. The framework provides two different algorithms: A Riemann track follower [34] fitting helices to a set of hits by an extended Riemann fit and a Hough Transform Pattern recognition algorithm [17]. The Riemann Pattern Recognition is used in the final analysis, because of its better performance with the 2 dimensional clustering. The Riemann Pattern Recognition algorithm associates three dimensional space points provided by the clusters to tracks for which a helical shape is assumed. A helix is fitted to a set of hits by an extended Riemann fit. This fit makes use of the Riemann Transformation, a stereographic projection mapping a plane onto the so-

27 Chapter 3 Experimental Techniques and Methods called Riemann sphere with diameter of 1 on top of the origin of the complex plane. The Riemann Transformation maps circles and straight lines on the plane to circles on the sphere corresponding to planes in space, thus reducing the challenging task of circle-fitting on the plane to the task of plane-fitting on the Riemann sphere. The Riemann sphere is scaled to appropriate size with respect to the detectors geometry. After the fast fitting algorithm, the hits along the track are sorted properly and estimates of the track parameters are provided to the fitting algorithm to reconstruct particle trajectories. A schematic of the algorithm is shown in figure 3.9. The 3.3 Riemann Pattern Recognition

s it h d e Hit-Track Correlators rt Cluster Check hit against o s Cluster r each tracklet e v Cluster o Proximity Correlator p Cluster o Tracklet o L Hit Tracklet Hit Tracklet Helix Correlator Assign hit to best matching track New tracklet If no tracklet matches, create a new one

Figure 3.9: Scheme of the track building process Figure 3.9: Scheme of the track building process with the Riemann track follower [34] ↵ versus the z-positions of the clusters is then performed, which delivers the helix parameters m and t. algorithm starts with a first tracklet which contains only one hit, then the presorted After that, the hits are sorted again, now by their angle. Steep tracks (✓ < 30 clusters are looped and each hit is checked against each existing tracklet. If both or ✓ > 140)areleftsortedbyz. This technique makes sure that the hits are well hit-tracksorted along correlators the track, are which matched, is important the hit for is assigned track fitting. to the best matching tracklet. A matching correlator delivers a matching quality. Two correlators are applied: 3.3.4A proximity Track correlatorBuilding checks the proximity of a cluster to a track by finding • the nearest cluster in the tracklet and delivering the distance between those Figure 3.9 illustrates the track building process: To begin with, the clusters are clusters as a matching quality. presorted by z,radiusR or angle . The idea is that the PR goes from areas of lowA track helix density, correlator where calculates tracks can bethe separated distance by between their proximity the cluster in space, and the to helix areas• of high track density. The very first tracklet is built and contains only one defining the tracklet. By Newton’s method, the minimum distance is found hit at this time, then the algorithm loops through the presorted clusters. Each hit and delivered as a matching quality. is checked against each existing tracklet. If one or several matching criteria (“hit- Iftrack the matching correlators” quality)arefulfilled,thehitmaythenbeassignedtothebestmatching of a correlator is smaller than a definable cut, the tracklet survivestracklet. the correlator, otherwise if no tracklet matches a hit, a new tracklet is If a hit-track correlator is applicable, it delivers a matching quality. Two cor- created. If the root mean square of the tracklet’s hits to the fitted helix is less than relators are applied: a definable cut, then the tracklet is stored and can be further processed. Due to outliers,The noiseProximity hits, incorrectly Correlator checks assigned proximity hits, fragmentary in space, by finding tracks the of particles nearest with low energy• cluster loss in and the tracklet. even defect It is readout always applicable, channels, and the the actual matching tracks quality might is not be found asthe a distance whole in of the the twoprocess cluster of positions. track building. Because of that, a second level tracklet merging is performed, where the tracklets are presorted and compared to The Helix Correlator calculates the distance of the cluster to the helix that • defines the tracklet. Newton’s method is employed to find the minimum distance. If the tracklet has not been fitted, the correlator is not applicable. 28 The matching quality is the distance to the helix.

If the matching quality is smaller than a deﬁnable cut (proximity- and helix-cut), the tracklet survives the correlator.

23 3.3 The TPC Reconstruction Chain 3.3 Riemann Pattern Recognition

If all correlators are survived, merge Track-Track Correlators tracklets ts Proximity Correlator le ck a tr Cluster r e Cluster v Dip Correlator o Cluster p o o Tracklet L Tracklet Tracklet Riemann Correlator Tracklet Check tracklet againts other tracklets

Figure 3.10: Scheme of the track merging process Figure 3.10: Scheme of the track merging process [34] or chips can also cause gaps. If the PR is sectorized (cf. Sec. 3.3.6), it is necessary to recombineeach other. Thetracks track crossing merging the algorithm sector borders. is shown schematically in figure 3.10. Like in the track finding process certain track-track correlators have to be matched in Therefore, a second level tracklet merging is performed. Similar to the track order for two tracks to be merged: building process, the tracklets are presorted, and then compared to each other. A proximity correlator compares the position of the first and last hits of the Again,• there are several track-track correlators which all (in this point the merging is di↵erenttwo to tracklets. the track If the building) distance have between to be the applicable position of and the survived.hits is smaller than a definable proximity cut, the proximity correlator is survived. The Proximity Correlator compares the position of the first and last hits of • A dip correlator compares the dip angles of the two tracklets, which are defined the• two tracklets. If the smallest distance is smaller than the proximity-cut, as the angle between a line parallel to the z-axis and a tangent on the helix of a thetrack. correlator If the relative is survived. z-positions of the tracks match and the absolute difference TheofDip the dip Correlator angles iscompares smaller than the the dip definable angles ✓ angle-cut,of the two the tracklets. dip correlator Therefore, is survived. • both tracks have to be fitted. But not only has the absolute di↵erence of the dipA angles helix correlator✓ to be creates smaller anew than track the temporarilyangle-cut, alsocontaining the relative the hitsz of-positions both • oftracks. the tracks A helix have fit to is match. performed Thus, and the a cut distance on the of root-mean-square the two helices of at the a the startingdistance point of the of hits the to tracklet the helix with is applied. less hits If is the calculated. two tracks It together has to be do smaller not thanhave the enoughhelix-cut hits. to be fitted, this correlator is not applicable. 3.3.4If only Track one Representation of the tracks is fitted, the helix-distances of all hits of the unfitted tracklet are calculated and compared with the helix-cut. If none of the tracks Theis unfitted fitted, the tracks correlator found by is the not pattern applicable recognition and the are tracklets parametrized cannot in be a 5 merged. dimensional track parametrization in virtual detector plane coordinates with the state T vectorFinally,p = (q/p, the u tracklets0, v0, u, v) have. Here toq passdenotes the theHelix particle’s Correlator charge,. Forp its tracks momentum, with few • u, vhits,the position the helix of fitits mighttrack on not the be (virtual) very accurate, detector plane and for and straightu0, v0 the tracks, direction some cosinesparameters of the track of inthe the helix plane. (i.e. Figure radius, 3.11 center)shows a virtual are not detector well defined. plane as used Thus in it is thenot GENFIT reasonable track parametrization. to directly compare Further the information helix parameters. on the treatment of tracks can be found in [23] and [34]. Instead, a new track is created temporarily, containing the hits of both tracks. A helix fit is performed and a RMS-cut on the RMS of the distance of the hits to the helix is applied. 29 If the two tracks together do not have enough hits to be fitted, this correlator is not applicable.

25 Chapter 3 Experimental Techniques and Methods

Chapter 3: The TPC Reconstruction Chain

u = (x o) u − · v = (x o) v − a ·u u = · 0 a n a · v v = · 0 a n ·

with x : position in space in a master Figure 3.15: Virtual detector plane for Figure 3.16: Virtual detector plane for coordinate system, a : direction of the Figurea space-point 3.11: Virtual hit [23]. detector plane for a awirehit[23]. space point hit [23] track and o : origin of the plane in a master coordinate system These coordinates are only meaningful in combination with the parameters that make up the plane: The master coordinate system is defined by the ALICE local coordinate system of the IROCThe as origin introduced of the in plane: figureO 1.2.=(O ,O ,O )T . • x y z T 3.3.5 KalmanTwo perpendicular Track Fitting unit vectors that span the plane: U =(Ux,Uy,Uz) and • T V =(Vx,Vy,Vz) . The Track Fitting is achieved with a Kalman filter [25] [34], an algorithm to produce The normal vector of the plane: N =(N ,N ,N )T = U V an optimal• estimate of a system state from a seriesx y ofz noisy measurements.⇥ It is implemented in GENFIT, a generic toolkit for track reconstruction for experiments Internally, the RKutta method and the material e↵ects work in the 7-dimensional in particle and nuclear physics [23]. Further information on the working principle of master reference system. The coordinates are: the Kalman filter can be found in [23]. The position in space: x =(x, y, z)T . • 3.4 Extraction of Specific Energy Loss Data The direction of the track: a =(a ,a ,a )T . • x y z To extractCharge specific over energy momentum loss data of the (dE/dx particle:) fromq/p. a track, a dE/dx task optimized for the• detector geometry has been implemented in the analysis framework. AThe reconstructed transformations track from is extrapolated plane- to master to the reference first padrow system of and the vicedetector. versa Fromcan therebe obtained it is iteratively using the being following extrapolated equations, to where the nextp is the padrow. momentum, The length pointing of in the trackdirection between of thetwo plane’s rows, calculated normal vector. as the The magnitude auxiliary of parameter the differenced 2 indicates of the track’s the positioncourse at of two the neighbouring particle: It is rows, +1 if isthe assigned particle as crosses∆ex. The the plane sum of in all the pad direction hits in of the respectivethe plane’s padrow normal corresponding vector, and to1otherwise. the track is assigned as ∆E. The energy loss per 2d is called “spu” in the code.

34 30 3.4 Extraction of Specific Energy Loss Data padrow ∆E/∆x is stored as a dE/dx sample, which is used in the calculation of the truncated mean. A second version of the dE/dx task has also been implemented, where the summa- tion over the pad hit’s amplitudes is carried out in a region around the track instead over the amplitudes of pad hits assigned to the track by the pattern recognition. In this way possible deficiencies in the track finding algorithms can be overcome. The region around the track is defined by a rectangular box around the track with definable width and heigth.

Figure 3.12: Illustration of the dE/dx task at work, the track (cyan) is extrapolated to the ﬁrst padrow, from where the track is extrapolated iteratively to the next padrow. The pad hits (colored spheres) in the respective padrow in a region around the track (grey box) are summed up and together with the length of the track between two padrows they contribute to the speciﬁc energy loss.

Chapter 4 Results and Discussion

4.1 Data Selection

During the beam time, data was acquired during 84 runs, which are listed in the appendix A. To investigate optimal parameters for clustering and pattern recognition, run 681 with standard HV settings and 69% gain and run 694, with IBF HV settings (TF2: 800 V/cm) and 103% gain were selected as benchmarks in this analysis. In run 681 a total of 81 961 events was recorded, whereas in run 694 a total of 63 005 events was recorded. The gas amplification of the GEMs in run 681 was measured to a gain of 1500, whereas the gas amplification in run 694 was measured to a gain of 5200 [36]. In a first analysis the occupancy of pads was investigated to find pads with unusually many signals. The occupancy of pads is shown in figure 4.1 using a logarithmic scale. The boundaries of the IROC are drawn with black lines.

Figure 4.1: Occupancy map for run 681 with marked shape of the IROC.

The pads with the pad IDs 465, 537, 754, 978, 2271, 2272 and 3057 measured

33 Chapter 4 Results and Discussion unusually many signals, which indicated that mainly noise was measured with these channels. A comparision between the amplitude distribution of such a pad and a neighbouring pad, which measured a reasonable amount of signals is shown in figure 4.2. Since the noise significantly worsened the efficiency of the pattern recognition, these channels were excluded from the analysis. In further studies the effect of a suitable threshold for pad hits could be investigated.

106 104 105 3

# of entries 4 10

10 # of entries 3 10 102 102 10 10 1 1 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 sample amplitude sample amplitude

Figure 4.2: Comparision of the amplitude distributions for pad 3057 and pad 3056 in run 681

The readout window of the pads was much longer than the maximum drift time of particles in the test box, therefore only signals with time bin below a threshold of tcut = 4.5 µs (90 samples) were considered in the analysis. A distribution of the sample’s amplitudes and timestamps, which motivated the applied cut, can be seen in ﬁgure 4.3.

300

Sample time and amplitude 105 Entries 1.43677e+08 250 Mean x 5.946 Mean y 115.5 104 RMS x 9.078 200 RMS y 82.56 sample time (samples) 103 150

102 100

50 10

0 1 0 10 20 30 40 50 sample amplitude (ADC channels)

Figure 4.3: Distribution of sample timestamps and amplitudes for run 681 and 694

The gain correction obtained by the analysis of University of Tübingen, which was described in section 1.3, was applied to the samples’ amplitudes.

34 4.1 Data Selection

Due to a bad connector in the experimental setup, the first 4 rows had to be excluded from the analysis. The last 3 rows were excluded from the analysis because the tracks seemed distorted on the edges, which was confirmed by the analysis of Martin Ljunggren [30] and can be seen in figure 4.4. The pattern recognition improved by excluding these rows.

Figure 4.4: x- and z- cluster positions for event 33 in run 681

Because the Constant Fraction Discriminator, which was discussed in section 3.3.1, only worked on a fraction of the signals, the time of a pad hit was assigned by subtracting the shaping time from the timestamp of the maximum amplitude of the pulse. Otherwise a bias might have been intruduced by using two diﬀerent time calculations. In ﬁgure 4.5 a pad hit extracted by the PSA is shown.

amplitude (ADC channels) 5

0 5 10 15 20 25 30 35 time (samples)

Figure 4.5: Pad hit extracted by the PSA algorithm, the time assigned to the pad hit is indicated by the black line

35 Chapter 4 Results and Discussion

4.2 Track Reconstruction

Different reconstruction methods were tested for their capability of reconstructing particle tracks, which are needed for the dE/dx analysis. The reconstruction, which was used in the dE/dx analysis, makes use of a two dimensional clustering in one row and time, as described in section 3.3.2. In contrast to 3 dimensional clustering, the determination of neighbouring pads was unambigu- ous, because despite the padplane’s geometry, the left and right neighbour of a pad are well-defined. In the clustering a timeslice of tslice = 1.05 µs (21 samples) was used for clustering in z-direction. The distributions of how many clusters were found in an event and how many clusters were found in events where the pattern recognition found one track, are shown in figure 4.6 for run 681.

×103 ×103 9 9 8 8

# of entries 7 # of entries 7 6 6 5 5 4 4 3 3 2 2 1 1 0 0 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 # of clusters per event # of clusters per single track event

Figure 4.6: Clusters per event / single track event for run 681

As expected for 56 pad rows included in the analysis and the track extending over the rows, the distribution peaks at this value. Comparing both benchmark runs, run 694 has generally more clusters per event, which can be explained by the higher gas amplification. The average cluster size of a cluster is shown in figure 4.7 for run 681. The distributions of the cluster size in three dimensions and in two dimensions being very similar indicates, that most clusters consist only of one pad hit in z-direction. Due to the higher gas amplification in run 694, more clusters include pad hits two or more pads. The pattern recognition was done with the Riemann Track Finder with the pa-

36 4.2 Track Reconstruction

6 106 10 105 # of entries 105 # of entries 104 4 10 103

2 103 10 10 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 3d cluster size 2d cluster size

Figure 4.7: Cluster size in three dimensions and cluster size in two dimensions (x and y) for run 681 rameters listed in table 4.1, which were obtained by carefully tuning the cuts in a custom 3D event display. It was also used to create ﬁgures 3.8 and 4.10.

Table 4.1: Parameters of the reconstruction Scaling factor of riemann sphere 80 Minimum number of hits for a helix ﬁt 6 Cuts for the hit-track correlators Proximity cut 1.5 cm Stretch of proximity cut in z 1.0 Helix cut 0.4 cm RMS cut 0.4 cm Cuts for the track-track correlators Proximity cut 5 cm Dip angle cut 0.8 rad Helix cut 2.0 cm Helix RMS cut 1.0

The number of tracks found by the pattern recognition is shown in figure 4.8. The distributions for both runs being very similar in shape indicates that the pattern recognition works equally well for runs with different parameters. The number of clusters per track is shown in figure 4.9. The small local maximum at 26 clusters per track can be explained with the geometry of the readout area which can be seen in the occupancy map in figure 4.1. Tracks crossing the IROC near the boundaries of the readout area are only registered up to x < 107 cm, which results in a track extending only over half the readout area. The cutoff at 6 clusters per track originates from the cut parameter in the pattern recognition. The distributions for

37 Chapter 4 Results and Discussion

×103 ×103 60 45 50 40 35

# of entries 40 # of entries 30 30 25 20 20 15 10 10 5 0 0 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 tracks per event tracks per event

Figure 4.8: Number of reconstructed tracks per event for run 681 and run 694 run 681 and run 694 are very similar in shape both peaking at the expected value of 56 clusters per track. The peak of the distribution of run 694 is more narrow compared to run 681, indicating that in run 681 more tracks have gaps in them. A single track event and a multiple track event is shown in ﬁgure 4.10.

4 10 104 # of entries # of entries 103 103

102 102

0 10 20 30 40 50 60 0 10 20 30 40 50 60 clusters per track clusters per track

Figure 4.9: Number of clusters per reconstructed track for run 681 and run 694

38 4.2 Track Reconstruction

(a) Single track event (20)

(b) Multiple track event (11)

Figure 4.10: Diﬀerent types of events in run 681

39 Chapter 4 Results and Discussion

The Kalman filter was applied with 2 iterations. The quality of the track fitting can be estimated on the basis of the track’s residuals1 shown in figures 4.12, 4.13, 4.14 and 4.15. The residual is defined as the distance from the track to a cluster. The very narrow peak at zero in the y-residual can be explained with tracks extending over one pad per row, resulting in a near zero residual. The z-residual’s asymmetric shape is not fully understood. For runs with higher gain the distribution becomes more symmetric. Probably the primitive time determination causes the asymmetric shape, which could be improved with further studies. To obtain an estimate for the resolution of the detector from the residuals, three Gaussians were fitted to the distribution of the residuals. For the y-residuals the Gaussian G1 was used to describe the narrow peak, whereas for the z-residuals it was used to describe the peak’s asymetry. Gaussian G2 and G3 were used to fit the shape of the residual. The resolution of the residuals was obtained by the means of the weighted mean of G1 and G2. The y-resolution was estimated to be 377.31 µm for run 681 and 312.19 µm for run 694. The resolution for run 694 is better because of the larger cluster size in this run. The resolution of the z-residuals was estimated to be 546.33 µm for run 681 and 614.63 µm for run 694. The space point resolution of the ALICE TPC in z for the test box drift length was measured with cosmics to be 350 µm [7].

×103 2.5 400 350 2 300 # of entries # of entries 1.5 250 200 1 150 100 0.5 50 0 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 2 4 6 8 10 chi2/NDF chi2/NDF Figure 4.11: χ2/NDF distribution of the reconstructed tracks for run 681 and 694

The χ2/NDF distribution shown in figure 4.11 is an indicator for the quality of a fit and is expected to peak at 1, if the error estimation was done correctly. Despite the biased error on the cluster position, the distributions show the expected shape, but do not peak at 1. The difference between the distributions for runs with low and high gas amplification shows, that the error calculation is done incorrectly. Further work is necessary to calibrate the error calculation.

1By mistake the residuals were biased by including the cluster for which the residual is calculated in the ﬁt of the track. Since most tracks consist of 56 clusters, the eﬀect should not bias the residuals much.

40 4.2 Track Reconstruction

×103 ×103 Residuals Y 22 Residuals Z 50 Narrow Peak Fit (G1) Entries 3289236 20 Second Peak Fit (G1) Entries 3289236 Residual Fit (G2) Mean 0.0003701 Residual Fit (G2) Mean -0.009608

Background Fit (G3) Background Fit (G3) RMS 0.1027 40 RMS 0.09313 18 2 Global Fit 2 χ / ndf 1.057e+04 / 291 Global Fit χ / ndf 1.59e+04 / 691

# of entries # of entries 16 5000 0.2 G1 int 1.8e+04 ± 1.7e+01 G1 int ± 14 G1 mean -0.1015 ± 0.0004 30 G1 mean 0.0002493 ± 0.0000092 G1 σ 0.04098 ± 0.00030 G1 σ 0.0006541 ± 0.0000080 12 G2 int 1.546e+04 ± 3.613e+01 G2 int 2e+04 ± 0.9 10 G2 mean -0.008942 ± 0.000101 20 G2 mean 5.492e-06 ± 2.866e-05 8 G2 σ 0.03432 ± 0.00009 G2 σ 0.01408 ± 0.00004 G3 int 4388 ± 14.9 G3 int 1.2e+04 ± 2.1e+01 6 G3 mean 0.01959 ± 0.00019 10 G3 mean -0.0005112 ± 0.0000594 4 G3 σ 0.1262 ± 0.0002 G3 σ 0.07715 ± 0.00009 2 0 0 -0.4 -0.2 0 0.2 0.4 -0.4 -0.2 0 0.2 0.4 residuals y (cm) residuals z (cm)

Figure 4.12: y-residuals of the reconstructed tracks for run 681 Residuals Y Residuals Z Entries 3289236 Entries 3289236 Mean 0.0003701 104 Mean -0.009608 3 4 3 RMS 0.09313 RMS 0.1027 2 / ndf ×10 10×10 χ2 / ndf 1.057e+04 / 291 χ 1.59e+04 / 691 # of entries # of entries Residuals Y Residuals Z G1 int 5000 ± 0.2 22 G1 int 1.8e+04 ± 1.7e+01 50 Narrow Peak Fit (G1) Entries 3289236 Entries 3289236 Second Peak Fit (G1) G1 mean -0.1015 ± 0.0004 G1 mean 0.0002493 ± 0.0000092 Residual Fit (G2) 20 Mean -0.009608 3 Mean 0.0003701 Residual Fit (G2) G1 σ 0.04098 ± 0.00030 Background Fit (G3) 3 G1 σ 0.0006541 ± 0.0000080 10 RMS 0.09313 18 Background Fit (G3) RMS 0.1027 G2 int 1.546e+04 ± 3.613e+01 40 10 G2 int 2e+04 ± 0.9 2 Global Fit 2 χ / ndf 1.057e+04 / 291 Global Fit χ / ndf 1.59e+04 / 691 G2 mean -0.008942 ± 0.000101

# of entries # of entries 16 G2 mean 5.492e-06 ± 2.866e-05 5000 0.2 G1 int 1.8e+04 ± 1.7e+01 G1 int ± G2 σ 0.03432 ± 0.00009 G2 σ 0.01408 ± 0.00004 14 G1 mean -0.1015 ± 0.0004 4388 14.9 G1 mean 0.0002493 ± 0.0000092 G3 int ± 30 G3 int 1.2e+04 ± 2.1e+01 2 2 G1 σ 0.04098 ± 0.00030 10 G3 mean 0.01959 ± 0.00019 G1 σ 0.0006541 ± 0.0000080 12 10 G3 mean -0.0005112 ± 0.0000594 G2 int 1.546e+04 ± 3.613e+01 G3 σ 0.1262 ± 0.0002 G2 int 2e+04 ± 0.9 10 G3 σ 0.07715 ± 0.00009 G2 mean -0.008942 ± 0.000101 20 G2 mean 5.492e-06 ± 2.866e-05 8 G2 σ 0.03432 ± 0.00009 G2 σ 0.01408 ± 0.00004 -0.4 -0.2 0 0.2 G3 int 0.4 4388 ± 14.9 -0.4 -0.2 0 0.2 0.4 G3 int 1.2e+04 ± 2.1e+01 6 residualsG3 mean 0.01959 y ±(cm) 0.00019 residuals z (cm) 10 G3 mean -0.0005112 ± 0.0000594 4 G3 σ 0.1262 ± 0.0002 G3 σ 0.07715 ± 0.00009 2 0 0 -0.4 -0.2 0 0.2 0.4 -0.4 -0.2 0 0.2 0.4 residuals y (cm) residuals z (cm)

Figure 4.13: z-residuals of the reconstructed tracks for run 681 Residuals Y Residuals Z Entries 3289236 Entries 3289236 Mean 0.0003701 104 Mean -0.009608 4 RMS 0.09313 RMS 0.1027 2 / ndf 10 χ2 / ndf 1.057e+04 / 291 χ 1.59e+04 / 691 # of entries # of entries G1 int 5000 ± 0.2 G1 int 1.8e+04 ± 1.7e+01 41 G1 mean -0.1015 ± 0.0004 G1 mean 0.0002493 ± 0.0000092 3 G1 σ 0.04098 ± 0.00030 3 G1 σ 0.0006541 ± 0.0000080 10 G2 int 1.546e+04 ± 3.613e+01 10 G2 int 2e+04 ± 0.9 G2 mean -0.008942 ± 0.000101 G2 mean 5.492e-06 ± 2.866e-05 G2 σ 0.03432 ± 0.00009 G2 σ 0.01408 ± 0.00004 G3 int 4388 ± 14.9 G3 int 1.2e+04 ± 2.1e+01 2 2 10 G3 mean 0.01959 ± 0.00019 10 G3 mean -0.0005112 ± 0.0000594 G3 σ 0.1262 ± 0.0002 G3 σ 0.07715 ± 0.00009

-0.4 -0.2 0 0.2 0.4 -0.4 -0.2 0 0.2 0.4 residuals y (cm) residuals z (cm) Chapter 4 Results and Discussion

×103 ×103 50 Residuals Y Second Peak Fit (G1) Residuals Z Narrow Peak Fit (G1) Entries 2606129 16 Entries 2606129 Residual Fit (G2) Residual Fit (G2) Mean 2.59e-06 Mean 0.00862 Background Fit (G3) 14 Background Fit (G3) 40 RMS 0.09046 RMS 0.1068 Global Fit Global Fit 2 χ2 / ndf 1.56e+04 / 291 χ / ndf 4414 / 691

# of entries # of entries 12 671.3 10.7 G1 int 1.8e+04 ± 1.9e+01 G1 int ± 0.2327 0.0029 30 G1 mean -2.043e-06 ± 2.156e-05 10 G1 mean ± G1 σ 0.09669 ± 0.00208 G1 σ 0.002 ± 0.000 G2 int 1.02e+04 ± 2.78e+01 G2 int 2e+04 ± 2.5e+01 8 G2 mean -0.01246 ± 0.00008 20 G2 mean -9.382e-06 ± 2.396e-05 6 G2 σ 0.03943 ± 0.00011 G2 σ 0.0104 ± 0.0000 G3 int 5359 ± 30.4 G3 int 9554 ± 15.5 4 G3 mean -0.001579 ± 0.000497 10 G3 mean -0.0005789 ± 0.0000653 G3 σ 0.1034 ± 0.0003 G3 σ 0.0748 ± 0.0001 2 0 0 -0.4 -0.2 0 0.2 0.4 -0.4 -0.2 0 0.2 0.4 residuals y (cm) residuals z (cm)

Figure 4.14: y-residuals of the reconstructed tracks for run 694 Residuals Y Residuals Z Entries 2606129 Entries 2606129 4 Mean 2.59e-06 10 Mean 0.00862 4 RMS 0.09046 RMS 0.1068 2 3 10 3 2 / ndf 10 10 χ / ndf 1.56e+04 / 291 χ 4414 / 691

× # of entries × # of entries 1.8e+04 ± 1.9e+01 G1 int 671.3 ± 10.7 50 Residuals Y Second Peak Fit (G1) G1 Residualsint Z Narrow Peak Fit (G1) 16 G1 mean 0.2327 ± 0.0029 Entries 2606129 EntriesG1 mean -2.043e-06 ± 2606129 2.156e-05 3 Residual Fit (G2) Residual Fit (G2) 10 Mean 2.59e-06 Mean 0.00862 G1 σ 0.09669 ± 0.00208 3 Background Fit (G3) G1 σ 0.002 ± 0.000 Background Fit (G3) 14 1.02e+04 ± 2.78e+01 RMS 0.09046 10 RMS 0.1068 G2 int 40 Global Fit G2 int 2e+04 ± 2.5e+01 Global Fit 2 χ2 / ndf 4414 / 691 G2 mean -0.01246 ± 0.00008 χ / ndf 1.56e+04 / 291 G2 mean -9.382e-06 ± 2.396e-05

# of entries # of entries 12 G1 int 671.3 ± 10.7 G2 σ 0.03943 ± 0.00011 G1 int 1.8e+04 ± 1.9e+01 G2 σ 0.0104 ± 0.0000 2 0.2327 0.0029 G3 int 5359 ± 30.4 G1 mean -2.043e-06 ± 2.156e-05 G1 mean ± 10 30 102 G3 int 9554 ± 15.5 G1 σ 0.09669 ± 0.00208 G3 mean -0.001579 ± 0.000497 G1 σ 0.002 ± 0.000 10 G3 mean -0.0005789 ± 0.0000653 G2 int 1.02e+04 ± 2.78e+01 G3 σ 0.1034 ± 0.0003 G2 int 2e+04 ± 2.5e+01 8 G3 σ 0.0748 ± 0.0001 G2 mean -0.01246 ± 0.00008 20 G2 mean -9.382e-06 ± 2.396e-05 6 G2 σ 0.03943 ± 0.00011 G2 σ 0.0104 ± 0.0000 G3 int 5359 ± 30.4 G3 int 9554 ± 15.5 -0.4 -0.2 0 0.2 0.4 -0.4 -0.2 0 0.2 0.4 4 G3residuals mean -0.001579 ±y 0.000497 (cm) 10 G3 mean -0.0005789 ± 0.0000653 residuals z (cm) G3 σ 0.1034 ± 0.0003 G3 σ 0.0748 ± 0.0001 2 0 0 -0.4 -0.2 0 0.2 0.4 -0.4 -0.2 0 0.2 0.4 residuals y (cm) residuals z (cm)

Figure 4.15: z-residuals of the reconstructed tracks for run 694 Residuals Y Residuals Z Entries 2606129 Entries 2606129 4 Mean 2.59e-06 10 Mean 0.00862 4 RMS 0.09046 RMS 0.1068 2 10 χ2 / ndf 1.56e+04 / 291 χ / ndf 4414 / 691 # of entries # of entries G1 int 1.8e+04 ± 1.9e+01 42 G1 int 671.3 ± 10.7 3 G1 mean 0.2327 ± 0.0029 G1 mean -2.043e-06 ± 2.156e-05 10 G1 σ 0.09669 ± 0.00208 3 G1 σ 0.002 ± 0.000 G2 int 1.02e+04 ± 2.78e+01 10 G2 int 2e+04 ± 2.5e+01 G2 mean -0.01246 ± 0.00008 G2 mean -9.382e-06 ± 2.396e-05 G2 σ 0.03943 ± 0.00011 G2 σ 0.0104 ± 0.0000 2 10 G3 int 5359 ± 30.4 2 G3 int 9554 ± 15.5 G3 mean -0.001579 ± 0.000497 10 G3 mean -0.0005789 ± 0.0000653 G3 σ 0.1034 ± 0.0003 G3 σ 0.0748 ± 0.0001

-0.4 -0.2 0 0.2 0.4 -0.4 -0.2 0 0.2 0.4 residuals y (cm) residuals z (cm) 4.2 Track Reconstruction

The distributions of the reconstructed track’s angles in the x-y-plane with respect to the x-axis (φ) and in the x-z-plane with respect to the x-axis (θ) are shown in ﬁgure 4.16 for run 681. The distribution of the track parameters of run 694 resemble those of run 681. The distributions show a very narrow peak, indicating that most tracks are almost parallel to the x-axis. In the φ distribution however one observes an additional peak at 0.012 rad. The origin of the peak could not be fully reasoned out. Because the track parameters of tracks with φ > 0.005 rad revealed no inconsistencies, these tracks were included in the dE/dx analysis.

×103 ×103 3.5 5 3 4

# of entries # of entries 2.5 3 2 1.5 2 1 1 0.5 × -3 × -3 0 10 0 10 -40 -20 0 20 40 -40 -20 0 20 40 φ (rad) θ (rad)

Figure 4.16: Distribution of the angles φ and θ of single tracks for run 681

In figure 4.17 the distributions of the fitted tracks’ y- and z-positions at the starting point of the fit are shown for run 681. The distinctive spikes in the distributions of the y-positions are caused by straight tracks that only extend over one pad per row. The asymetric shape of the distribution originates in the geometry of the readout region, which can be seen in figure 4.1. The peak in the distributions of the z- positions at 1.8 cm was excluded in the analysis of University of Tübingen. To be able to compare the results, the peak was also excluded in this analysis.

350 100 300 80 # of entries 250 # of entries 200 60 150 40 100 20 50 0 0 -4 -2 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 y-position (cm) z-position (cm)

Figure 4.17: Distribution of single track start positions in y and z for run 681

43 Chapter 4 Results and Discussion

4.3 Energy Loss Spectra

4.3.1 Data selection By restricting the analysis to single track events, the PID capabilities of the additional detectors could be utilized. The signal of the Čherenkov counter was used to distinguish electrons from pions, which is shown together with the signal of the Pb-Glass detector in ﬁgure 4.18. Single track events with a signal greater than 400 in the Čherenkov counter were interpreted as events with an electron, whereas single track events with a signal lower than 150 in the Čherenkov counter were interpreted as events with a pion.

Figure 4.18: Signal from the Čherenkov counter and signal from the Pb-Glass detector, PID cuts are indicated by red lines.

For the dE/dx-analysis only tracks with a sum of their dx samples > 35 cm were considered, in order to exclude incomplete and small tracks. In ﬁgure 4.19 the distributions of the sums of the dx-samples are shown for run 681. The distributions for other runs were similar in shape. Only tracks whose z-position at the beginning of the track was in the interval 2.7 cm to 10.6 cm were considered in the analysis. The lower limit was chosen to be able to compare with the Tübingen analysis and the upper limit was chosen because of the maximum drift length of the detector. The dE/dx task which collected all pad hits in a deﬁnable region around the track was used for the creation of dE/dx samples. By collecting all samples in an area around the track instead of only processing the samples assigned to the track, it is guaranteed that no sample amplitude and therefore no primary charge will be lost

44 4.3 Energy Loss Spectra

Figure 4.19: Distributions of the sum of dx samples for run 681 with cuts indicated by red lines due to perhaps an insufficient pattern recognition. A collection region of a square of 2 cm 2 cm around the track turned out as the best parameter. × 4.3.2 Method of the Truncated Mean The energy loss spectra were obtained by the method of the truncated mean because of the long tail of the straggling function. A certain fraction of the lowest and/or highest values of the dE/dx samples is discarded before calculation of the mean, so that by calculating the truncated mean, the most probable value of the energy loss distribution is obtained. Although the amount of data is reduced by this procedure, the fluctuations of the mean values are kept to a minimum, as the outliers from the tail of the straggling function are omitted in calculating the mean value. By convention in this analysis, a truncation of [5, 75] means that 5% of the lowest samples and 25% of the highest samples are discarded. The truncations [0, 75], [5, 75], [10, 75], [0, 70], [5, 70] and [10, 70] were tested with a beam momentum of 1 GeV/c for standard settings with different HV scale factors. The effect of the truncation settings on the energy resolution for electrons and pions is shown in figure 4.20 and 4.21. Based on the analyzed data one optimal truncation setting for all runs cannot be determined, as even for standard settings the best truncation settings vary for different HV scaling factors. However the choice of [10,70] seems promising for standard settings.

45 Chapter 4 Results and Discussion

12 truncations [ 0,75] truncations [ 5,75] 11.5 truncations [10,75] truncations [ 0,70] 11 truncations [ 5,70] truncations [10,70] (dE/dx) electrons (%) σ 10.5

9.5

9 68 69 70 71 72 73 74 HV scaling factor (%)

Figure 4.20: Electron energy resolution for diﬀerent truncations (standard HV settings)

14 truncations [0,75] 13.5 truncations [5,75] truncations [10,75] 13 truncations [0,70] truncations [5,70]

(dE/dx) pions (%) 12.5 truncations [10,70] σ

11.5

10.5

10 68 69 70 71 72 73 74 HV scaling factor (%)

Figure 4.21: Pion energy resolution for diﬀerent truncations (standard HV settings)

46 4.3 Energy Loss Spectra

Findig the optimal truncations for all 103 runs can be investigated in further studies but is beyond the scope if this analysis. Since the choice of the truncations did not strongly alter the energy resolution, the truncations [5, 75] were chosen to compare the results with those of University of Tübingen, which used the same truncations. The eﬀect of the chosen truncations on a distribution of dE/dx samples of a Figure 4.22: dE/dx samples from single track can be seen in ﬁgure 4.22. event 40 in run 681, truncations [5, 75] indicated with red lines.

In figure 4.23 the energy loss spectra for standard HV settings, 1 GeV/c beam momentum with negative polarity are shown. The two peaks in the spectrum are due to electrons and pions. Electrons have a larger energy loss in matter due to their smaller mass and therefore a larger βγ for fixed momentum. The peaks are fitted with a combined fit of two Gaussians (green) and a polynomial of the 4th order (purple) to describe the background. The fit area was limited to dE/dx max 2σ(dE/dx). h i ± Since the energy loss of the particle is independent of the gas amplification, the ratio of the gas amplification gain and the mean energy loss should be a constant for different HV scaling factors. For the standard HV settings with scaling factors 71 %, 72 % and 73 % an estimation with gains provided in [36] showed good agreement with figure 4.23. The relative resolution depends on the fluctuations in the primary particle’s ionization, described by the straggling function, and the fluctuations in the gas amplification. The fluctuations of the straggling function, which are determined by the average number of primary inelastic collisions, usually dominate. One would expect the relative resolution to be independent of the gas amplification gain. However in figure 4.23 one observes a small improvement of the resolution for higher scaling factors, which could result from the loss of charge due to zero supression. Further studies could investigate the cause of this effect.

47 Chapter 4 Results and Discussion

×103 ×103 1.4 Separation Power = 4.3 Separation Power = 4.4 Pions Pions 1 1.2 Fitted Mean µ = 55.6 ± 0.1 Fitted Mean µ = 75.3 ± 0.1

# of entries σ/µ [%] = 12.244 ± 0.096 # of entries σ/µ [%] = 11.625 ± 0.094 1 Electrons 0.8 Electrons Fitted Mean µ = 90.1 ± 0.1 Fitted Mean µ = 121.9 ± 0.1 0.8 σ/µ [%] = 10.445 ± 0.054 σ/µ [%] = 10.068 ± 0.051 0.6 0.6 0.4 0.4

0.2 0.2

0 0 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 dE/dx (a.u.) dE/dx (a.u.)

(a) 69 % HV scaling (b) 70 % HV scaling

Separation Power = 4.4 Separation Power = 4.5 450 700 Pions Pions Fitted Mean µ = 101.2 ± 0.1 400 Fitted Mean µ = 134.7 ± 0.2 # of entries 600 σ/µ [%] = 11.530 ± 0.113 # of entries σ/µ [%] = 11.545 ± 0.144 350 Electrons Electrons 500 Fitted Mean µ = 162.7 ± 0.1 300 Fitted Mean µ = 216.7 ± 0.2 σ/µ [%] = 9.753 ± 0.059 σ/µ [%] = 9.967 ± 0.080 400 250

300 200 150 200 100 100 50 0 0 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 dE/dx (a.u.) dE/dx (a.u.)

Separation Power = 4.4 350 Pions Fitted Mean µ = 178.5 ± 0.2

# of entries 300 σ/µ [%] = 11.134 ± 0.145 Electrons 250 Fitted Mean µ = 287.7 ± 0.2 200 σ/µ [%] = 9.580 ± 0.065

150

100

0 0 50 100 150 200 250 300 350 400 dE/dx (a.u.)

(e) 73 % HV scaling

Figure 4.23: Energy loss spectra for standard HV settings, 1 GeV/c (-) beam momentum with the truncations [5,25].

48 4.4 Comparision of the data with the PAI model predicion

4.4 Comparision of the data with the PAI model predicion

The energy resolution prediction of the PAI model given by equation 2.16 depends on the number of dE/dx samples entering the calculation of the truncated mean. To verify the prediction with the measured data, the reconstructed tracks of run 681 were artificially shortened, simulating a smaller detector providing less samples. The prediction was calculated with the pressure in the PS East Area experimental hall P = 950 hPa and a sample size of ∆x = 0.75 cm. In figure 4.24 the energy resolution for electrons and pions is shown with the prediction of the energy resolution given by the PAI model. The relative resolution measured in the experiment is larger than 0.43 the prediction but the data is in good agreement with the n− dependency of the prediction. The energy resolution of pions is worse than the energy resolution of electrons, perhaps due to the different interaction of pions compared to electrons.

electrons 28 pions 26 PAI prediction 24 22 (dE/dx)/ (%)

σ 20 18 16 14 12 10 10 15 20 25 30 35 40 45 50 55 # of dE/dx samples

Figure 4.24: Energy resolution for diﬀerent number of dE/dx samples taken from run 681

49 Chapter 4 Results and Discussion

4.5 Results and comparision with the Tübingen analysis

The values for the relative resolution and the separation power were obtained for runs with beam momenta of 1 GeV/c, 2 GeV/c, 3 GeV/c and 6 GeV/c. The results for the runs with beam momentum 1 GeV and negative beam polarity are shown in figure 4.25 for the respective gain of the HV settings and the value of TF 2 in case of IBF settings. The results for the same settings with positive beam polarity are shown in figure 4.26 and 4.27. For IBF HV settings with positive beam polarity and momentum of 1 GeV no data was avaliable. In the analysis of University of Tübingen the dE/dx samples of a track were obtained by calculating the truncated mean of the clusters’ amplitude. The stepsize ∆x = 0.75 cm was assumed to be constant. To compare the results of this analysis to those of University of Tübingen, one has to multiply the values of dE/dx obtained h i in this analysis by the factor of 0.75 to get the same scale. The mean energy loss differs for different HV settings, because the arbitrary units depend on the gas amplification gain. The mean energy loss of the particle in gain adjusted units is expected to be constant for fixed momentum. In further beam times it could be investigated, if the energy loss is constant in gain adjusted units. A proper gain callibration is needed, which was not done for this test run. The dependency of the electron resolution on the HV scaling factor for standard settings shows the same behaviour as in the Tübingen analysis. The electron energy resolution for different settings could be reproduced. The obtained value for the resolution for TF2 = 200 V/cm and a HV scaling factor of 100 % is 2 % worse than in the analysis of Tübingen. The different treatment of runs with low gas amplification in the analysis of Tübingen by reducing the cuts explains this disagreement. The calculated resolution for TF2 = 600 V/cm and a HV scaling factor of 107 % should be taken with caution and has a higher uncertainty. A trip occured during the run resulting in less data. While the resolution for electrons is in agreement with the analysis of Tübingen, for pions a 1 % worse resolution was obtained in this analysis. In figure 4.27 the pion energy resolution for a positive beam polarity and a HV scaling factor of 73 % deviates 2 % from the other values. This is caused by a second peak in the pion energy loss spectrum that biased the fit. The energy loss spectrum of particles, that deposited a signal below 150 in the Čherenkov counter, is shown in figure 4.29. Since the energy loss of pions and muons is comparable, the second peak could be attributed to muons contaminating the beam. The separation power is shown in figure 4.28 for p =1 GeV/c, 2 GeV/c, 3 GeV/c and 6 GeV/c. The obtained values for beam momenta of 1 GeV/c and 2 GeV/c agree with the analysis of University of Tübingen, but the results for 3 GeV/c are not as expected. One would expect the separation power of pions and electrons to become smaller for larger momenta. The mean energy loss of pions approaches the mean

50 4.5 Results and comparision with the Tübingen analysis energy loss of electrons because of the beginning relativistic rise of pion mean energy loss, which can be seen in ﬁgure 2.1.

51 Chapter 4 Results and Discussion

400 15 electrons electrons 350 pions 14 pions 300 13

250 12 (dE/dx)/ (%) 200 σ 11

150 10

100 9

50 8

7 66 67 68 69 70 71 72 73 74 75 76 66 67 68 69 70 71 72 73 74 75 76 HV scaling factor (%) HV scaling factor (%)

(a) hdE/dxi, standard HV settings (b) σ(dE/dx), standard HV settings

500 400 TF 200 TF 200 450 TF 400 350 TF 400 400 TF 600 TF 600 TF 800 300 TF 800 350 Std. ⋅ 100/69 pions Std. ⋅ 100/69

electrons 300 250 250 200

200 150 150 100 100 50 50

98 100 102 104 106 108 98 100 102 104 106 108 HV scaling factor (%) HV scaling factor (%)

14 14 TF 200 TF 400 13 13 TF 600 TF 800 12 Std. ⋅ 100/69 12

11 11 (dE/dx)/ (%) pions σ (dE/dx)/ (%) electrons

σ 10 10 TF 200 TF 400 TF 600 9 9 TF 800 Std. ⋅ 100/69 8 8 98 100 102 104 106 108 98 100 102 104 106 108 HV scaling factor (%) HV scaling factor (%)

(e) σ(dE/dx)e, IBF HV settings (f) σ(dE/dx)π, IBF HV settings

Figure 4.25: Mean energy loss dE/dx (a.u.) and relative resolution σ(dE/dx) for h i standard and IBF HV settings, beam momentum p = 1 GeV/c and negative beam polarity with the truncations [5,25].

52 4.5 Results and comparision with the Tübingen analysis

400 electrons 350 pions 300

250

200

150

100

66 67 68 69 70 71 72 73 74 75 76 HV scaling factor (%)

Figure 4.26: dE/dx for standard settings, beam momentum p = 1 GeV/c and h i positive beam polarity

15 electrons 14 pions 13

12 (dE/dx)/ (%) σ 11

7 66 67 68 69 70 71 72 73 74 75 76 HV scaling factor (%)

Figure 4.27: σ(dE/dx) for standard settings, beam momentum p = 1 GeV/c and positive beam polarity

53 Chapter 4 Results and Discussion

) 8 ) 8 σ σ TF 200 TF 200 7 TF 400 7 TF 400 TF 600 TF 600 6 TF 800 6 TF 800 Std. ⋅ 100/69 Standard ⋅ 100/69 5 5 separation power ( separation power ( 4 4

3 3

2 2

1 1

98 100 102 104 106 108 98 100 102 104 106 108 HV scaling factor (%) HV scaling factor (%)

(a) p = 1 GeV/c, (-) (b) p = 2 GeV/c, (-)

) 8 ) 8 σ σ TF 200 TF 200 7 TF 400 7 TF 400 TF 600 TF 600 6 TF 800 6 TF 800 Standard ⋅ 100/69 Std. ⋅ 100/69 5 5 separation power ( separation power ( 4 4

3 3

2 2

1 1

98 100 102 104 106 108 98 100 102 104 106 108 HV scaling factor (%) HV scaling factor (%)

Figure 4.28: Separation power (σ) for standard and IBF HV settings with the truncations [5,25].

500

# of entries 400

300

200

100

0 0 50 100 150 200 250 300 350 400 dE/dx (a.u.)

Figure 4.29: Energy loss spectrum for run 862, with Čherenkov counter cut < 150

54 Chapter 5 Conclusions and Outlook

A good energy loss resolution is crucial for reliable PID. The GEM based ALICE TPC has to provide a comparable energy loss resolution to the MWPCs used before the upgrade. In this thesis the energy loss resolution and the separation power of an IROC prototype equipped with GEMs has been investigated. With the fopiroot framework, tracks could be reconstructed from the ADC samples measured at the PS. A dE/dx task designed for the geometry of the IROC prototype has been created to generate dE/dx samples from tracks. Macros to determine the quality of the track reconstruction and to analyze the dE/dx samples were written. By automatization of the relevant analysis macros, a different set of parameters can be conveniently tested in a further analysis. From the track parameters, an estimate for the position resolution was calculated to be 300 µm to 400 µm in y- and 550 µm to 600 µm in z-direction. The energy loss resolution of the ALICE IROC prototype for different HV settings was in the interval 9 % to 11 % for electrons and in the interval 11 % to 14 % for pions. The results for the separation power between electrons and pions were spread around 4 σ for a beam momentum of 1 GeV/c and around 3 σ for a beam momentum of 2 GeV/c. The obtained values agreed for a beam momentum of with a previous analysis of the data by Jens Wiechula and Martin Ljunggren [36]. Open questions remain, though: The dependency of energy loss measurements from the HV settings should be investigated, for instance by calculating the energy loss in gain-adjusted units. It should be clarified, whether this effect originates from the data analysis or from the hardware. The analysis could be improved by creating a better gain map. In the Tübingen analysis application of the gain map improved the resolution by 0.5 % [36]. Nevertheless the gain correction failed for some pad rows. By creating a gain map with a test source like Krypton, a better gain correction could be applied. Unfortunately the detector was damaged in a subsequent run, so a gain map of the prototype for the same conditions as in the beamtime cannot be measured. Otherwise the pad rows, for which the gain correction failed, could be excluded in the analysis, which would result in dE/dx less samples but in a better gain correction. The energy loss resolution could be further improved with a optimal set of truncations.

55 Chapter 5 Conclusions and Outlook

The analysis of different truncations has shown, that further work is necessary to determine an optimal set of truncations for the final HV settings. Instead of the primitive fitting of a Gaussian to the energy loss spectra, a convolution of a Gaussian and a exponential decay function could be used to fit the energy loss spectra more appropriately. This fitting method was used for the energy loss measurements with data of the FOPI-TPC [16]. In the scope of this thesis only energy spectra of runs with beam momentum of 1 GeV/c were discussed, however the tools to further investigate the data were created and all 84 runs were processed, ready to be discussed.

56 57 Appendix A List of runs during beam time

Appendix A List of runs during beam time

momentum HV scaling TF2 run number polarity remarks (GeV/c) factor (%) (V/cm) problem with 680 1 - 69 3730 ﬁle 681 1 - 69 3730 682 1 - 70 3730 683 1 - 71 3730 684 1 - 72 3730 685 1 - 73 3730 686 1 - 100 200 687 1 - 100 400 688 1 - 100 600 690 1 - 100 800 691 1 - 103 200 692 1 - 103 400 693 1 - 103 600 694 1 - 103 800 698 1 - 105 200 699 1 - 105 400 700 1 - 105 600 702 1 - 105 800 703 1 - 107 200 704 1 - 107 400 trip, problem 705 1 - 107 600 with ﬁle 706 1 - 107 600 trip 709 1 - 107 600 trip 713 2 - 100 200 714 2 - 100 400 715 2 - 100 600 716 2 - 100 800 717 2 - 103 200

58 momentum HV scaling TF2 run number polarity remarks (GeV/c) factor (%) (V/cm) 718 2 - 103 400 719 2 - 103 600 720 2 - 103 800 DAQ stuck 723 2 - 103 800 724 2 - 105 200 DAQ stuck 726 2 - 105 200 recheck 727 2 - 103 800 settings 731 2 - 105 400 733 2 - 105 600 734 2 - 105 800 trip 735 2 - 105 800 736 2 - 107 200 737 2 - 107 400 trip 739 2 - 107 400 busy error 740 2 - 107 400 busy error 768 2 - 69 3730 769 2 - 70 3730 770 2 - 71 3730 771 2 - 72 3730 773 2 - 73 3730 777 2 - 73 3730 783 2 - 73 3730 795 3 - 69 3730 816 3 - 70 3730 817 3 - 71 3730 818 3 - 100 400 820 3 - 100 600 trip 829 3 - 100 600 830 3 - 103 200 831 3 - 103 400 832 3 - 105 200 834 3 - 107 200 838 3 - 105 400 841 3 - 103 600 842 3 - 100 800

59 Appendix A List of runs during beam time

momentum HV scaling TF2 run number polarity remarks (GeV/c) factor (%) (V/cm) 851 1 + 69 3730 856 1 + 69 3730 858 1 + 69 3730 859 1 + 70 3730 860 1 + 71 3730 861 1 + 72 3730 862 1 + 73 3730 867 6 + 69 3730 868 6 + 70 3730 869 6 + 71 3730 870 6 + 72 3730 DAQ stuck 871 6 + 72 3730 872 6 + 73 3730 873 6 + 100 400 876 6 + 103 200 879 6 + 105 200 881 6 + 107 200 882 6 + 103 400 883 6 + 105 400 884 6 + 100 600 886 6 + 103 600 887 6 + 100 800 889 1 - 100 200 891 1 - 103 200 892 1 - 105 200 893 1 - 100 400 busy error 896 1 - 100 400 897 1 - 107 200 898 1 - 103 400 899 1 - 105 400 900 1 - 100 200

The dE/dx samples of the runs 851, 856 and 858 were merged in the analysis, since the runs had the same settings. The same was done for the dE/dx samples of the runs 773, 777 and 783. Runs with trips (with exception of run 709), DAQ errors and incorrectly merged ﬁles were not considered in this analysis.

60 Appendix B Results of the analysis for higher beam momenta

61 Appendix B Results of the analysis for higher beam momenta

400 15 electrons electrons 350 pions 14 pions 300 13

250 12 (dE/dx)/ (%) 200 σ 11

150 10

100 9

50 8

7 66 67 68 69 70 71 72 73 74 75 76 66 67 68 69 70 71 72 73 74 75 76 HV scaling factor (%) HV scaling factor (%)

(a) hdE/dxi, standard HV settings (b) σ(dE/dx), standard HV settings

500 400 TF 200 TF 200 450 TF 400 350 TF 400 400 TF 600 TF 600 TF 800 300 TF 800 350 Std. ⋅ 100/69 pions Std. ⋅ 100/69

electrons 300 250 250 200

200 150 150 100 100 50 50

98 100 102 104 106 108 98 100 102 104 106 108 HV scaling factor (%) HV scaling factor (%)

14 14 TF 200 TF 400 13 13 TF 600 TF 800 12 Std. ⋅ 100/69 12

11 11 (dE/dx)/ (%) pions σ (dE/dx)/ (%) electrons

σ 10 10 TF 200 TF 400 TF 600 9 9 TF 800 Std. ⋅ 100/69 8 8 98 100 102 104 106 108 98 100 102 104 106 108 HV scaling factor (%) HV scaling factor (%)

(e) σ(dE/dx)e, IBF HV settings (f) σ(dE/dx)π, IBF HV settings

Figure B.1: Mean energy loss dE/dx and relative resolution σ(dE/dx) for standard h i and IBF HV settings, beam momentum p = 2 GeV/c and negative beam polarity with the truncations [5,25].

62 400 15 electrons electrons 350 pions 14 pions 300 13

250 12 (dE/dx)/ (%) 200 σ 11

150 10

100 9

50 8

7 66 67 68 69 70 71 72 73 74 75 76 66 67 68 69 70 71 72 73 74 75 76 HV scaling factor (%) HV scaling factor (%)

(a) hdE/dxi, standard HV settings (b) σ(dE/dx), standard HV settings

500 400 TF 200 TF 200 450 TF 400 350 TF 400 400 TF 600 TF 600 TF 800 300 TF 800 350 Std. ⋅ 100/69 pions Std. ⋅ 100/69

electrons 300 250 250 200

200 150 150 100 100 50 50

98 100 102 104 106 108 98 100 102 104 106 108 HV scaling factor (%) HV scaling factor (%)

14 14 TF 200 TF 400 13 13 TF 600 TF 800 12 Std. ⋅ 100/69 12

11 11 (dE/dx)/ (%) pions σ (dE/dx)/ (%) electrons

σ 10 10 TF 200 TF 400 TF 600 9 9 TF 800 Std. ⋅ 100/69 8 8 98 100 102 104 106 108 98 100 102 104 106 108 HV scaling factor (%) HV scaling factor (%)

(e) σ(dE/dx)e, IBF HV settings (f) σ(dE/dx)π, IBF HV settings

Figure B.2: Mean energy loss dE/dx and relative resolution σ(dE/dx) for standard h i and IBF HV settings, beam momentum p = 3 GeV/c and negative beam polarity with the truncations [5,25].

63 Appendix B Results of the analysis for higher beam momenta

400 15 electrons electrons 350 pions 14 pions 300 13

250 12 (dE/dx)/ (%) 200 σ 11

150 10

100 9

50 8

7 66 67 68 69 70 71 72 73 74 75 76 66 67 68 69 70 71 72 73 74 75 76 HV scaling factor (%) HV scaling factor (%)

(a) hdE/dxi, standard HV settings (b) σ(dE/dx), standard HV settings

500 400 TF 200 TF 200 450 TF 400 350 TF 400 400 TF 600 TF 600 TF 800 300 TF 800 350 Std. ⋅ 100/69 pions Std. ⋅ 100/69

electrons 300 250 250 200

200 150 150 100 100 50 50

98 100 102 104 106 108 98 100 102 104 106 108 HV scaling factor (%) HV scaling factor (%)

14 15 TF 200 TF 400 13 14 TF 600 TF 800 12 Std. ⋅ 100/69 13

11 12 (dE/dx)/ (%) pions σ (dE/dx)/ (%) electrons

σ 10 11 TF 200 TF 400 TF 600 9 10 TF 800 Std. ⋅ 100/69 8 9 98 100 102 104 106 108 98 100 102 104 106 108 HV scaling factor (%) HV scaling factor (%)

(e) σ(dE/dx)e, IBF HV settings (f) σ(dE/dx)π, IBF HV settings

Figure B.3: Mean energy loss dE/dx and relative resolution σ(dE/dx) for standard h i and IBF HV settings, beam momentum p = 6 GeV/c and positive beam polarity with the truncations [5,25].

64 Appendix C Acknowledgements

I want to express my deepest gratitude to Prof. Laura Fabbietti for making this thesis possible. It was very exciting to work with data from a particle physics experiment connected to the LHC and to learn about the reconstruction of particle tracks from simple ADC signals. Despite her busy schedule she took her time to give me suggestions for my work and asked questions that focused me on the physics behind the data analysis. My sincerest thanks go out to Dr. Bernhard Ketzer who not only thaught me a lot about particle detection and the underlying physics in his lecture on particle detectors but also encouraged me and gave many helpful suggestions for my work. Regarding his inspiring motivation and deep knowledge of experimental physics, I am very grateful for his involvement in my work. Laura and Bernhard established a great working group. I would like to thank the people at E18 where I worked: I want to thank Johannes Rauch for the well- documented code and for his advise on ﬁnding the best parameters for the Riemann Pattern recognition. He is not only a gifted programmer and great guy, but also a great musician at the keyboard. Felix Böhmer and Stefan Huber gave helpful advice on coding and especially Felix is an expert for programming languages. I would like to thank Jens Wiechula for answering my questions regarding his analysis. I want to thank Sverre Dørheim for advising me during my thesis. In the beginning he took a lot of his time to help me with the Linux enviroment, the framework and ROOT, since I started the thesis with very limited knowledge of data analysis and started to learn C++ programming only a few months before the beginning of my thesis. By asking questions he helped me to break more than one mental block and his encouragement and friendly spirit helped me over many unexpected problems with programming. Sverre, I wish you and your girlfriend all the best! Thank you for advising me, I learned a lot (not only about physics) and enjoyed being your roommate. I would like to thank Andreas Mathis, Christopher Bilko and Jacopo Margutti, with whom I had the privilege to experience shifts in the beam time for Andreas’ bachelor thesis. It was exciting to see, how data is taken in a particle physics experiment. I would also like to thank Robert Glas, Julia Stadler, Andreas Mathis and

65 Appendix C Acknowledgements

Stefan Wallner for the good times we shared in programming classes and during my thesis and for their advice. Special thanks go out to Christopher Mittag and Wolfgang Neumeier for their advice on writing and on making computer graphics. I want to thank my parents for supporting me in my courses of study. Without your support and love I would not have been able to write these lines.

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