Directional Dark Matter Search with the Newsdm Experiment

GRAN SASSO SCIENCE INSTITUTE

DOCTORAL THESIS

Directional dark matter search with the NEWSdm experiment

Author: Supervisors: Valerio GENTILE Prof. Giovanni DE LELLIS Prof. Salvatore CAPOZZIELLO

A thesis submitted in fulﬁllment of the requirements for the degree of Doctor of Philosophy in the Astroparticle Physics

January 13, 2019

“And no-one showed us to the land And no-one knows the where or whys But something stirs and something tries And starts to climb towards the light”

Echoes, Pink Floyd iii Acknowledgements

I would like to thank all the people who supported me during my PhD experience. Firstly, I would like to express my gratitude to my Supervisors: Prof. Giovanni De Lel- lis who really taught me what the scientific method is; Prof. Salvatore Capozziello from whom I learnt that there is not a unique way to explain something. I owe a special ac- knowledgment to Prof. Francesco Vissani that I consider to be my first unofficial Supervi- sor and, especially, a friend: you believed in me more than I have ever done. I would like to thank my Referees, Dr. Pierluigi Belli, Dr. Marco Selvi and Prof. Francesco Arneodo, whose comments and suggestions have surely improved the quality of this work. I would also thank Prof. Vitaly Kudryavtsev and Dr. Luciano Pandola for their precious advices on my simulation studies. I would like to thank Antonia who was crucial for my professional growth: you have taught me that no limit is just that and that every effort, sooner or later, will be repaid. I would like to thank my colleagues: Andrey, Asada and Naka-san for their invaluable support throughout the different activities in my PhD work and all the people in Napoli, L’Aquila and Nagoya groups who are part of this scientific adventure. I owe a lot to my closest friends, wherever they are now, and in particular to my new friends met at GSSI: sharing this experience with you made it unique and valuable. I would like to thank my family: my father who has always stressed me the importance of studying (I will never be able to repay you); my mother and my grandmother who have fully and unconditionally supported me; Antonia, Giusy, Domenico, Carmine, Mena, Giuseppe, Eleonora, Alessandra and who is coming up :). You all are my inestimable value. Finally, I would like to thank Prof. Francesco Auletta, who was my teacher at fifth year of high school: if during your first lecture you had not kicked me out of the classroom, most likely I would not be beating my fingers on the keyboard now. iv

Contents

Acknowledgements iii

Introduction 1

1 The dawn of the darkness4 1.1 Early times and ﬁrst evidences...... 5 1.2 Framework of the modern cosmology...... 9 1.3 On the origin and last fate of the Universe: the ΛCDM model...... 13 1.4 Strong candidates for dark matter: WIMPs...... 17 1.5 WIMPs halo models...... 19 1.6 An alternative point of view: f(R) theories...... 21

2 Directional dark matter search 24 2.1 An overview on dark matter search...... 24 2.2 Direct dark matter search...... 27 2.3 Results of direct experiments...... 30 2.3.1 Ionization in high purity Germanium detectors...... 31 2.3.2 Scintillator crystals...... 32 2.3.3 Cryogenic bolometers...... 34 2.3.4 Liquid noble-gas detectors...... 35 2.3.5 Threshold detectors and novel techniques...... 37 2.3.6 WIMP-nucleon exclusion plot...... 37 2.4 Directional dark matter search...... 39

3 Nuclear Emulsions for WIMP Search with directional measurement 41 3.1 Nuclear emulsion technique and Nano Imaging Tracker...... 43 3.1.1 NIT emulsion production...... 44 3.1.2 Chemical treatments and handling...... 46 v

3.2 Background sources...... 47 3.2.1 External background sources...... 48 Environmental gamma source...... 48 Environmental neutron source...... 48 Muon-induced neutron and cosmic muons background...... 50 Neutrino diffuse background...... 51 3.2.2 Internal background sources...... 53 Electrons induced by 14C...... 53 Radiogenic Neutrons...... 56 3.2.3 Instrumental background...... 56 3.3 The NEWSdm project...... 58 3.4 Readout strategy...... 60 3.4.1 Shape analysis for candidate tracks...... 61 3.4.2 Candidate validation with the resonance effect of polarised light.. 62 3.4.3 Optical microscope for LSPRs analysis...... 66 3.5 Sensitivity...... 68

4 Background simulation 71 4.1 Input parameters...... 71 4.1.1 Neutron sources...... 72 4.1.2 Cosmic muons...... 73 4.1.3 Environmental gammas and electrons from 14C...... 75 4.2 Simulation of NIT response to electrons...... 78 4.3 Intrinsic neutron and electrons from 14C background...... 81 4.4 Technical test simulation...... 83 4.5 Simulation of the pilot experiment...... 85 4.5.1 Opera emulsion as a veto...... 87 4.6 Discussion on simulation results...... 90

5 Resonance effect of polarised light in NIT emulsions 91 5.1 Scanning and analysis processes...... 91 5.2 Plasmon variables...... 93 5.3 Test beam with Carbon ions...... 95 5.3.1 Simulation of the test beam...... 98 5.3.2 Scanning of the data...... 105 5.4 Position accuracy...... 105 vi

5.5 Shape analysis...... 107 5.6 Plasmon analysis...... 109 5.6.1 Microtracks and Npeaks...... 111 5.6.2 Isolated grains...... 111 5.7 Efﬁciency and track length threshold with plasmon analysis...... 114 5.8 Summary...... 118

6 Neutrino studies with NEWSdm detector 122 6.1 Coherent elastic neutrino-nucleus scattering...... 123 6.2 Neutrino ﬂoor for the NEWSdm detector...... 125 6.3 Supernova neutrinos with the NEWSdm detector...... 128 6.3.1 Supernova neutrino source...... 129 6.3.2 Supernova neutrino signal...... 130 6.3.3 Background sources...... 133 6.3.4 Results...... 133 6.4 Neutrinos from nuclear reactors...... 137 6.5 Neutrinos from spallation neutron source...... 138 6.6 Conclusions on neutrino studies...... 139

Conclusions 141 vii

List of Figures

1.4 All-sky WMAP measurement of the CMB radiation temperature [30]. The lowest temperatures are represented by blue regions while the highest by red regions. The small fluctuations shown are of magnitude O(µK) with the average temperature measured to be 2.72548 ± 0.00057 K...... 14 1.5 The CMB power spectrum as a function of angular scale. Red line is the best fit to the model, and the grey band represents the cosmic variance. [31] 15 1.6 (Left): Curvature and expansion of universes containing both matter and a cosmological constant Λ. The highlighted regions indicate the best fitting values from CMB and galaxy cluster data added to the Supernova Cosmol- ogy Project (SCP) results [37]. (Right): The abundance relative to H of 4He, 2H, 3He and 7Li as a function of baryon density [38]...... 16 1.7 The density as a function of Galactocentric radius for several radial profiles of the DM halo of the Milky Way [50]...... 21 1.8 Best fit of rotation curves for the galaxies NGC 4455 (left) and NGC 5023 (right). The data are represented by dots, the Newtonian potential by the short dashed line, the correction term by the long dashed line. The total rotation curve vc(R) is represented by the solid line [52]...... 23 1.9 Hubble’s diagram for Type Ia Supernovae. The red line represents the best fit of the theory with the observed data with 1σ error bars. The yellow band represents the 1σ uncertainty [55]...... 23

2.1 Diagram of possible dark matter detection channels. The arrows indicate the direction of the reaction [58]...... 25 2.2 Typical representation of the sensitivity region for dark matter experiment. The black line represents an upper limit reference curve while the colored ones show the variations due to different properties of the detector. The closed curve represents the signal contour in case of an observation [57]... 31 2.3 Direct dark matter techniques [57]...... 32 viii

2.4 DAMA/LIBRA annual modulation versus the time exposure [76]...... 33 2.5 Schematic representation of the single phase (left) and double phase operation mode [57]...... 36 2.6 Signal indications (closed curves) and exclusion limits (open curves) for low (left) and high (right) WIMP mass in the spin-independent case [57, 96]. 38 2.7 Signal indications (closed curves) and exclusion limits (open curves) for low (left) and high (right) WIMP mass in the spin-dependent case [57].... 38 2.8 Schematic representation of the Earth motion through the Milky Way..... 40 2.9 Hammer-Aitoff projection of the WIMP ﬂux distribution [109]...... 40

3.1 Distribution of the crystal diameter measured with a transmission electron microscope (TEM) for U-NIT (left) and NIT (right) [137]. Different colours represent different production batches...... 45 3.2 Flux of environmental gamma in underground LNGS halls [139]...... 49 3.3 Environmental neutron flux in underground LNGS halls. [141]...... 50 3.4 The total muon flux (left) and the total muon-induced neutron deduced flux for several underground sites. [143]...... 51 3.5 The differential energy spectrum for muon-induced neutrons at different underground sites [143]...... 52 3.6 Solar and atmospheric neutrino flux and diffuse supernova neutrino background (DSNB) [146]...... 52 3.7 Sensitivity to electrons of NIT emulsions versus the temperature [147].... 55 3.8 Nuclear (dashed) and electron (solid) stopping power versus the kinetic energy for C (red), Kr (blue) and e− (black) [147]...... 55 3.9 Neutron flux from intrinsic contamination in NIT emulsions [152]...... 57 3.10 Number of background tracks as a function of the fog density for different track lengths...... 58 3.11 Schematic representation of the reference system in spherical coordinates. The θ and φ angles represent the 3D angle of the reicoled nucleus and its projection in the emulsion plane, respectively...... 59 3.12 Schematic representation of the experimental set-up for an exposure of 10 kg per year. The equatorial telescope is represented by the two green arms, the shield by the cyan cylinder and the NIT stack in yellow...... 60 3.13 Schematic (left) and real (right) picture of the shielding for the technical test installed in underground Gran Sasso laboratory...... 61 ix

3.14 Major axis versus minor axis for the 400 keV Kr-ion sample (left) and not exposed sample (right). Red and blue dots represent clusters with an ellipticity larger than 1.5...... 63 3.15 2D anglular distribution of clusters surviving the ellipticity cut (e > 1.5) for the 400 keV Kr-ion sample (left) and not exposed sample (right)...... 64 3.16 Schematic representation of LSPRs effect [162]...... 64 3.17 Scattered-light spectra from Ag particles with spherical (left) and elliptical (right) shape. The inset shows the particle image taken from the Scanning Electron Microscope (SEM) [159]...... 65 3.18 Resonance light effect exploited using different polarization angles of the incident light on an elliptical cluster from a 100keV C-ion sample. On the left are reported the dx and dy displacements of the cluster barycenter versus the polarization angle. On the right is reported the barycenter shift in the xy−plane...... 65 3.19 Optical microscope for dark matter search assembled in Napoli University. 67 3.20 Optical microscope with color camera (top) and TEM (bottom) images of nano-rods of 45 × 80 nm2 (left) and 45 × 120 nm2 (right)...... 69 3.21 Left: Exclusion curve at 90% conﬁdence for WIMP in the (mass,cross-section) plane for 100 expected background events and 100 kg year exposure. Right: Exclusion limits for the NEWSdm detector with 10 ton × year exposure and 30 nm threshold (solid blue curve) and with 100 ton × year exposure and 50 nm threshold (dashed red curve)...... 70

4.1 Event display of 100 primary particles with secondaries (A) and nuclear (B) and electron (C) recoil in GEANT4...... 72 4.2 Monte Carlo simulation of environmental neutrons...... 74 4.3 Monte Carlo simulation of cosmogenic neutrons...... 74 4.4 Monte Carlo simulation of radiogenic neutrons...... 75 4.5 Monte Carlo simulation of the energy spectrum of cosmic muons at LNGS. 76 4.6 Monte Carlo simulation of the angular distributions of cosmic muons at LNGS...... 76 4.7 Monte Carlo simulation of environmental gammas...... 77 4.8 Monte Carlo simulation of electrons from 14C...... 77 4.9 (A) Schematic representation of gamma interaction in GEANT4. (B) dE/dx versus the fraction of the total track length for primary (blue) and secondary (red) electrons...... 79 x

4.10 Schematic representation of DBSCAN method (A) and its application on an electron track (B)...... 80 4.11 (A) Box for radioactive source exposure of NIT sample. Event display of NIT exposure to 241Am (B) and its energy spectrum (C)...... 81 4.12 Electron density versus energy deposit in small clusters. Red and blue circles refer to two different scanned regions. The horizontal green dotted-line represents the measured electron density...... 82 4.13 Event display of 1 kg of NIT emulsion exposed to radiogenic neutrons.... 82 4.14 Shielding for 10g × month: lateral view (A), axonometric view (B) and top view (C)...... 84 4.15 Event display of NIT stack with emulsion films in yellow and the base in white (A), of the inner shell (red) with the detector (B), of the outer shells (green and blue) filled with shielding materials as Polyethylene and Copper (C and D)...... 86 4.16 Rate of background events, normalized to 10 kg yr exposure, induced by external neutron sources versus the shielding thickness for the polyethylene and water options...... 88 4.17 (A) Event display of NIT films (yellow) among OPERA films (blue). (B) Scatter plot of charged particle positions in a layer of NIT emulsion...... 89 4.18 Event display of false positive recoils (red triangles) linked to charged particles as µ (A) and d and p (B)...... 89

5.1 Schematic illustration of the grain reconstruction process. 2D merged clusters are represented in red and the best-focus cluster in blue. 2D merged clusters are linked to form the reconstructed grain represented in green... 93 5.2 Track length distributions of WIMP-induced recoils in the NEWSdm detector obtained by SRIM simulation. Different colors represent different WIMP masses...... 94 5.3 Event displays of BFPCs for two isolated grains...... 96 5.4 XY scatter plot of BFPCs positions for a static grain (5.4a) and a moving grain (5.4b)...... 97 5.5 Event display of BFPCs for a npeak grain...... 97 5.6 Track length distribution obtained by SRIM simulation for 100 keV (A), 60 keV (B), 30 keV (C), 10 keV (D) Carbon ion beams...... 99 5.7 Last hit positions, as provideed by SRIM simulation, in the emulsion plane (XY) for 100 keV (A), 60 keV (B), 30 keV (C), 10 keV (D) Carbon ion beams.. 100 xi

5.8 Monte Carlo simulation of the crystals dispersed in a NIT emulsion..... 101 5.9 Coordinates (x, y, z) and radius of the simulated crystals...... 101 5.10 (A) Schematic illustration of a track passing through the crystal pattern. Representation of zero crystal (B), one crystal (C) and n-crystals (D) categories...... 103 5.11 Track length distributions and related cumulative functions for the n-crystals category of 100 keV (A,B), 60 keV (C,D) and 30 keV (E,F) C ion samples.... 104 5.12 Schematic illustration of marginal points outside (left) and inside (right) the crystals...... 105 5.13 (x, y) grain positions measured with (black) and without (red) polarized light before (A) and after (B) the alignment process...... 106 5.14 Residual distribution of the aligned grains...... 106 5.15 Position accuracy for the x (A) and y (B) coordinate...... 107 5.16 2D angular distribution obtained by the data (red) and the SRIM+Crystals simulation (blue) for the 10 keV C ion sample...... 108 5.17 2D angular distribution obtained by the data (red) and the SRIM+Crystals simulation (blue) for the 100 keV (A), 60 keV (B), 30 keV (C) C ion sample.. 109 5.18 Track length threshold achieved with shape analysis with 1σ (dark teal) and 2σ (light teal) error bands for the 100 keV (A) and 60 keV (B) C ion samples. 110 5.19 2D angular distribution obtained by the data (red) and the SRIM+Crystals simulation, with a track length threshold at 190 nm (blue) for the 100 keV (A), 60 keV (B), 30 keV (C) C ion sample...... 110 5.20 Track length versus the φ angle of micro-tracks and npeaks grains for 100 keV (A), 60 keV (B), 30 keV (C) and 10 keV (D)...... 112 5.21 2D angular distribution of npeaks grains obtained by shape (blue) and plasmon (red) analysis for the 100 keV (A), 60 keV (B), 30 keV (C) and 10 keV (D). 113 5.22 Distributions of the barycenter displacement for the 100 keV (A), 60 keV (B), 30 keV (C) and 10 keV (D)...... 115 5.23 2D angular distribution of moving grains (red) and static grains (blue) for the 100 keV (A), 60 keV (B), 30 keV (C) and 10 keV (D)...... 116 5.24 2D angular distribution of moving grains obtained by shape (blue) and plasmon (red) analysis for the 100 keV (A), 60 keV (B), 30 keV (C) and 10 keV (D)...... 117 5.25 Track length threshold achieved with plasmon analysis with 1σ (dark teal) and 2σ (light teal) error bands for the 30 keV C ion sample...... 118 xii

5.26 2D angular distribution of static grains obtained by shape (blue) and plasmon (red) analysis for the 100 keV (A), 60 keV (B), 30 keV (C) and 10 keV (D)...... 119 5.27 Track length threshold achieved by adding the plasmon analysis with 1σ (dark teal) and 2σ (light teal) error bands for the 100 keV (A) and 60 keV (B) C ion samples...... 120 5.28 Sensitivity curve of NEWSdm experiment assuming zero background and a track length threshold of 120 nm...... 121

6.1 Feynman diagram of the CENNS process...... 123 6.2 Energy dependent cross-section for CEνNS after integrating the differential cross-section (Eq. 6.1) over the solid angle...... 124 6.3 Dependence of the track length of neutrino-induced recoils from the neutrino energy...... 125 6.4 The neutrino floor (orange-dotted) for a Xe/Ge target in the WIMP-mass cross-section plane...... 126 8 6.5 Event rate induced by ν( B) (red) and Mχ = 6 GeV (blue) as a function of the recoil energy for a Xenon target...... 127 6.6 Neutrino floor (black-dotted line) for the NEWSdm detector...... 128 6.7 (A) Fluences for the three neutrino species as defined in Eq. 6.4. (B) Total number of events (from Eq. 6.2) of supernova neutrino induced recoils per ton of active mass, as a function of the threshold on the recoiling nucleus energy...... 130 6.8 Number of expected events per ton of active mass as a function of the distance D of the supernova explosion...... 131 6.9 (A) Track length versus transferred energy for the target nuclei of NIT emulsions. (B) Track length distribution in NIT emulsions of supernova neutrino induced recoils in the range [0.05, 1] µm...... 131 6.10 Distributions of the emulsion angles θe (a) and φe (b) of supernova neutrino induced recoils in the NEWSdm detector...... 132 6.11 Mollweide projection in a Galactic-like coordinate system of the induced 8 recoils from B solar neutrinos: the latitude corresponds to θe while the longitude to φe − π/2. The magenta line marks the neutrino arrival direction, i.e. from the Sun to the Earth...... 134 xiii

6.12 PDFs of recoiled nuclei, normalized to 1, induced by supernova neutrinos (blue), solar neutrinos from 8B (green) and radiogenic neutrons (red). The track length, θe and φe distributions are shown in panels (a), (b) and (c), respectively...... 135 6.13 Mean signiﬁcance as a function of the exposure time for a 30 ton mass detector (blue dotted line), for the supernova neutrino signal (a) and the 8B neutrinos (b)...... 136 6.14 Residuals between the measured and expected distance...... 136 6.15 Neutrino spectrum for each isotope in nuclear reactors according to the Huber and Mueller parametrization [199]...... 137 6.16 (A) Track length distribution in NIT emulsions of reactor neutrinos induced recoils. (B) Dispersion factor (black squares) and neutrino induced recoil rate (red circles) versus the NIT exposed mass...... 138 6.17 (A) Energy spectrum for prompt and delayed neutrinos at SNS. (B) Track length distribution in NIT emulsions of nuclear recoils induced by neutrinos from the spallation neutron source. An exposure of 10 kg yr it has been assumed...... 140 xiv

List of Tables

1.1 Current values for the density parameter Ω in the Benchmark Model for our Universe [23, 39]...... 17

3.1 Chemical composition of NIT emulsion and fraction mass of its constituents. 45 3.2 Energy deposit for electrons and ions in NIT emulsions...... 54

4.1 Flux of external and internal sources at LNGS...... 73 4.2 Background rate from intrinsic neutrons and electrons from 14C...... 83 4.3 Estimation of the background rate, normalized to [10 g month]−1, induced by the external sources for the technical test...... 84 4.4 Background rate estimation induced by external gamma and neutron sources for 10 kg yr exposure with a shielding made of 100 cm of polyethilene.... 87 4.5 Density of electron-induced grains in NIT emulsions for the technical test and the pilot experiment...... 90

5.1 Event fraction of the three categories for each sample...... 102 5.2 Event fraction with marginal points inside or outside the crystals...... 103 5.3 Event fraction for each category of grains in the dataset...... 111

6.1 Ton per year exposure required in order to expect one neutrino-induced event for different track length thresholds...... 127

xvi

To the rising sun. . .

Introduction

Direct Dark Matter searches are nowadays one of the most exciting research topics. Many observations and experimental evidences in the last decades suggest a key role of dark matter in the origin and evolution mechanisms of our Universe, although its intrinsic nature is still unknown. Several experimental efforts are concentrated on the development, construction, and operation of detectors looking for the scattering of target nuclei with Weakly Interactive Massive Particles (WIMPs). Furthermore, the need for an increasing sensitivity for the WIMP observation makes direct dark matter detectors able to detect the coherent elastic neutrino-nucleus scattering CEνNS which is an irreducible background source unless directional information can be exploited. Directional dark matter detectors are usually based on low-pressure gas time projection chambers which cannot achieve a sufficient target mass to be sensitive to the supposed low rate WIMP interactions. NEWSdm (Nuclear Emulsions for WIMP Search with directional measurement) is meant to be the first experiment with a solid target for directional dark matter searches: the use of a nuclear emulsion based detector, acting both as target and tracking device, would allow to extend dark matter searches beyond the neutrino floor and provide an unambiguous signature of the detection of Galactic dark matter. The novel emulsion technology, based on the use of nuclear emulsion films with nanometric AgBr crystals, called NIT, makes it possible to record the sub-micrometric tracks produced by the WIMP scattering off a target nucleus. The present PhD work covers several aspects of the NEWSdm experiment. The first one is the evaluation of the background sources affecting dark matter searches in underground laboratories: the intrinsic radioactivity of target materials, the environmental radioactivity and neutrons produced by the spallation of cosmic muons in the surrounding rock. I have performed simulation studies for the technical test with a 10 g detector mass planned for the beginning of 2019, and for the pilot experiment of 10 kg×year exposure. The out- come of these studies have driven the design of the detector shield in terms of material Introduction 2 composition and dimensions. I was involved in the different phases of the preparation for the 10 g test: optimization of the detector layout, preparation of the NIT samples in underground facilities, monitoring of the environmental conditions during the exposure, development of the exposed samples. The detection of WIMP induced nuclear recoils in a solid medium presents us a considerable challenge since the expected signature is represented by a few hundred nanometers- long tracks. NIT emulsions are the best tracking detector since they allow to reconstruct tracks down to a few hundred nm and optical microscopes, although limited by the optical resolution limit, are currently the best devices for the scanning both in terms of speed and feasibility. The observation of track lengths shorter than the diffraction limit is therefore crucial for the NEWSdm experiment. This challenging requirement can be achieved by exploiting the resonance effect of polarized light: nanometric metallic grains behave differently when illuminated by light with different polarization angles. I have worked on the characterization of the response of resonant light effect by analysing NIT samples exposed to C ion beams, defining for the first time the procedure and selection criteria for the signal selection. It was possible to benchmark with real data the capability to reconstruct nuclear recoils induced by WIMPs. An emulsion based detector with nanometric resolution can offer the unique possibility to overcome the neutrino floor and, at the same time, it will be sensitive to coherent elastic neutrino-nucleus scattering. I have studied the capability of the NEWSdm experiment of observing Supernova neutrinos, Solar neutrinos, reactor and spallation neutron source neutrinos. My thesis is divided in six chapters organized as follows: Chapter 1 contains a brief review on the dark matter problem in the modern cosmology context. A description of WIMP dark matter candidate is provided; Chapter 2 reports an overview of the dark matter search techniques focusing in particular on direct and directional search; Chapter 3 contains a description of the NEWSdm detector and focuses on the nanometric nuclear emulsions, the background sources affecting underground laboratories, the experimental concept and the read-out strategies; Chapter 4 focuses on the GEANT4 simulation of external and intrinsic background sources. The optimization of the shield for the technical test and pilot experiment is discussed; Introduction 3

Chapter 5 contains the study of resonance effect of polarized light with samples exposed to Carbon ion beams;

Chapter 6 reports the neutrino simulation studies with nanometric nuclear emulsions: neutrino ﬂoor, supernova neutrinos, solar neutrinos, neutrinos from reactors and neutrinos from spallation neutron source. 4

Chapter 1

The dawn of the darkness

"Fiat lux on the darkness"

Since the earliest times humans felt like they were the centre of the Universe. The progres- sive control of the nature, the supremacy over all other existing species and the belief that everything in the world is based on the human experience led to the certainty of the human mankind to be the most important entity in the whole Universe. As a consequence, the geocentric model became an essential postulate in the explanation of all celestial objects moving through the sky. On the other side, the natural instinct to overcome the limits in the knowledge has driven, although off and on, an ongoing development of science and technique. The Copernican revolution [1] and the Darwinism [2] have been the ﬁrst attacks to the special role of the Earth and of the human being, respectively. The rise of the scientiﬁc method by Galileo Galilei [3] and the industrial revolution made possible, on an objective basis, the investigation of all the phenomena and the mastery of them. In that historical background Isaac Newton discovered the fundamental laws of gravitation which determine the motion of the astronomical objects [4] and the invention of the telescope gave the possibility to deeply inspect them. The Universe started to look ever-widening and more unknown with the Earth and the Sun just like ordinary pawns of a boundless cosmic chessboard. In the early 20th-century Albert Einstein published the theory of Special Relativity (SR)[5] and of General Relativity (GR)[6] which led to modern cosmology. The idea of an absolute universal time has been wiped out by a notion of time depending of the reference frame while the cosmological principle states that "there is nothing special about our location in the Universe". Nevertheless, the awareness of a non centrality of the mankind both in space and time boosted once again the scientists in the search for all the countless questions linked to such a mysterious, dark Universe. Chapter 1. The dawn of the darkness 5

1.1 Early times and ﬁrst evidences

Lord Kelvin was among the first to use the kinetic theory of gases in the analysis of the Milky Way. Taking gravitation into account, he supposed a relationship between the velocity dispersion of stars and the total amount of mass in our galaxy, which therefore appeared to be larger than the stars that could be seen. He concluded that — " Many of our stars, perhaps a great majority of them, may be dark bodies " [7]. On the other hand, since the velocity dispersion obtained by the Kelvin’s estimation was of the same order of magnitude of the expected one, Henry Poincaré in the 1904 replied that — " there is no dark matter, or at least not so much as there is of shining matter ” [8]. For the first time the term Dark Matter was coined to indicate something that had to be smaller than the visible matter the most part of the Universe is made of. This statement would have been completely overturned at the end of the century. In the early 1930s Frank Zwicky gave the first clear proof of a significant amount of missing matter studying the velocity dispersion of galaxies in the Coma cluster. Using the observed Doppler effect in the galactic spectra he calculated the velocity of the stars belonging to the cluster. Then, he applied the virial theorem to relate the gravitational potential energy of the cluster to its kinetic energy :

GM ≈ σ2 (1.1) R where G is the gravitational constant, M the total mass of the system, R the distance of stars from the center of the cluster and σ the velocity dispersion. The galaxy velocities were too fast compared to the ones expected from the their mutual gravitational pull. Consequently, the total estimated mass of the cluster was about 400 times larger than the visible mass inferred by the galaxy luminosities. In this context, Zwicky wrote — " If this would be conﬁrmed, we would get the surprising result that dark matter is present in much greater amount than luminous matter " [9]. In the 1970s, Kennet Freeman and, separately, Vera Rubin and Kent Ford published two important studies about the rotation curves of spiral galaxies that contain almost the total mass in a central region called bulge from which a ﬂat rotating disk is formed. The velocity v of a star with a mass m moving at a distance r from the galaxy centre can be obtained by equalising gravitational and centrifugal forces:

mv2 GM(< r)m = (1.2) r r2 Chapter 1. The dawn of the darkness 6 where M(< r) is the mass of the galaxy inside the radius r. For a star in the bulge one expects v ∝ r while v ∝ r1/2 is expected in the thin disc. Observing some galaxies Free- man found that not only the velocities of stars and gases do not decrease with the distance from the center, but in some cases the matter is moving faster at larger radii [10]. Few years later, Rubin and Ford were studying the Andromeda galaxy. They found that the velocities stayed rather constant with radius [11] (see Fig. 1.1). These anomalies, confirmed by other observations, could be only explained assuming that each galaxy is surrounded by a large halo of dark matter. Whilst evidences of dark matter were obtained though observations on large scales, on the other hand the comprehension of its intrinsic nature moved towards the smaller scale of the particle physics [13]. From the beginning, the missing matter problem was addicted to cold stars or solid bodies too faint to be detected with available telescopes [14]. The Massive Compact Halo Objects (MACHOs) which including also neutron stars and black holes, were considered one of the most convincing candidates to solve the enigma [15]. Moreover, theories like the Modified Newtonian Dynamics (MOND) suggested an extension of the gravitational laws to explain the observation on galactic scales [16]. The dark matter problem came out through several evidences of gravitational origin of the visible matter. In the early 1990s, the gravitational lensing became the most direct technique to observe dark matter effects on photons. Being the light bent by the gravitational field of massive objects, the profile distribution of dark matter in the galactic halo can be reconstructed exploiting the distortion of images (strong and weak lensing) or by the change in the received brightness amount (microlensing) of a light source [17]. The Eros2 project, using the microlensing technique, showed that the MACHOs cannot account for all the missing matter in the galactic dark halo [18]; in particular, these astrophysical objects represent just a few percent of the mass in the galactic halo [19]. In the same period, the idea of a dark matter made of a not-yet discovered subatomic particle began to arise above all the other conjectures and several observations enhanced this change of perspective. The most spectacular evidence for the particle nature of the dark matter has recently been provided by the Bullet Cluster which refers to the collision of two galaxy clusters. In fig. 1.2 gravitational lensing together with X-ray emission observations used to detect the hot intracluster medium (ICM), show a separation of the baryonic component from the supposed dark matter halo. The two clouds of hot x-ray emitting gas, inferred from Chandra X-ray Observatory, is shown in magenta after the collision, the dark matter halos in blue are interpolated by the gravitational lensing. The bullet-shaped cloud on the right is distorted by the collision. The clear feature of this composite image is the large gap between the gas distributions and dark matter halos which behave Chapter 1. The dawn of the darkness 7

FIGURE 1.1: Rotation curves of several spiral galaxies. The contribution of visible matter (dashed), gas (dotted) and dark matter halo (dash-dot) is shown. Data are represented by black squares, the dark matter model by solid lines [12]. Chapter 1. The dawn of the darkness 8

FIGURE 1.2: Composite image of galaxy cluster 1E0657-56 [22]. The hot gas distributions are shown in magenta, the dark matter halos in blue. as a collision-less particles weakly interacting [20, 21]. Without dark matter, the centre of gravitational lensing should follow the baryonic matter. Therefore, the Bullet Cluster is considered an important proof against the MOND theories. From the cosmological point of view, the intrinsic collision-less nature of hypothetical dark matter particles would be crucial not only to explain some properties of galaxies but also the formation of the structures that are nowadays visible in the Universe. A powerful proof to support dark matter has been provided by the angular power spectrum of Cosmic Microwave Background (CMB), which will be discussed in the following. The measurements of the anisotropy peaks have given important constraints on the amount of baryonic matter which would represent only one quarter of the whole mass in the Uni- verse [23]. In the light of what has been observed until now, although the most convincing interpre- tation of dark matter consist of weakly interacting subatomic particles, a clear proof of the existence of such fundamental constituents of the Universe, despite all efforts, has not been provided yet. Chapter 1. The dawn of the darkness 9

1.2 Framework of the modern cosmology

The requirement of a dark matter made of undiscovered particles with speciﬁc properties not only is of use to explain some galactic anomalies but also to the evolution of the Uni- verse. The modern cosmology arises in the ﬁrst decades of the last century with the Ein- stein Field Equations (EFE) (1915) and the Hubble-Lemaître law, obtained independently by Georges Lemaître (1927) and Edwin Hubble (1929); it is based on the cosmological principle which supports an isotropic and homogeneous Universe at large scales. The EFE represent one of the most apical point in the comprehension of the Universe reached by the human brain. They show a deep connection between the space-time metric and the mass-energy amount of the Universe in the following graceful way

1 8πG R − Rg = − T (1.3) µν 2 µν c4 µν where Rµν is the Ricci tensor, R the scalar curvature, gµν the metric tensor, Tµν the energy- momentum tensor, G the gravitational constant. Sir John Archibald Wheeler summarized the deeper meaning of the Eq. 1.3 using these famous words: "matter tells space-time how to curve, and space-time tells matter how to move". The EFE caused two fundamental conse- quences in the description of the Universe. The former is that we live in a curved space- time where the Euclidian metric is not valid any more. The latter is that the curvature of the space-time, due to the presence of a mass, is the source of the gravitational field; gravity therefore is not an ordinary force involving two massive objects but a distortion of the space-time geometry. In this framework, even the electromagnetic radiation feels gravity and therefore the lensing effect occurs. Until then it was a common idea that the Universe is static and eternal. When Einstein used the GR to describe for the first time the dynamic of an homogeneous Universe, he re- alised that even an infinite Universe is condemned to collapse inwards. As a consequence, he added a new term in the EFE, the so-called cosmological constant Λ, whose aim was to balance the deflation without changing the GR theory. The EFE used then to describe the Universe are: 1 8πG R − Rg − Λg = − T (1.4) µν 2 µν µν c4 µν

As shown in the 1.4, Λ is not linked to the Tµν tensor, it appears rather a general property of the Universe. Many criticism raised at that time because of Λ, but after not so many years it became unavoidable to explain the evolution of the Universe. Chapter 1. The dawn of the darkness 10

FIGURE 1.3: A plot of distance versus velocity for a set of 1355 galaxies [24]. Hubble-Lemaître law is given by the best ﬁt to the data.

At the end of 1920s Lemaître and Hubble were the ﬁrst to ﬁnd out that the we live in an accelerating Universe by studying the relationship between the galaxies redshift and their distance from the Earth. Farther are the galaxies, faster they move away from us (see Fig. 1.3), according to the Hubble-Lemaître law:

~v = H0~r (1.5) where H0 is the Hubble’s constant. An accelerating expansion of the Universe in the GR framework can be explained only with the presence of Λ, whose nature is still unknown. In order to ﬁnd a solution for an isotropic, homogeneous and accelerating Universe an appropriate metric of the space-time is needed. Since the distance between two points changes with time, the cosmological expansion can be expressed as

~r = a(t)~x (1.6) Chapter 1. The dawn of the darkness 11 where~r is the real distance, ~x the co-moving distance and a(t) a scale factor representing the relative expansion of the co-moving coordinate system. Using the 1.6 in the 1.5, the Hubble’s constant can be written in terms of a(t)

a˙(t) H(t) = . (1.7) a(t)

The Hubble parameter is usually deﬁned in terms of the dimensionless reduced Hubble parameter h H(t) = 100 h km s−1 Mpc−1 (1.8) where the current observations give at present h0 = 0.674 ± 0.005 [25]. According to the cosmological principle and the expanding Universe, the FLRW1 metric is simplest model to describe our Universe and generally it is reported as

dr2 ds2 = c2dt2 − a2(t) + r2(dθ2 + sin2θdφ2) (1.9) 1 − κr2 where κ is a parameter used to describe the curvature of the Universe which can be closed ( κ = 1), open (κ = −1) or flat (κ = 0). For a flat Universe we come back to the Euclidean metric where a straight line is the shortest distance between two points and the sum of the angles of a triangles is π rad. Using the FLRW metric, one can derive the most important equation in the cosmology, the Friedmann equation describing the evolution of the Universe. Friedmann studied the Universe as a perfect friction-less fluid with density ρ and pressure p within the framework of the GR and he found the following relation:

a˙ 2 κc2 Λ 8πG + − = ρ (1.10) a a2 3 3 where κ = −2U/mc2x2 with U the total energy that is a constant. It is worth noting that k is independent from x thus preserving the homogeneity hypothesis, since U ∝ x2. Furthermore, to solve the Friedmann equation we need to know how the density ρ evolves with the time. From the ﬁrst law of thermodynamics dE + pdV = TdS and assuming a

1Friedmann-Lemaitre-Robertson-Walker metric Chapter 1. The dawn of the darkness 12 reversible adiabatic expansion dS = 0 one can obtain the ﬂuid equation:

a˙ p ρ˙ + 3 ρ + = 0 (1.11) a c2 where the time-variation of density is reported in terms of the Hubble parameter. By deriving the Friedmann equation (1.10) and substituting ρ˙ from the Eq. 1.11, one can obtain the acceleration equation:

a¨ 4πG 3p Λ = − ρ + + . (1.12) a 3 c2 3 which does not depend on the curvature parameter κ. If Λ is positive it acts as a repulsive force against the attractive one due to the gravitation; therefore, it is often called dark energy. As seen above, the evolution of the Universe is strictly linked to the density of its constituents: radiation (ρr), matter (ρm), dark energy (ρΛ ≡ Λ/8πG). It is useful to deﬁne these densities with respect to the critical density ρc

3H2(t) ρ (t) = (1.13) c 8πG which represents the density required to have a ﬂat Universe with Λ=0. The density parameter Ω(t) is then deﬁned for each components as:

ρr ρm ρΛ Ωr ≡ , Ωm ≡ , ΩΛ ≡ . (1.14) ρc ρc ρc and the total density parameter Ωtot(t) is their sum. From the Eq. 1.10 one can write the curvature as a2 H2(t) κ = Ω − 1 (1.15) c2 tot where one obtains: a negative curvature if Ωtot < 1, a positive curvature if Ωtot > 1, while a ﬂat geometry corresponds to Ωtot = 0. It is worth noting that only the curvature cannot determine the last fate of the Universe since it depends also on the relative amount of each component. Chapter 1. The dawn of the darkness 13

1.3 On the origin and last fate of the Universe: the ΛCDM model

" There is a theory, which states that if ever anyone discovers exactly what the universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another theory, which states that this has already happened. Douglas Adams"

The Hubble-Lemaître law and the cosmological principle suggest that at very beginning of times the whole Universe was just a space-time singularity with an infinite density. Then, a formidable explosion, known as Big Bang, caused the expansion and the cooling of the Universe with the resulting formation of the structures such as galaxies which are becoming further apart. In the earliest times the Universe was made of a hot plasma of photons, baryons and electrons. Electrons were trapped because of Thomson scattering with the plasma and they had a typical black-body spectrum. After ∼ 3 × 106 years, the expansion of the Universe cooled the plasma to ∼ 3000 K allowing the recombination of electrons and ionized baryons in neutral atoms (recombination epoch). From this point the Universe became transparent to the radiation and the black-body photons were free to escape away. The small fluctuations of matter density gradually pulled the nearby atoms increasing the gravitational attraction and cloud gas, stars and galaxies started to form the structures that we see at present. The CMB is a strong evidence of this scenario. In the 1965 Arno Penzias and Robert Wil- son [26] were the first to discover an almost isotropic electromagnetic radiation coming from the space that is not linked to any astrophysical object. The radiation, mainly evident in the microwave region, has a thermal black body spectrum at T = 2.75 K [27]. The CMB is thought to be the relic radiation of photons coming from a spherical surface called the surface of last scattering. The properties of the CMB has been largely investigated by the Cosmic Background Ex- plorer (COBE) [28] and the Wilkinson Microwave Anisotropy Probe (WMAP) [29] experiment and currently by the Planck satellite [23]. Although the CMB is isotropic at the level of 1 part in 106 (see Fig. 1.4), the small temperature fluctuations are extremely important to estimate several cosmological parameters and provide excellent constraints on cosmological models. The angular power spectrum of the CMB, obtained by the multipole expansion using Legendre polynomials, represents the temperature variations between two points within an angular distance θ (see Fig. 1.5). The amplitude of the peaks, the width Chapter 1. The dawn of the darkness 14

FIGURE 1.4: All-sky WMAP measurement of the CMB radiation temperature [30]. The lowest temperatures are represented by blue regions while the highest by red regions. The small fluctuations shown are of magnitude O(µK) with the average temperature measured to be 2.72548 ± 0.00057 K. and their position depend on the energy-matter content before and after the recombination epoch. In the region 100 ≤ l ≤ 1000 these peaks are called acoustic peaks since they are related to the temperature oscillation in the baryon-photon plasma of the early Universe. The first peak at l ∼ 200 gives an important estimates of the total density parameter that would be very close to 1; so it describes the geometry of a flat early Universe but not its topology. The height of each peak and their position provides estimates for the baryon density and other cosmological parameters. Constraints on Ωm and ΩΛ, whereas the radiation contribution is negligible, are given also from other experiments studying the redshift of the Supernova and the Baryonic Acoustic Oscillation (BAO) of galaxy clusters (see Fig. 1.6 (left)). In particular, Supernova Type Ia (SNIa) explosions are noteworthy for measuring the expansion of the Universe since they show a nearly uniform intrinsic luminosity such to be considered standard candles. The apparent brightness of a SNIa reveals how far in space, and therefore in time, it is: by comparing the apparent brightness with its redshift, which tells us how much the Universe expanded after the explosion, it is possible to study the Chapter 1. The dawn of the darkness 15

FIGURE 1.5: The CMB power spectrum as a function of angular scale. Red line is the best fit to the model, and the grey band represents the cosmic variance. [31] evolution over time of the expansion rate of the Universe, thus to determine the role of Λ at large redshifts [32]. In addition, BAO are a result from photon-baryon fluid density fluctuations due to the gravitational attraction and radiation pressure before the recombination epoch whose signs are imprinted both in the CMB through the acoustic peaks in the angular power spectrum and in the matter distribution in the galaxy power spectrum. The peak location in BAO signal of galaxy clusters provides a standard ruler for measuring the expansion rate. The scale of the ruler is calibrated by acoustic peaks in the CMB where peak positions allow to determine the distance travelled by the fluid from the Big Bang until recombination (sound horizon). Measuring the acoustic scale as a function of the redshift probes the volume of the Universe and therefore the expansion rate [33]. Only a small region with Ωm ∼ 0.3 and ΩΛ ∼ 0.7 is in agreements with all the data sets and the total density parameter Ωtot is very close to 1. Thus the Universe seems to be spatially flat, accelerating and expanding forever; in addition, it is made of dark energy for two-thirds, while matter represents only the 30%. An important argument supporting the Big Bang is the Nucleosynthesis theory (BBN) [34] of the origin of the light elements (D, 3He, 4He, 7Li). According to BBN, they were formed Chapter 1. The dawn of the darkness 16 in the early stage of Universe’s history, while the heavier ones would be produced later inside the stars. In Fig. 1.6 (right) it is reported the abundance relative to light elements as a function of baryon density. The horizontal lines indicate experimentally observed abundances and the curved lines correspond to computed values. The grey vertical line highlights agreement between observation and theory. Despite the significant discrepancy of the 7Li, addressed as Lithium problem [35], the theory predicts the abundances of light elements with a very high accuracy, compared with the experimental observations, if the baryonic density parameter Ωb is within the limits [36]

2 0.021 ≤ Ωbh ≤ 0.025 (95% CL) (1.16)

Using the value reported for h0, we found an upper limit of Ωb < 0.055 that is very far from Ωm ∼ 0.3. According to this result and other evidences from rotational curves and gravi-

FIGURE 1.6: (Left): Curvature and expansion of universes containing both matter and a cosmological constant Λ. The highlighted regions indicate the best ﬁtting values from CMB and galaxy cluster data added to the Super- nova Cosmology Project (SCP) results [37]. (Right): The abundance relative to H of 4He, 2H, 3He and 7Li as a function of baryon density [38]. Chapter 1. The dawn of the darkness 17 tational lensing, the total matter content in the Universe seems to be mainly dominated by a non-baryonic component Ωχ which behaves differently from the ordinary baryonic matter and therefore would represent the dark matter amount. The importance of dark matter is more straightforward if we look at the astrophysical structures in the present Universe. The CMB anisotropies describe the origin of the structures that then grew up through gravitational attraction. However, the small content of baryonic matter in the Universe is not enough to form the structures observed nowadays. Instead, the introduction of the dark matter provides the right yield of gravitational attraction needed to have objects such as galaxies and galaxy clusters that we observe now. The formation of structures requires a non-relativistic dark-matter, usually called cold dark matter (CDM), which can interact with the baryonic matter and differs from the hot dark matter which can travel freely. The cosmological model that ﬁts better with the observations is called ΛCDM model from the two main components the Universe is made of. For the sake of clarity the density parameters estimated by the WMAP and Planck experiments are reported in Tab. 1.1.

PARAMETER VALUE −5 Total radiation Ωr = 8.4 × 10 Baryonic matter Ωb = 0.049 ± 0.001 Non baryonic dark matter Ωnbdm = 0.268 ± 0.002 Total matter Ωm = 0.315 ± 0.020 Dark energy ΩΛ = 0.685 ± 0.020 Total density parameter Ωtot = 1.0005 ± 0.0033

TABLE 1.1: Current values for the density parameter Ω in the Benchmark Model for our Universe [23, 39].

1.4 Strong candidates for dark matter: WIMPs

As we have seen so far, compelling evidences show that luminous matter provides ∼ 3% of the total expected matter amount in the Universe, while adding the dark baryonic matter one can account only for ∼ 16%. The non-baryonic dark matter content is therefore ﬁve times larger. After the cosmological principle and the relativity of time, the most promising scenario Chapter 1. The dawn of the darkness 18 is that our Universe, excluding the dark energy, is dominated by a kind of matter far from everything we knows as reality. From being the center of the Universe the human mankind seems to be instead, as far as we know, just the most intellectual singularity ever created. Beyond the countless evidences of a missing matter on the galactic scale, the presence of dark matter becomes absolutely crucial to explain the formation of structures on cosmological scale. Even if all the matter of Universe was baryonic, there would be no enough time after the decoupling to form the galaxies and cluster of galaxies. Being dark matter particles unaffected by radiation, the density perturbations could quickly grow and after- wards attract the ordinary matter giving rise to the present Universe. This is possible only if dark matter particles were non-relativistic when they freeze out. The non-baryonic dark matter candidate ideally should have the following properties:

• cold, to give rise to the formation of the large scale structure;

• neutral, i.e. not interacting electromagnetically but only through the gravitations;

• collisionsless, with a very low interaction cross-section since they are still unob- served;

• massive, to account for the total amount of matter in the Universe;

• stable, to be in sufﬁcient quantity at the present day to explain the dynamics of galaxies.

In the Standard Model there are no particles with all these features and therefore the intrinsic nature of the dark matter is still unknown. A full review of candidates beyond the SM can be found in the Refs. [40, 41]. In the following, I will focus on the highly supported hypothesis of a dark matter made of Weakly Interacting Massive Particles, known as WIMPs. WIMPs are supposed to be in thermal equilibrium in the early Universe with the num- 3 ber of dark matter particles nχ ∝ T , where T was the temperature of Universe at that time. Two WIMPs therefore would collide producing other particles and the reverse reaction would happen with the same rate. Then, as the temperature cooled down, the 3 −m /T WIMPs density started to drop with nχ ∝ T e χ , where the Boltzmann factor takes into account the suppression of the dark matter particles, since the reverse process of two ordinary particles in two WIMPs was not allowed because particles did not have enough energy to produce the dark matter. Chapter 1. The dawn of the darkness 19

Solving the Boltzmann equation for its relic number density the density parameter for WIMPs can be written as

2.6 × 10−10 GeV−2 Ω h2 ∼ ∼ 0.1 (1.17) χ hσvi where hσvi is the average reaction rate of the thermal annihilation. For a 100 GeV mass particle with a weak-scale mediator a rate compatible with the current dark matter density can be retrieved. This coincidence is usually called WIMP miracle even if there is not a direct connection between WIMPs particle and the Fermi constant. Although the Standard Model does not include these kind of particles there are several extensions that could contain WIMPs candidates, e.g. one of the most important is the neutralino which is the Lightest Supersymmetric Particle (LSP) in Supersimmetry (SUSY) models [42].

1.5 WIMPs halo models

According to the observed rotation curves in the galaxies several models are arisen to describe the WIMPs proﬁle density distribution which is an essential parameter for their detection. In addition, these models have to be compatible with the structure formation simulations. In the following some of the most used are brieﬂy described. In order to avoid the unphysical divergence at centre, dark matter halos are usually parametrised with a pseudo-isothermal sphere with the following density ρ ρ (r) = 0 (1.18) Iso 2 1 + r r0

−2 −3 where the local WIMP density ρ0 ranges from 0.2 to 0.4 GeV cm [43] and rc is the core radius [44]. This density profile fits very well many rotation curve data showing a flat rotation curves at large radii. Although it is common to refer to this model as the Standard Halo Model (SHM), many features such as spiral arms, bar instabilities, col- lapses, mergers cannot be enclosed for a multiple description and are difficult to address analytically [45]. N-body simulations are powerful tools to investigate the formation and evolution of galaxies and study this collective behaviour [46]. The Navarro–Frenk–White (NFW) profile follows from N-body simulations of structure Chapter 1. The dawn of the darkness 20 formation with cold dark matter. The density profile is given by [47]

ρ δ ρ (r) = crit c (1.19) NFW 2 r 1 + r rs rs where ρcrit is the critical density, δc a dimensionless density and rs is a scale radius. The NFW density profile appears to be approximately universal since it provides a good description of cold dark matter halo masses from single galaxies to the halos of galaxy clusters. However, the NFW profile diverges as r−1 as r goes to zero showing a cuspy dark matter profile at small radii while the rotation curves of most low-mass galaxies suggest a core density profile with a flat mass distribution at centre. This discrepancy is usually called cuspy halo problem. The results of numerical simulations seem slightly improved by the Einasto profile given by [48] 2 r γ ρEin = ρ−2exp − − 1 (1.20) γ r−2 where r−2 is the radius of the sphere that contains half of the total mass, ρ−2 is the density at r−2 and γ is a numerical constant that assures the condition M(rs) = Mtot/2 with Mtot the total mass of the galaxy. Although the Einasto profile goes to ρ0 for r → 0, unlike the NFW profile which has a divergent density at centre, it is as well affected by the cuspy halo problem. A more cored density profile is provided by the Burkert profile [49] ρ ρ (r) = 0 (1.21) Burk 2 1 + r 1 + r rs rs where rs is the core radius and ρ0 the central density. The Burkert profile provides a very good fit for the observed rotation curves of dwarf galaxies. In Fig. 1.7 the density profile for each model is reported. It is worth nothing that all these models assume a spheri- cally symmetric dark matter density profile usually with an isotropic velocity distribution. On the other hand, numerical simulations of dark matter halos with baryons show anisotropies in the velocity distribution and in general deviations from the Maxwellian spectrum [51] which could affect the sensitivity of direct detection detectors. Chapter 1. The dawn of the darkness 21

FIGURE 1.7: The density as a function of Galactocentric radius for several radial proﬁles of the DM halo of the Milky Way [50].

1.6 An alternative point of view: f(R) theories

According to the ΛCDM model, well-known also as the concordance model since many astrophysical observation are explained within it, dark energy and dark matter play the leading role in the dynamics of the Universe. Although the cosmic acceleration and the missing matter problem are usually identiﬁed with such new enigmatic components, alternative point of views consider this puzzling paradigm as a ﬁrst signal that the General Relativity is not working at large scales without invoking the presence of new fundamental constituents. Extended Theories of Gravity (ETGs) examine the possibility that other curvature invari- ants, instead of the Ricci scalar, could contribute in the EFE. The simplest extension con- n sists of replacing the curvature scalar R with a generic power-law function f (R) = f0R , with f0 a normalisation constant and n > 1 the slope of the gravity lagrangian. Then, it is possible to derive the following equation

(m) 1 1 Tµν G = g [ f (R) − R f 0(R)] + f 0(R); −g f 0(R) + (1.22) µν f 0(R) 2 µν µν µν f 0(R) or in a more compact way m Tµν G = Tcurv + (1.23) µν µν f 0(R) Chapter 1. The dawn of the darkness 22

m curv where Tµν is the standard matter-energy tensor and Tµν defines a curvature stress-energy tensor of the fourth order derivatives of the metric gµν and, as a consequence, of the fourth order of gravity [52,53]. From Eq. 1.23 it is straightforward that an extension of the space- curv time metric gives rise to a new term Tµν which can be interpreted as a non-standard mass-energy tensor accounting for the missing matter and energy problems, although deriving from purely geometrical considerations. For clarification purposes, it is important to underline that ETGs are not alternative to the GR but just an extension of it, since in the the weak-field limit (Solar System scales) they have to reproduce the Newtonian gravity. Higher order gravity leads to corrections in the gravitational potential which can be written, for a point-like mass and using a Schwarzschild-like metric, as " # Gm r β Φ(r) = − 1 + (1.24) 2r rc where β is a parameter that controls the shape of the correction terms, rc is a scale-length depending on the mass of the system. The former is expressly related to the n parameter and therefore has to be an universal quantity; the latter is depending on the astrophysical system under study, this means that the gravitational potential is not invariant at any scales. For a central potential the circular velocity is

" β# 2 dΦ Gm r vc = r = 1 + (1 − β) (1.25) dr 2r rc where the first term is just half of the Newtonian potential and the second may be larger than the previous one. If r rc the second term becomes negligible and the classical potential is recovered. In this way, rotation curves of galaxies can be fitted also at large radii without invoking the presence of additional matter (see Fig. 1.8)[52]. Nevertheless, dark matter is crucial to accelerate the formation of the structure which grow from a gravitational instability. However, the gravitational potential from f(R) theories changes the limit of instability leading to a faster growth of perturbations of standard matter [54]. f(R) theories with n 6= 1 are also able to fit the Hubble-Lemaître law for the Type Ia Supernovae considering only the ordinary matter and without the introduction of the cosmological constant (see Fig. 1.9)[55]. Chapter 1. The dawn of the darkness 23

FIGURE 1.8: Best ﬁt of rotation curves for the galaxies NGC 4455 (left) and NGC 5023 (right). The data are represented by dots, the Newtonian potential by the short dashed line, the correction term by the long dashed line. The total rotation curve vc(R) is represented by the solid line [52].

FIGURE 1.9: Hubble’s diagram for Type Ia Supernovae. The red line represents the best ﬁt of the theory with the observed data with 1σ error bars. The yellow band represents the 1σ uncertainty [55]. 24

Chapter 2

Directional dark matter search

In the last decade scientists solved some of the most important open questions in physics such as the discovery of the Higgs boson, the conﬁrmation of the neutrino oscillation in appearance mode and, recently, the ﬁrst observations of gravitational waves. Unfortu- nately, the dark matter nature is still a big question mark, despite all efforts made until now. However, most of the attention is now focused on the dark matter search and a the community of scientists working on this challenge is rapidly increasing. Several experiments are hunting for an incontrovertible proof about the existence of the dark matter; different signatures are under investigations, different techniques have been developed for this purpose, others are emerging right now. In this Chapter, I will report an overview about dark matter searches giving more empha- sis on direct dark matter search and in particular on the power of the directionality. Although there is a wide plethora of dark matter candidates that have different nature and interaction type, in the next sections I will deal with the WIMP case only following the approach of Refs. [56, 57].

2.1 An overview on dark matter search

The search for dark matter particles is currently one of the main aims of the astrophysics and particle physics. Three channels involving these undiscovered particles are largely investigated (see Fig. 2.1):

1. collider search: production of dark matter particles from standard matter;

2. indirect search: production of standard matter from annihilation of dark matter particles; Chapter 2. Directional dark matter search 25

3. direct search: coherent scattering of dark matter particles with standard matter.

FIGURE 2.1: Diagram of possible dark matter detection channels. The arrows indicate the direction of the reaction [58].

In the ﬁrst channel the collision of electrons and protons at very high energies could produce pairs of dark matter particles. Since the latter do not interact electromagnetically, their presence can be deduced only observing events with missing transferred momentum and energy. The process can be summarized as follows:

pp −→ χχ¯ + X (2.1) where p is a proton, χ(χ¯) a dark matter (anti-)particle and X represents the hadronic jet. After the discovery of the Higgs boson at the Large Hadron Collider (LHC), the AT- LAS [59] and CMS [60], experiments are now looking for the signatures of new particles produced in the collisions such as WIMPs especially in the low-mass region (O(. 1GeV)). The main evidences of dark matter come from astrophysical objects as stars and galaxies. In particular, dark matter signal can come from regions where the dark matter density is expected to be higher, such as galactic center, the inner halo of our galaxy, the center of the Sun. Therefore, self-annihilation or decay processes would occur with the production of standard model particles, whose ﬂux can be measured. Several annihilation processes Chapter 2. Directional dark matter search 26 under investigation are:

χχ¯ −→ γγ, γZ, γH (2.2) χχ¯ −→ qq¯, W+W−, ZZ where some products decay in e+e−, pp¯, dd¯ and neutrinos. Indirect search of dark matter is therefore focused on the measurement of the Cosmic Rays flux from charged particles and antiparticles, photons and neutrinos. Several experiments look for channels and energy ranges where the signatures of decay or annihilation processes of dark matter particles could be detected over the background from standard astrophysical processes. The direct annihilation of WIMP particles to monochromatic γ−rays of high energy can provide a signature difficult to explain by any astrophysical source. Therefore, the detection of these γ−ray signals coming from the galactic center is considered a smoking-gun. Satellite telescopes like Fermi-LAT [61] and many others [62] are looking for a clear hint. An indirect probe for WIMPs can be provided by the charged cosmic rays in the p¯ and e+ channels. In particular, the p¯/p and e+/e− ratios are mainly investigated since anti-particles are rarely produced in the standard processes and even a small contribution of dark matter annihilation to charged pairs could enhance their contribution beyond the systematic acceptance region. The PAMELA experiment reported a positron excess for energies larger than 10 GeV [63] then confirmed also by the AMS experiment [64]. Although these results suggest an additional source of positrons, astrophysical sources like pulsars could naturally explain the observed excess. Another important signature is provided by the dd¯ ratio since the expected dark matter signal from anti-deuteron is four order of magnitude larger than that predicted from standard background for energies smaller than 1 GeV/n. Dark matter particles can also be trapped by the gravitational field of massive objects like the solar core or the Earth’s inner core. If their density is large enough they can undergo pair annihilation giving rise to high energy neutrinos (Eν > 1 GeV), being the WIMP mass supposed to range from the GeV to TeV scale. WIMP-induced neutrinos from the Sun are very interesting since the energy of electron neutrinos produced in nuclear reactions are of the MeV range and therefore the observation of GeV solar neutrinos of whatever flavour would be another strong signature. In the same way, WIMP-induced neutrinos from Earth’s core may travel up to the Earth’s surface, where neutrino telescopes could detect them. The energy cut-off for WIMP-induced neutrinos due to the absorption is ∼ 100 GeV for those coming from the solar core, and ∼ 10 TeV for those coming from Chapter 2. Directional dark matter search 27 the Earth’s core. Neutrino detectors sensitive to high energy cosmic neutrinos are Ice- Cube [65], ANTARES [66] and SuperKamioKande [67]. Finally, large efforts are in progress for the direct dark matter search, based on the detection of nuclear recoils induced by the scattering of WIMP particles off target nuclei

χ + N −→ χ + N. (2.3)

Many experiments located in underground laboratories exploit different techniques based mainly on ionization, scintillation and phonon excitation, or a combination among them. A detailed knowledge of the dark matter properties in the Milky Way, the particle and nuclear physics concerning the WIMP-nucleus coherent scattering is required to identify signal features. In the Sec. 2.2 a brieﬂy description of the experimental signatures of dark matter is reported.

2.2 Direct dark matter search

Assuming the Milky Way surrounded by a dark matter halo composed by WIMP parti- 5 −2 −1 cles, their ﬂux on the Earth is large enough (∼ 10 (100GeV/mχ) cm s ) so that a small fraction of weak-interacting particles can elastically scatter off a target nucleus. The aim of direct detection experiments is to measure the energy Er and the event rate R of the WIMP-induced nuclear recoils. The differential recoil spectrum for a WIMP and a nucleus with masses mχ and mN, respectively, is usually written as1

Z vmax dR ρ0 3 dσWN = dv v fdet(~v, v~E, t) (2.4) dEr mNmχ vmin dEr where

• ρ0 is the local WIMP density;

• dσWN/dEr is the coherent elastic WIMP-nucleus cross section;

• vmin is the smallest WIMP velocity which can give a recoil with energy Er;

• vmax is the WIMP escape velocity in the Earth reference frame;

1In the following equations c = 1 is set. Chapter 2. Directional dark matter search 28

• v~E is the velocity of the Earth with respect to the galactic halo; ~ • v = |v| and fdet(~v, t) are the dark matter speed and the velocity distribution in the detector rest frame.

The energy recoil Er in the non-relativistic regime is given by

2 2 2 ? q µNv (1 − cos θ ) Er = = (2.5) 2mN mN ? where q is the momentum transfer, µN = mχmN/(mχ + mN) is the reduced mass and θ the scattering angle in the center of mass frame. For a WIMP with mass of O(100 GeV) the energy of recoiled nucleus is of O(10 keV). Then, the minimum velocity is obtained for cos θ? = −1 and it is equal to q 2 vmin = (mN Er)/2µN. (2.6)

Integrating Eq. 2.4 over the recoil energies, the event rate per kilogram per day is given by Z ∞ Z vmax ρ0 3 dσWN R = dEr dv v fdet(~v, v~E, t) (2.7) Ethr mNmχ vmin dEr where Ethr is the threshold energy which depends on the detector. As reported in the Eqs. 2.4 and 2.7, the number of expected induced recoils depends on the WIMP-nucleus interaction model and the kinematic model of WIMP particles in the Milky way. The coherent elastic WIMP-nucleus scattering depends on the nature of WIMP couplings with nucleons and in a non-relativistic limit can be separated in spin independent and spin dependent interactions. In the former an equal coupling of dark matter with protons and neutrons is assumed; the latter is sensitive to the contributions from protons and nucleons to the nuclear spin. The WIMP-nucleus cross-section can be written as

dσ m WN = N (σSI F2 (E ) + σSD F2 (E )) (2.8) 2 2 0 SI r 0 SD r dEr 2µNv

2 where for each terms σ0 is the cross-section at the zero momentum transfer and F (Er) is the form factor to account for the ﬁnite size of the nucleus. If the momentum transfer q Chapter 2. Directional dark matter search 29 is small, F2(q) −→ 1 since the collision occurs with the whole nucleus; for high momentum transfer, instead, the WIMP becomes sensitive to the nuclear structure of the target nucleus and F2(q) 1. For a spin independent interaction one obtains

4µ2 σSI = [Z f p + (A − Z) f n]2 (2.9) 0 π where f p and f n, with f p ' f n, are the coupling factors of WIMPs on protons and neutrons. Hence, the cross-section grows linearly with A2. The form factor is usually described by the Helm’s parameterization 2 sin qr − qr cos qr ( ) ≡ ( ) = −(qs) /2 n n n F Er F q 3e 3 (2.10) (qrn) where rn is an effective nuclear radius and s is a measure of the nuclear skin thickness [43]. For the spin dependent interaction one obtains

32 J + 1 σSD = µ2G2 · [a hSpi + a hSni]2 · (2.11) 0 π F p n J where GF is the Fermi coupling constant, ap,n are the effective spin dependent WIMP- nucleon couplings on protons and neutrons, hSp,ni are expectation values of the proton and neutron group spins and J is the total spin of the nucleus. The form factor is usually parameterized in the isoscalar (a0 = ap + an) and isovector (a1 = ap − an) couplings

2 2 S(q) = a0S00(q) + a0a1S01(q) + a1S11(q) (2.12) using the relation S(q) F2(q) = (2.13) S(0) 2 where the parameters Sij are determined experimentally and with F (0) = 1, as expected when the momentum transfer is small. It is worth noting that for heavy targets (A > 20) the spin independent interaction is the leading term in the cross-section. The WIMPs velocity distribution is generally described by an isotropic Maxwell-Boltzmann Chapter 2. Directional dark matter search 30 distribution

2 1 (~v − v~E(t)) f (~v, v~E, t) = √ exp − Θ(|~v − v~E(t)| − vmax) (2.14) 2πσ 2σ2 √ where σ = 3/2v0 is the velocity dispersion and v0 the galaxy rotation velocity. This velocity proﬁle distribution corresponds to an isothermal spherical dark matter distribution as assumed in the Standard Halo Model (see Sec. 1.5). It is important to note that the motion of the Earth around the Sun affects the count rate which shows a sinusoidal annual modulation with a maximum when the velocity of the Sun and the orbital velocity of the Earth are parallel and a minimum when they are anti- parallel. The Earth’s velocity can be factorised as

vE(t) = v + vorb cos γ cos [ω(t − t0)] (2.15) where v~ is the velocity of the Sun in the galactic rest frame, vorb is the orbital velocity of the Earth around the Sun and cos γ accounts for its inclination with respect to the Sun’s trajectory into the Milky Way, t0 is the date of the peak in the annual modulation, towards the Cygnus constellation, and ω = 2π/year is the revolution orbit frequency. Finally, the expected WIMP-nucleus interaction rate depends from astrophysical and particle physics inputs and from two unknowns, the cross-section and mass of the WIMP.As a result, the sensitivity region of direct dark matter search experiments is usually expressed in the WIMP mass cross-section plane, as reported in Fig. 2.2. Experimental results can be represented either as upper limit curves in absence of signal or as closed regions in the parameter space if an observation is claimed. Several factors affect the sensitivity curve of an experiment: a lower energy threshold corresponds to a sensitivity to lower WIMP masses; longer is the exposure time lower is the cross-section explored unless systematic effects intervene; smaller target nuclei reduce the overall sensitivity. In addition other effects can have a role in the detector sensitivity as uncertainties on assumed models and/or systematic errors in experimental procedures.

2.3 Results of direct experiments

Direct dark matter search is mainly performed exploiting three different effects occurring when a WIMP-induced recoil travels in a detector: • ionization of target atoms; Chapter 2. Directional dark matter search 31

FIGURE 2.2: Typical representation of the sensitivity region for dark matter experiment. The black line represents an upper limit reference curve while the colored ones show the variations due to different properties of the detector. The closed curve represents the signal contour in case of an observation [57].

• scintillation of excited target nuclei; • phonon production in cryogenic crystals. Some experiments focus on a single channel while others foresee a double channel strategy using a combination of two of the three effects above-mentioned. A schematic representation of the current strategies is reported in Fig. 2.3.

2.3.1 Ionization in high purity Germanium detectors The ﬁrst limits on Cold Dark Matter candidates have been derived at the end of 1980s using an Ultra-low Background Germanium Detector [68]. The improvement of the technology, focused on the reduction of the background level and on the energy threshold, led High Purity Germanium (HPGe) detectors to be sensitive to WIMP masses of a few GeV/c2. Germanium detectors work at cryogenic temperatures (∼ 77 K)2; they use only the ionization signal as a detection technique and they cannot discriminate signal events from

2It is the temperature of liquid nitrogen. Chapter 2. Directional dark matter search 32

FIGURE 2.3: Direct dark matter techniques [57]. the expected background. In addition, the high energy resolution of these detectors and the rise-time of the ionization signal are used to characterize and reduce the event rate induced by background sources. The CoGeNT (Coherent Germanium Neutrino Technology) experiment [69], located in Soudan underground laboratory, uses 443 g of germanium crystals as a cryogenic detector for WIMP particles. It observed an annual modulation of the measured event rate in the (0.5 − 2)keVee energy range with an exposure time of 3.4 y and a signiﬁcance for the WIMP observation at 2.2σ CL. Other experiments which also make use of Germanium detectors are MAJORANA [70], CDEX [71] and TEXONO [72].

2.3.2 Scintillator crystals Incoming particles in a scintillating material can excite the target nuclei which emit photons because of the following de-excitation. Inorganic crystals like NaI(Tl) and CsI(Tl) are mainly used for dark matter search where only the scintillation signal, proportional to the absorbed energy, is collected. Hence, the discrimination of incident particles is not possible even if multiple hits in different crystal are rejected since the weakly interacting WIMPs are expected to produce a single hit. These kind of detectors usually operate at Chapter 2. Directional dark matter search 33 room temperature which is an important feature for several years exposures. The dark matter observation is inferred by the annual modulation signal if the integrated background is sufficiently low. This needs naturally high pure crystals and active vetoes to achieve a strong reduction. The experiments DAMA/NaI and its successor DAMA/LIBRA-phase1 [73] makes use of ultra-low radioactive NaI(Tl) crystals coupled to low background photo-multipliers to detect the particle interactions. The detector, located at Gran Sasso Underground Labora- tory (LNGS), with an exposure mass of 1.33 ton × y covering fourteen annual cycles, is observing an annual modulation signal in the (2 − 6)keVee range. The maximum peak is compatible within 2σ CL with the expected phase due to dark matter interactions and the significance of the observation is 9.3σ [74]. In Fig. 2.4 it is reported the annual modulation of the single-hit event rate after the constant background rate subtraction versus the time exposure. Recently, the results obtained by DAMA/LIBRA-phase2 confirm the signal for the annual modulation at 9.5 σ C.L. in the energy region (1–6) keV [75]. Assuming the signal observed by DAMA/LIBRA due to WIMP-nucleus scattering, two mass regions result at (10 − 15)GeV/c2 and (60 − 100)GeV/c2 for scattering off sodium and iodine, respectively. Although the DAMA/LIBRA signal is a clear hint of a physical phenomenon,

FIGURE 2.4: DAMA/LIBRA annual modulation versus the time exposure [76]. no other experiments have conﬁrmed yet the observation in the same signal region. On the contrary, many experiments excluded the signal as being due to WIMP-nucleus interaction. Several explanations of the DAMA/LIBRA signal have been proposed involving the seasonal variation of the neutron background, the annual modulation of atmospheric muons, the convolution of muons and modulated neutrinos due to the varying Sun-Earth Chapter 2. Directional dark matter search 34 relative distance [77]; but none is able to reproduce the DAMA signal as shown in Ref. [78]. In order to test independently the DAMA/LIBRA results, the SABRE experiment [79] will use a detector based on high pure NaI(Tl) crystals deployed in an active liquid scintillator veto. SABRE will operate with twin detectors; one located in northern hemisphere, at LNGS, the other located in the southern hemisphere, at Stawell Underground Physics Laboratory (SUPL) to avoid seasonal background effects.

2.3.3 Cryogenic bolometers Cryogenic detectors are capable to measure the energy deposited by an incoming particle as phonons, i.e. vibrations of the crystal lattice. The phonons produced by the dissipated energy can be separated in thermal and athermal phonons. The former can be measured by the induced temperature rise with typically ∆T = E/C ∼ 1 µK, where E is the released energy and C the detector’s heat capacity. The latter are a fraction of the initial phonons not at equilibrium and can provide information on the energy and the position of the recoil. In addition to the phonon signal, cryogenic bolometers can also perform particle discrimination exploiting the charge or the scintillation signal. The CDMS II experiment [80] is located at Soudan Underground Laboratory and is made of nineteen Germanium and eleven Silicon detectors of 230 g and 110 g, respectively. The detection of the signals is based both on phonon excitation and ionization. A fraction of the energy deposited in the semiconductor crystal by a recoil is used to produce electron- hole pairs which drift to opposite electrodes thanks to the electric field across the crystal. The remaining part of the deposited energy is used to produce a population of athermal phonon vibrations within the crystal. CDMS II has not found any evidence for an annual modulation of the event rate [81]; this result disagrees in particular with the observation of the CoGeNT experiment which also uses a germanium target. A follow-up experiment is SuperCDMS [82] which currently set the most sensitive exclusion limits at low WIMP masses [83]. The combination of phonon and scintillation signals to detect the WIMP-nucleus interaction is used by the CRESST-II experiment, located at LNGS with a detector based on scintillating CaWO4 crystals at very low temperature (O(mK)) [84]. With a total exposure of 730 kg d from 2009 to 2011, it observed an excess of events corresponding to a significance of 4.7σ [85]. In the 2013, after an improvement of the background detection efficiency, with an exposure of 29.35 kg d the previous signal was not confirmed anymore. Chapter 2. Directional dark matter search 35

An exclusion limit was set on spin-independent WIMP-nucleon scattering which probes a new region of parameter space for WIMP masses below 3 GeV/c2 [86].

2.3.4 Liquid noble-gas detectors The use of liquid noble-gas detectors, in particular LAr and LXe, is a very attractive strategy for the direct dark matter search. These detectors show an high scintillation efficiency and can reach high standard level of purity and large volumes. The passage of ionizing radiation through the detector produces the ionization and the excitation of the target. A first scintillation signal is produced in the sensitive volume of the liquid phase of the detector, together with the electrons due to ionization. These electrons can recombine to produce further scintillation light or can be driven by a strong electric field towards the gaseous phase of the detector, where they produce a secondary scintillation signal (elec- troluminescent) proportional to the amount of ionization. Detectors operating in single phase mode typically use a spherical target made by liquid only and the detection of the scintillating light is performed by the surrounding photo- multipliers (see Fig. 2.5 left). In the two-phase operation mode, both the liquid and the gaseous forms of the target are used, separated by a phase transition region (see Fig. 2.5 right). The information given by the photo-multipliers at the edges of the detector and the time interval between the primary and secondary signals allows a 3D reconstruction of the event as a Time Projection Chamber (TPC). The discrimination between electronic recoils (ER) induced by the main background sources (e−, γ) and nuclear recoils (NR) induced by neutrons or WIMPs is performed using the pulse-shape discrimination (PSD) and the charge-to-light signal ratio. The PSD arises because the excited states (excimers) that produce the luminescence can exist in two states: singlet and triplet. Triplet state has a longer decay time (∼ 1.3 µs in Ar) and are much more prevalent in ER interactions while nuclear recoils events will lead to excimers with a short-lived singlet-state (∼ 6 ns in Ar) resulting in a faster recombination. The PSD allows a particle discrimination at the level of 107 in LAr using only the scintillation signal. For LXe detectors the small difference between the decay constants of singlet-state (∼ 4 ns) and triplet-state (∼ 22 ns) results in a less rejection power [87]. Nevertheless, the choice of a Xenon target entails several advantages: half part of LXe is made of non-zero spin isotopes as 129Xe and 131Xe which provide additional sensitivity to spin-dependent WIMP interactions [88]; the high density of xenon provides a large self-shielding power. In double-phase detectors a further discrimination is obtained by the ratio between the scintillation and ionisation signals since, depending on particle type, it allows to discriminate Chapter 2. Directional dark matter search 36

FIGURE 2.5: Schematic representation of the single phase (left) and double phase operation mode [57]. background from signal-like events. Single-phase detectors with LAr are DEAP [89] and CLEAN [90] at Sudbury Neutrino Observatory (SNO), while XMASS experiment [91] uses LXe at Kamioka Observatory. WARP [92] at LNGS has been the ﬁrst experiment using LAr in Double-phase operation mode; currently the DarkSide experiment [93] after reaching 50 kg of active mass detector is planning in the future to scale up to 20 t [94]. At LNGS the XENON collaboration is using LXe in Double-phase operating mode and, recently, scaled from 100 kg (XENON100) up to 1 t (XENON1T) of active mass [95], producing the strongest exclusion limit of 30 GeV/c2 WIMPs mass at 4.1 × 10−47 cm2 and 90% C.L. [96]. Other experiments are using LXe TPC: PandaX [97] at Jin-Ping Underground Laboratory with 500 kg of active mass, ZEPLIN [98] which operated at Boulby Underground Lab- oratory, LUX [99] at the Sanford Underground Laboratory with 250 kg of active mass. ZEPLIN and LUX collaborations have joined to build a multi-tons detector with ∼ 7 t of LXe [100]. Although Liquid Noble-gas detectors have achieved ton-scale masses and a very large sensitivity compared to the other detection techniques, it is worth noting that they have not observed any excess of signal events above the background predictions thus excluding Chapter 2. Directional dark matter search 37 a large region in the WIMP-mass cross-section plane. Furthermore, XENON100 has not observed any annual modulation of the signal event rate therefore excluding the DAMA result as due to dark matter electron interactions at 5.7σ CL [101].

2.3.5 Threshold detectors and novel techniques Threshold detectors are mainly bubble chambers, with a super-heated liquid as target material. The energy deposition of a particle crossing the liquid produces the local nucle- ation of a bubble at the interaction site. The formation of the bubble produces a pressure peak that triggers the CCD cameras placed around the detector to record the event. The 3D reconstruction of the track position is then performed. The temperature and the pressure of the liquid are optimised in order to prevent the bubble formation from electronic recoils, characterised by a lower dE/dx value. Only a large energy deposition, such as from a nuclear recoil, will provide enough energy to detect a signal. The SIMPLE [102], PICASSO [103] and COUPP [104] experiments use this technique. The last two detectors have joined their efforts to build the PICO experiment at SNOLAB [105]. New experiments are growing using novel techniques for the direct dark matter detection: DAMIC is a detector based on silicon charge-coupled devices (CCDs) [106] at SNOLAB, TREX-DM experiment is a low background Micromegas-based TPC for low-mass WIMP detection at Canfranc underground laboratory [107], NEWS-G experiment uses Spherical Proportional Counters (SPCs) with light noble gases to search for low-mass WIMPs [108].

2.3.6 WIMP-nucleon exclusion plot Direct detection experiments explore signiﬁcant portions of the WIMP mass-cross-section parameter space, while part of it is not accessible via collider or indirect detection techniques. Fig. 2.6 and 2.7 show the current spin-independent and spin-dependent land- scapes, where strict upper limits exist for higher mass WIMPs. The hints for WIMP signals measured by DAMA/LIBRA and CoGeNT are represented as closed contours while the cross-section limits provided by other experiments are reported as curves in the parameter space. Chapter 2. Directional dark matter search 38

FIGURE 2.6: Signal indications (closed curves) and exclusion limits (open curves) for low (left) and high (right) WIMP mass in the spin-independent case [57, 96].

FIGURE 2.7: Signal indications (closed curves) and exclusion limits (open curves) for low (left) and high (right) WIMP mass in the spin-dependent case [57]. Chapter 2. Directional dark matter search 39

2.4 Directional dark matter search

The motion of Solar System through the galaxy creates an apparent wind of dark matter particles, as observed in the Earth frame, blowing from a preferred direction that approximately corresponds to the Cygnus constellation (see Fig. 2.8). Since the events induced by main background sources are expected to be isotropic, the detection of a peaked signal in the Earth’s motion direction could provide an unambiguous proof of the galactic origin of the dark matter. Moreover, directionality offers the unique possibility to overcome the limit imposed by the neutrino floor. In Fig. 2.9 is reported the Hammer-Aitoff projection of the WIMP flux distribution in Galactic coordinates assuming a 100 GeV c−2 WIMP mass. Directional detectors aim to measure the direction of the WIMP-induced recoils with good angular resolution in order to discriminate them from the isotropic background. Of particular interest is even the head-tail discrimination of the recoil which could be measured by the non-uniform energy loss of the recoiling nucleus as a function of the travelled distance. However, the expected track lengths of scattered nuclei are of the order O(100 nm) in solid and liquid materials thus making their reconstruction challenging. So far most of the directional detection have focused on low-pressure gas time projection 3 chambers. These detectors typically make use of CS2, CF4 and He, where the last two are also sensitive to the spin-dependent interactions. The interaction of charged particles or photons with the gas produce primary electron-ion pairs; free electrons are drifted by applying an homogeneous electric field to the anode where a readout device with a sub- millimetric spatial resolution is located. In order to lower the detection energy threshold an electron amplification device is used before the readout plane. Typically Multi-Wire Proportional Chambers (MWPCs), Micro Pattern Gaseous Detectors (MPGDs), Gas Elec- tron Multipliers (GEM), optical readouts (CCD and CMOS) are used. The expected track length of the WIMP-induced recoils in low-pressure gas TPC is of O(1 mm) and therefore large enough to be resolved; nevertheless, the actual limiting factor of this approach is the difficulty to achieve a sufficient gas target mass to be sensitive to the supposed low rate WIMP interactions. In particular, the challenging task for TPC detectors is the construction of large-volume detectors (∼ 103 m3) with high spatial resolution and ultra low background level. The main experiments operating with low-pressure gas detectors are: NEWAGE [110], DMTPC [111], MIMAC [112], DRIFT [113]. A new and promising approach for a directional dark matter detection based on a solid target made of nanometric nuclear emulsion films will be widely described in the Chapter3. Chapter 2. Directional dark matter search 40

FIGURE 2.8: Schematic representation of the Earth motion through the Milky Way.

FIGURE 2.9: Hammer-Aitoff projection of the WIMP ﬂux distribution [109]. 41

Chapter 3

Nuclear Emulsions for WIMP Search with directional measurement

Nuclear emulsions have a long tradition in the particle physics field starting from the discovery of pion in the 1947 [114] to the first observation of νµ → ντ oscillations in appearance mode in 2015 [115]. Essentially they are silver-halide crystals dispersed in gelatin acting as independent detection channels. The passage of a ionizing particle may activate the crystals which record its path with a very high spatial resolution. Since 1896, when Henry Bequerel firstly observed the blackening of photographic films in contact with uranium salts [116], nuclear emulsions are used to study particles . From the beginning of the last century the development of the nuclear emulsion technique attracted the interest of several physicists. Kinoshita in the 1910 [117] observed α particles inside the emulsions as tracks by means of optical microscopes. The first turning point occurred in the 1946 when the production of very sensitive nuclear emulsions allowed to detect tracks due to minimum ionizing particles, in particular mesons. Using these emulsions exposed to cosmic-rays the pion was detected through its decay into a muon [114]. In the middle of the nineteenth century detectors based on nuclear emulsion films were associated to passive materials made of plastic or metal plates in order to form a sandwich structure called Emulsion Cloud Chamber (ECC) [118]. So far, the ECC represents the most significant breakthrough for the nuclear emulsion technique. Detectors based only on nuclear emulsions were used mainly to visualize the vertex of an interaction; with the ECC, instead, the direct observation of the decay vertex of a particle is not always possible since its position may be located in the passive material. Nevertheless, the ECC provides a better estimation of the kinematic parameters through the multiple coulomb scattering which allows to perform the particle identification and measure its momentum with high accuracy. Furthermore, the ECC made it possible to achieve large-mass detectors thanks Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 42 to the metallic plates by reducing costs with respect to detectors made of emulsions only. The ECC were used successfully in experiments with cosmic-rays leading to the discovery of new particles. In the 1971 the production and the decay of a new short-lived particle was observed in ECC [119]; after three years the same particle was detected in a e−e+ annihilation experiment [120] and in a fixed target experiment [121]: it was called J/ψ, a meson resonance which confirmed the existence of the quark charm. In the 1985, by an- alyzing the interactions of a π− beam in a bulk of nuclear emulsions a new elementary particle called beauty [122] was observed. However, nuclear emulsions were partially abandoned because of the laboriousness and the slowness of the analysis. The idea of a tomographic read-out of the emulsion films [123] and the development of automated scanning systems drove to a wider use of detectors based on nuclear emulsions: the DONUT experiment which observed for the first time ντ interactions [124], the CHORUS [125] experiment and the OPERA [126] experiments which studied νµ → ντ oscillations [127]. The detector used by the OPERA collaboration was the largest ECC ever built with a target mass of 1.25 kt in order to observe the rare ντ charged-current interactions. The collaboration has recently published the final results of ten νµ → ντ candidates with two expected background events [127]. The improvements of the ECC layout and the ongoing progress in the read-out systems make still nuclear emulsions an appealing detector in several physics fields:

• study of cosmic-rays with GRAINE experiment [128];

• search for cold and ultra-cold neutrons [129, 130];

• study of double-hypernuclei [131];

• measurements of antimatter with AEgIS experiment [132];

• muon measurements at accelerators;

• neutrino-nucleus interactions with NINJA project [133];

• neutrino interactions, charm studies and search for dark matter within the SHiP experiment [134];

• muon radiography for archaeological and applied purposes [135];

• medical applications with the FOOT experiment [136]; Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 43

Beyond the above mentioned research ﬁelds, a new kind of nuclear emulsions with nanometric crystal has been developed in order to perform directional dark matter searches. The Nuclear Emulsion for WIMP Search (NEWSdm) experiment proposes a very innovative approach for detecting WIMPs with directional measurements. The detector will be located at Gran Sasso Underground laboratory to reduce the cosmic muon ﬂux since a very low background level is required to observe the extremely rare interaction of WIMP with the ordinary matter. A full description of the nuclear emulsion technology, the background sources affecting underground laboratories, the experimental concept and the readout strategy will be reported in the following.

3.1 Nuclear emulsion technique and Nano Imaging Tracker

Nuclear emulsions are made of silver halide crystals, typically silver bromide (AgBr) with a small fraction of iodide, immersed in an organic gelatin. The passage of a charged particle through the emulsion produces along its path atomic-scale perturbations since electrons in the valence band are transferred in the conduction band, with an energy gap of 2.684 eV in AgBr. Then, free electrons move inside the crystal until they are captured by sensitization centers which are created at surface through a chemical treatment (see 3.1.2). After this process, called electronic process for latent image formation, the ionic process occurs, consisting in the formation of a silver atom from the reaction of an interstitial silver ion, which can move through the lattice, with a trapped electron (Ag+ + e− → Ag). It is essential for the formation of the latent image that a large fraction of electrons and positive holes (AgBr)+ are captured separately in order to prevent a fast recombination. The alternation of the electronic and ionic processes several times at the same site leads to the formation and the growth of a silver cluster. In particular, if the cluster is formed by at least four Ag atoms it becomes a latent image center, i.e a detection channel, and can be developed (see 3.1.2) to be observed as a dark grain on a white background (or vice-versa) by means of optical microscopes with enough resolution. The formation and the stability of latent images depend also on the temperature and humidity of the working environment since as they increase the sensitivity decreases and the preservation of grains is unstable. This effect is called fading and in some cases may be artiﬁcially induced to erase all the grains stored in the emulsion before the exposition (refreshing technique). The spatial resolution of a detector-based on nuclear emulsions depends on the size of its crystals. The identiﬁcation and the directional measurement of a track in emulsion may Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 44 be performed only if a charged particle pass through at least two crystals. The minimum track length that can be detected thus depends on the average distance between the crystals. Typical crystal size ranges from 0.2 µm to 0.3 µm as used by the OPERA experiment. As remarked in Sec. 2.4, the WIMP-nucleus elastic scattering for a WIMP mass ranging from 10 GeV to 10 TeV typically produces in a solid detector recoils with short track lengths (O(100 nm)). Therefore, smaller crystal size are required to ensure the observation of the signal. The production of nuclear emulsions of few tens of nanometer size crystals is recently started at Nagoya University in Japan: the Nano Imaging Tracker (NIT) and the Ultra Nano Imaging Tracker (UNIT) with AgBr crystals of (44.2 ± 0.2) nm and (24.8 ± 0.1) nm (see Fig. 3.1), respectively [137]. The average number of crystals per micrometer is ∼ 14 for NIT emulsions and ∼ 25 for UNIT emulsions which corresponds to an average distances between crystals of ∼ 71 nm and ∼ 40 nm. The above reported values represent the minimum detectable track length in these emulsions.

3.1.1 NIT emulsion production The production of NIT 1 emulsions requires three steps using a dedicated machine: particle formation, desalination phase and re-dispersion. Firstly, AgBr crystals are produced by mixing in a thermostatic bath, containing a solution of gelatin and polyvinyl alcohol (PVA), AgNO3 and NaBr according to the following reaction:

+ − AgNO3 + NaBr → AgBr + Na + NO3 . (3.1)

The presence of gelatin and PVA ensures the stability and the uniformity of the grain size of the crystals. In addition, a small fraction of NaI is used to increase the sensitivity of the crystals. In the second phase a reduction process enables the removal of residual + − ions (Na , NO3 ) using a flocculation method. Finally, the re-dispersion step in which an homogeneous distribution of the crystals in gelatin is achieved with a constant rotational speed (∼ 1000 rpm) of the thermostatic bath at (50 ± 1)◦C for about one hour. The final product is ready to be poured on a plastic or glass film. It is worth underling that all the operations must be done in dark room since crystals are already sensitive to the light soon after their formation. The fraction of each constituent and the chemical composition of the single element of NIT emulsions are reported in Tab. 3.1, respectively.

1From now with the term NIT we are also including the UNIT case unless it is explicitly stated. Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 45

FIGURE 3.1: Distribution of the crystal diameter measured with a transmission electron microscope (TEM) for U-NIT (left) and NIT (right) [137]. Different colours represent different production batches.

Density 3.44 g/cc Element Mass fraction % Ag 44.5 Br 31.8 I 1.9 C 10.1 N 2.7 O 7.4 H 1.6 Constituent Mass fraction % AgBr-I 78.1 Gelatin 16.8 PVA 5.1

TABLE 3.1: Chemical composition of NIT emulsion and fraction mass of its constituents. Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 46

3.1.2 Chemical treatments and handling After the production of the NIT gel, chemical treatments are needed to prepare nuclear emulsions for the measurement and for the analysis of the stored data. Before an exposure, three steps are performed: 1. pouring treatment which consists on heating NIT gel up to ∼ 40 ◦C in order to dilute and pour it on rigid supports such as acrylic or glass slides with suitable size;

2. Halogen Acceptor sensitization through a solution of sodium sulfite (Na2SO3) to increase the efficiency of the crystals to form latent images; 3. coating treatment using only gelatin to protect the NIT surface. After each process, NIT films dried in dark room with controlled humidity (> 50%) and temperature (∼ 20 ◦C). After having packed them into under vacuum in Aluminum foil bags, NIT films are ready to be exposed. After the exposure, the emulsions are developed to be later analyzed. The development treatment consists of six steps:

1. presoak, consisting in immersing emulsion films in a solution of sodium sulfate (Na2SO4), is performed to facilitate the penetration of the developer agent inside the whole emulsion thickness; 2. development, consisting in immersing emulsion films in a solution of water and Metol Ascorbic Acid (MAA) developer, is performed to make visible the grains contained in the emulsions by the reduction of silver ions in the silver halide crystal to metallic silver filament. The reaction can be expressed as follows:

+ + Red + nAg Ox + mH (3.2)

where Red and Ox are the reduction and oxidation agents, respectively; n is the number of ions and m the number of protons produced. The ampliﬁcation of the grains is very high (O(108)) allowing the observation by means of optical microscopes. The developer agent is chosen to reduce only the crystals which contain a latent image center leaving unchanged the others. The process is performed at (5 ± 0.2)◦C for ten minutes so that all crystals with grains are reduced. Temper- ature and duration of the process have to be very precise to reduce the intrinsic background of the emulsions; indeed, some crystals because of the thermal excitation are developed even if they do not contain a latent image center forming the so-called fog grains. Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 47

3. stop-bath, consisting in immersing emulsion ﬁlms in a solution made of acetic acid, is performed to stop immediately the development process thus having a precise control on the duration thereof;

4. fixation bath, consisting in immersing emulsion films in a solution made of sodium or ammonium thiosulphate solution, is performed to remove all the not sensitized silver halides, which would slowly get brown and degrade the images at microscope, while does not affect the metallic silver atoms which form the grains. It is important to control, e.g. through the pH, the saturation level of the fix solution since it can affect the strength of the residual silver halides removal power. The fixation process lasts until the NIT films became transparent; from that point the emulsions are no longer sensitive and they can be exposed to light.

5. washing is performed after the ﬁxation with running water for about one hour to remove all the silver thiosulphate complexes in the emulsion;

6. drying of the emulsions at controlled humidity and temperature conditions.

After the drying process the emulsion ﬁlms are scanned with fully automated optical microscopes.

3.2 Background sources

The capability of detecting dark matter interactions cannot be disentangled from a deep knowledge of all the physical sources and instrumental effects that may inﬂuence this challenging measurement. Firstly, NIT emulsions are essentially insensitive to minimum ionizing particle (MIP), e.g. muons and protons, since they are expected to produce ∼ 3 electron-hole pairs in an AgBr crystal while at least 4 Silver atoms are required to form a latent image [138]. Secondly, it is important to characterize the signal-like events as a sequence of at least two or more aligned grains in a very narrow distance (O(∼ 100) nm); therefore a background event is really dangerous only if produces at least two grains in NIT. The background sources for the NEWSdm experiment can be divided in two main categories: external backgrounds from neutrons, gamma rays and neutrinos; intrinsic radioactivity of detector components. The former is in common for all the experiments and is typically reduced placing the detector underground and using an appropriate shield; the latter is an irreducible source of radiation and can be only reduced by using very high Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 48 purity materials. In addition, a third category is the instrumental background which is not linked to any physical source but is related to the production, development and analysis processes. It is worth noting that neutrons are currently the most dangerous background source since the induced recoils can mimic the WIMP-nucleus interaction.

3.2.1 External background sources The external background sources affecting underground laboratories are the environmental gammas and neutrons which essentially depend from the materials inside the experimental hall and the surrounding rock; the muon and cosmogenic neutron ﬂux which strongly depend on the site depth; the diffuse neutrino background which becomes extremely dangerous for a ton-scale mass experiment.

Environmental gamma source Environmental gamma source originates from the decays in the Thorium and Uranium chains whose products are strong gamma emitters, and from decays of common isotopes (40K, 60Co and 137Cs) present in the surrounding materials. In Fig. 3.2 it is reported the gamma spectrum measured in Hall B at LNGS with a NaI(Tl) scintillation detector [139]. The energy of γ−rays ranges from tens of keV up to 2.6 MeV which is the highest energy from the Thorium chain. Three are main interaction mechanisms of γ−rays with the matter: photoelectric effect dominant up to few hundreds keV, pair production which prevails above a few MeV, and the Compton scattering which is the most probable process for the energies in between. All these mechanisms result into the production of electrons with energies of few keV which can sensitise the AgBr crystals. The environmental gamma ﬂux at LNGS is 0.35 cm−2 s−1 [139] and can be suppressed using shields made of dense materials, usually lead and copper, or large water tanks.

Environmental neutron source Neutrons induced by the environmental radioactivity at LNGS halls are produced by two processes: the spontaneous fission and the (α, n) reaction. The former is a form of radioactive decay where a nucleus (generally with atomic numbers above 90) splits into two smaller nuclei and generally one or more neutrons. The rate of neutrons produced by spontaneous fission is determined by the 238U contamination in materials, since the number of fission per decay in all other elements is at least two orders of magnitude lower. Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 49

FIGURE 3.2: Flux of environmental gamma in underground LNGS halls [139].

The latter is the interaction of α−particles, emitted by Uranium, Thorium and their decay products, with the nuclei of light elements (O, Al, B, etc.) that are present in the rocks or in the detector material. In Fig. 3.3 it is reported the energy spectrum of radiogenic neutrons in the LNGS halls which are the dominant source of neutron background for energies up to 10 MeV (fast neutrons). The ﬂux at LNGS is 8.7 × 10−7 cm−2 s−1 [140]. The neutron background from environmental radioactivity can be reduced by using a passive shield. It is important to moderate the neutron to low energies, where it can readily be captured in materials with high absorption cross sections. The most effective moderators are elements with low atomic number, and therefore hydrogen-containing materials are the major component of most neutron shields. In this application, water, concrete, and parafﬁn are all inexpensive sources of bulk shielding. Since mean free paths of fast neutrons in such materials are typically tens of centimeters, thicknesses of 1 m or more are required for effective moderation of almost all incident fast neutrons. Once the neutron has been moderated, it can be eliminated through an appropriate capture reaction. A second component is normally used in neutron shields, either homogeneously mixed with the moderator or present as an absorbing layer near its inner surface. This additive is chosen to have a high neutron capture cross section, so that the moderated neutrons will preferentially undergo absorption within this material. Boron and lithium are common Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 50

FIGURE 3.3: Environmental neutron ﬂux in underground LNGS halls. [141]. components of neutron shields. The 10B(n, α) reaction has a high capture cross section at low energies, and boron can readily be incorporated into parafﬁn and other moderating materials.

Muon-induced neutron and cosmic muons background The main reason of placing dark matter detectors in underground laboratories is to reduce the number of produced muon-induced neutrons. Cosmogenic neutrons with energy spectrum extending up to the GeV are induced by muons penetrating underground through the rock, hence the yield depends on the depth of the underground laboratory. Deeper is the site, higher is the reduction of the cosmogenic neutron ﬂux as shown in Fig. 3.4. The Gran Sasso underground laboratories are located at ∼ 1.4 km under the mountain corresponding to ∼ (3.1 ± 0.2) km water equivalent (k.w.e.). At these depths, the muon ﬂux is reduced to 1 µ m−2 h−1, i.e. six orders of magnitude lower than the value measured at the surface, and the mean muon energy is about 250 ÷ 300 GeV [142]. At these energies, cosmogenic neutrons are produced mainly by three processes: (i) muon electromagnetic interaction with a nucleus, producing a nuclear disintegration and thus Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 51

FIGURE 3.4: The total muon flux (left) and the total muon-induced neutron deduced flux for several underground sites. [143]. neutrons; (ii) production of an electromagnetic cascade, in which high energy photons can cause spallation reactions; (iii) production of hadronic cascade, in which generated hadrons (π±, K±, K0, n, p) can also cause spallation reactions [144]. The neutron energy spectrum for each experimental site (see Fig. 3.5) is derived with the FLUKA simulation [145]. The muon-induced neutrons have a very hard energy spectrum (extending up to several GeV) and can penetrate to significant depth both in the surrounding rock and in the detector shielding materials. The total muon-induced neutron flux emerging from the rock in the cavern at Gran Sasso Underground Laboratory is 7.3 × 10−10 cm−2 s−1 and the average energy is 91 MeV [143]. Cosmogenic neutrons can be partially reduced by shielding the detector with several meters of hydrogen-containing materials. Furthermore, muons interacting in the shielding produce additional neutrons which can be rejected in the detector only via topological cuts.

Neutrino diffuse background Nowadays the most competitive detectors in direct dark matter search are scaling up their mass up to the ton-scale. Although they are increasing their sensitivity to observe the WIMP-nucleus, on the other hand they are also starting to be sensitive to solar, atmospheric, and diffuse supernova neutrinos whose ﬂuxes are reported in Fig. 3.6. The neutrino-nucleus coherent scattering produces recoils which cannot be distinguished from Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 52

FIGURE 3.5: The differential energy spectrum for muon-induced neutrons at different underground sites [143].

FIGURE 3.6: Solar and atmospheric neutrino flux and diffuse supernova neutrino background (DSNB) [146]. Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 53 dark matter interactions; therefore it is an irreducible background for direct dark matter experiments whose sensitivity will be limited by the so-called neutrino floor. Nevertheless, directional detectors not only would provide a straightforward proof for the dark matter existence but also the possibility to overcome the neutrino floor by measuring the direction of induced recoils. The capability of observing intriguing events such as coherent neutrino-nucleus elastic scattering for a near future ton-scale experiment based on NIT emulsions will be widely explored in the Chapter6.

3.2.2 Internal background sources The background induced by the intrinsic contamination of the materials is extremely dangerous for the observation of very rare events since it is produced inside the detector without any possibility to be shielded. For this reason, it is crucial for dark matter experiments the use of very low radioactive materials for each detector component, in order to reach the highest available purity standard. In the NEWSdm detector there are two dangerous intrinsic background sources: the former is represented by the intrinsic electrons due to the presence of the 14C isotope which undergoes β−decay; the latter is represented by the radiogenic neutrons from the decays of long-lived radio-isotopes (e.g. U, Th) in NIT constituents.

Electrons induced by 14C Beta rays produced in 14C may be a serious background source for NIT emulsions since the expected yield is 7.3 × 108 kg−1 y−1 [147]. Given the Carbon content and the natural 14 −10 isotopic abundance of C, a rejection power Rβ ≤ 10 is required for an experiment of ten kilograms per year mass exposure. In order to achieve this high rejection level several strategies are under investigation:

1. cancel out the amount of 14C by replacing the organic gelatin with synthetic poly- mers, e.g. PVA;

2. reduce the sensitivity of NIT emulsions to electrons through dedicated chemical treatments (e.g. Tetrazorium compound) [148];

3. reduce the sensitivity to electrons by keeping NIT emulsions at low temperatures (∼ 100 K) [147]. Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 54

The second approach is based on the different energy deposit per unit path length dE/dx expected for electron and WIMP induced recoils. WIMPs in the (1 − 1000) GeV c−2 mass range scatter off light (LN) and heavy nuclei (HN) of the target with higher dE/dx with respect to electron and proton recoils (see Tab. 3.2[149]). Therefore, it is possible to op-

Particle dE/dx [keV/µm] HN 1000 − 2000 LN 100 − 300 proton 50 electron 10

TABLE 3.2: Energy deposit for electrons and ions in NIT emulsions. timize the chemical treatment of NIT emulsions to make them sensitive only to particles with high energy deposit. The third approach intends to exploit the phonon effect in AgBr crystals. Electrons and light nuclei traveling in NIT emulsions typically loose their energy because of the electron stopping power, producing electron-hole pairs. Nuclear emulsions decrease their sensitivity with temperature since the interstitial silver ions reduce their power to trap the electrons which therefore recombine with the ions. NIT sensitivity to electrons is therefore strongly reduced at low temperatures (see Fig. 3.7) and, since they are expected to produce in the majority of the cases just one grain at the Bragg peak, the rejection power for a double chance coincidence of two grains is estimated to be ∼ 3 × 10−9 for NIT and ∼ 4 × 10−16 for the UNIT [147]. On the other hand, heavy nuclei with kinetic energies down to 1 MeV have a large nuclear stopping power (O(MeV/µm)) (see Fig. 3.8). The large energy deposition induced by nuclear recoils produces an atomic displacement in the crystals along the trajectory, transmitting phonons to the crystals. Since the phonon energy heats up the crystal, an interstitial silver ion will be able to move and produce a latent image speck. The phonon effect ensures enough sensitivity to nuclear recoils at low temperatures. In addition, the electron discrimination can be improved by exploiting the different response of the resonant effect of the polarized light which is described in the Sec. 3.4. Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 55

FIGURE 3.7: Sensitivity to electrons of NIT emulsions versus the temperature [147].

FIGURE 3.8: Nuclear (dashed) and electron (solid) stopping power versus the kinetic energy for C (red), Kr (blue) and e− (black) [147] Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 56

Radiogenic Neutrons The determination of the intrinsic neutron yield in NIT emulsions was estimated using two complementary techniques: the Inductively Coupled Plasma Mass Spectrometry (ICP MS) [150] and the gamma spectroscopy using the Germanium detectors of the STELLA facility [151] at LNGS. The former was used to measure directly the Th, and U concen- trations with high sensitivity (ranging from ppm down to ppt or ppq) while the latter is sensitive to γ−active daughter nuclides in the Th and U decay chains, thus checking the validity of the secular equilibrium assumption. This assumption was indeed used to derive the α production yield induced by the daughter nuclides produced in U and Th decay chain when only the contamination of the ﬁrst elements in the chain are measured, as it is the case in mass spectroscopy. From the ICP MS technique the intrinsic contamination was estimated to be (23 ± 7) mBq kg−1 for the 238U and (5.1 ± 1.5) mBq kg−1 for the 232Th [152]. The gamma spectroscopy provided comparable results for the Ag-Br-I compound; for the gelatin instead the con- centrations of 226Ra in the 238U were estimated to be ∼ 20 times smaller than the parent isotope. Since this result suggests a break in the secular equilibrium at this point, the upper part of the 238U chain is assumed to be at equilibrium with the same activity of the parent isotope measured by the ICP MS technique; the lower part of the chain is considered to be at equilibrium with the same activity of the 226Ra ((15 ± 5) mBq kg−1) measured by the gamma spectroscopy. Using these activities, the estimation of the the neutron intrinsic background due to the spontaneous ﬁssion and (α, n) reactions was estimated to be 1.2 ± 0.4 kg−1 y−1 [152]. The SOURCES4A code [153] was used to calculate the expected energy spectrum of intrinsic neutrons (see Fig. 3.9) which shows a peak at 0.7 MeV with tails up to 10 MeV.

3.2.3 Instrumental background Background sources not related to physical interactions between incoming particles with the target nuclei are deﬁned as instrumental. There are two instrumental background sources: (i) dust grains which are formed mainly during the production process of emulsions; (ii) fog grains which are random developed grains produced by the thermal excitation. Both components are generated during the gel production and in chemical treatments and do not increase with time since NIT ﬁlms are exposed at low temperature (< −80◦C). Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 57

FIGURE 3.9: Neutron ﬂux from intrinsic contamination in NIT emulsions [152]

The current dust level is about 5 × 10−2 per ten cubic micrometer but it can be strongly reduced by operating the NIT production in a clean room. In addition, dust grains usually show very irregular shapes or brightness saturation; they can be further discriminated during the analysis by applying appropriate selections. The probability of random coincidences of two or more fog grains is dangerous since they can mimic a WIMP-induced nuclear recoil. The current level of fog density in NIT is about 0.1 grains per ten cubic micrometer. The number of tracks produced by the chance coincidences depends on the minimum number of grains required to build a track (2) and increases with the track length. Assuming an average length between two grains of 100 nm for NIT and 50 nm for UNIT the corresponding number of tracks from chance coincidences amounts to 104 and 103, respectively. In order to achieve a negligible background induced by fog grains, a fog density of 10−3 grains per ten cubic micrometer is required as reported in Fig. 3.10. Several strategies are under investigation to lower the fog density level: (i) the use of puriﬁed gelatin that makes it possible to reduce by one order of magnitude the current fog density level; (ii) operating with a detector at low temperature to decrease the thermal excitation. As mentioned above for the electrons, the discrimination of fog grains can be further improved exploiting the resonance effect of polarised light. Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 58

FIGURE 3.10: Number of background tracks as a function of the fog density for different track lengths.

3.3 The NEWSdm project

The NEWSdm concept [154] is a detector based on the use of NIT emulsion films acting both as solid target and high resolution tracking device. The detector will be surrounded by a shielding to make negligible all the external background sources. The key point of the experiment is the placement of the detector on an equatorial telescope in order to keep NIT films constantly parallel to the galactic plane and oriented towards the expected average WIMP wind direction. to the galaxy plane. Therefore, in the detector frame WIMPs are mainly incoming from a preferred direction with the WIMP-induced recoils pointing in the opposite direction of the Cygnus constellation (see Fig. 3.11). A detector of 10 kg mass of NIT can be made of 50 µm thick-films assembled in a stack of 389 planes with a surface of 25 × 30 cm2 and 20 cm height. A plane is formed by an acrylic support (PMMA) of ∼ 280 nm thick and two NIT layers poured on both sides of the rigid support. The possibility to add between two NIT planes an OPERA-like emulsion is currently being evaluated. The additional plane would act as a trigger for all the radiation integrated by the detector along the exposure. In particular, OPERA-like emulsions may be very useful for the rejection of background events induced by the interactions of muons in the detector itself. Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 59

FIGURE 3.11: Schematic representation of the reference system in spherical coordinates. The θ and φ angles represent the 3D angle of the reicoled nucleus and its projection in the emulsion plane, respectively.

The emulsion detector will be encapsulated in a Plexiglas envelope where high purity Ni- trogen will be flushed to prevent the radon contamination; then, it will be connected to a cryostat to keep low cryogenic temperature (∼ 100 K). The shielding materials will be chosen in order to make negligible the total rate of background event (i.e. less than one track per kilogram per year) and, as a consequence, ultra pure materials are required to reach that purpose. Two configurations are currently under investigation: the former consists of a water tank 2 ÷ 3 m thick; the latter is a combination of a few meter of Polyethylene and a few tens of centimeters of Copper. The entire structure will be designed to make the movement of the equatorial telescope as simple as possible. A schematic representation of the detector layout is reported in Fig. 3.12. An equatorial telescope allows to cancel out the effect of the Earth rotation thus keeping the detector pointing to a fixed position in the sky. An equatorial telescope is typically composed by two rotation axes: the Polar axis and the Declination axis. The former is parallel to the rotation axis of the Earth and points to the North celestial pole. By rotating the Polar axis at a constant speed opposite to the Earth rotation, it is possible to cancel out the apparent daily motion of the celestial object. The latter is perpendicular to the Polar axis and allows to point to a fixed position in the sky. Both axes will be equipped with encoders to constantly check the position of the mechanics with high accuracy. A calibration procedure is foreseen to ensure a precise synchronizations of the mount with the apparent daily motion of the sky. A technical test with ten grams of NIT emulsions is currently under preparation aiming at measuring the detectable background from environmental and intrinsic sources and Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 60

FIGURE 3.12: Schematic representation of the experimental set-up for an exposure of 10 kg per year. The equatorial telescope is represented by the two green arms, the shield by the cyan cylinder and the NIT stack in yellow. validate estimate from simulations (see Chapter4). The information of a negligible background will pave the way for the construction of the pilot experiment with a ten kilogram per year of exposure mass. The experimental setup was installed in February 2017 in the Hall B of the Gran Sasso Un- derground Laboratory, behind the XENON1T detector. NIT emulsions will be stored in a cryostat (LAUDA RP 890C) to ensure the required temperature (below -40◦C) to reduce thermal excitation and fading. The shielding is made of polyethylene slabs, to absorb environmental and cosmogenic neutrons, and lead bricks, to absorb environmental gamma, 40 cm and 10 cm thick, respectively. A schematic picture of the shielding and the picture of the experimental setup installed in the Hall B is reported in Fig. 3.13.

3.4 Readout strategy

The development of high speed, automated scanning systems is needed to analyze the whole emulsion volume over a time scale comparable with the exposure time. Starting from the OPERA experience with the European Scanning System (ESS) [155–157] in Eu- rope and the Hyper Track Selector (HTS) [158] in Japan, an R&D on the development of a Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 61

FIGURE 3.13: Schematic (left) and real (right) picture of the shielding for the technical test installed in underground Gran Sasso laboratory. super-resolution optical microscope capable of reconstructing recoil tracks in NIT emulsions was carried out by the Napoli and Nagoya groups. In order to accomplish the challenging task of reconstructing tracks of few hundred nanometers an optimization for the dark matter search and new solutions in terms of tracking algorithm and nanometric spatial resolution are required. The NEWSdm experiment for the analysis strategy will adopt a two step approach: (i) candidate selection performed with optical microscopes which proﬁts of the improvements driven by the OPERA experiment, but limited to tracks longer than ∼ 200 nm because of the intrinsic optical resolution limit; (ii) candidate validation performed with a new concept of optical microscope, assembled in Napoli University, which allows to extend the reconstruction of tracks beyond the optical limit by exploiting the resonance effect of polarized light [159].

3.4.1 Shape analysis for candidate tracks WIMP-induced recoils are characterized by track lengths shorter than one micrometer in a solid detector. In NIT emulsions, mainly composed by Silver and Bromine, the expected signal from dark dark matter does not exceed few hundred nanometers. Although the R&D of automated scanning systems for emulsions-based detectors achieved a spatial Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 62 resolution beyond the sub-micron range, still optical microscopes cannot distinguish two grains closer than the optical limit: they would appear as a single cluster. Nevertheless, the cluster would have an elliptical shape, with the major axis along the actual direction of the recoiled nucleus, unlike single grains (e.g. fog grains) from thermal excitation that would appear as spherical clusters. Hence, the shape analysis performed on the cluster images can provide a first selection of signal-like events by exploiting the ellipticity information of the clusters. This principle was demonstrated using Krypton and Carbon ions implanted in a preferred direction [160]. A not exposed sample containing only fog grains was used as a reference. In Fig. 3.14 and 3.15 are reported the scatter plot of major and minor axes and the 2D angular distribution estimated by the elliptical fit of the clusters for the a sample with 400 keV Kr-ion implanted (left) and the reference sample (right). The red and blue dots represent the population of cluster with ellipticity larger than 1.5 for each sample. A clear angular peak in the direction of the implanted ions is obtained for the Kr-ion sample, while an isotropic distribution is observed for the reference sample. Using an X-ray microscope to check the selected clusters in order to ensure the presence of at least two grains within the cluster, an efficiency larger than 95% for this analysis strategy was estimated [161]. The angular resolution that can be achieved with the candidate selection phase depends on the convolution of the intrinsic resolution given by the shape analysis technique and the angular deviations caused by the scattering in the material which cannot be neglected for low energy ions (Ekin < 100 keV). The elliptical shape analysis performed with samples exposed to 60 keV and 80 keV Carbon ions has shown an overall angular resolution of ∼ 360 mrad [154]. Moreover, the intrinsic angular resolution was tested using NIT samples exposed to a 2.8 MeV neutron beam at the Fusion Neutron Source (FNS) in Japan. Since the track length of neutron-induced protons is longer than a few hundred nanometers, the scattering effect can be neglected on the clusters building up the track. By measuring the angular difference of elliptical clusters belonging to a proton track and its actual direction, the intrinsic angular resolution was estimated to be ∼ 230 mrad [154].

3.4.2 Candidate validation with the resonance effect of polarised light Localized surface plasmon resonances (LSPRs) have their origin in metallic nano-particles where the free conduction electrons are driven into oscillation due to strong coupling with incident light in the ultraviolet-visible (UV-Vis) band (see Fig. 3.16)[162]. The coupling Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 63

FIGURE 3.14: Major axis versus minor axis for the 400 keV Kr-ion sample (left) and not exposed sample (right). Red and blue dots represent clusters with an ellipticity larger than 1.5. affects the optical properties of nano-particles producing a resonance effect in the scattered light. The polarization dependence of the resonance frequencies strongly reﬂects the shape anisotropy, the size, the structure, the dielectric environment and the separation distance of nano-particles. The LSPRs effect can be exploited in NIT emulsions where nanometric metallic grains (e.g. Ag atoms after the development process), are immersed in a dielectric medium (e.g. the organic gelatin). In particular, the plasmonic resonance is sensitive to the shape of grains: clusters made by a single grain would have a spherical shape showing no dependence from the polarization angle of the incident light; on the contrary, elliptical clusters may show a strong dependence (see Fig. 3.17)[159]. Taking multiple measurements over the whole polarization range produces a displacement of the barycenter of the cluster, thus becoming sensitive to the actual presence of two grains (see Fig. 3.18). In this way, a measurement of track direction and the length beyond the optical resolution can be achieved. The LSPRs effect has been studied in NIT emulsions using samples exposed to Carbon ions of different energies where an unprecedented accuracy in the position of the clusters (< 10 nm) has been achieved, as will be reported in the Chapter5. Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 64

FIGURE 3.15: 2D anglular distribution of clusters surviving the ellipticity cut (e > 1.5) for the 400 keV Kr-ion sample (left) and not exposed sample (right).

FIGURE 3.16: Schematic representation of LSPRs effect [162]. Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 65

FIGURE 3.17: Scattered-light spectra from Ag particles with spherical (left) and elliptical (right) shape. The inset shows the particle image taken from the Scanning Electron Microscope (SEM) [159].

FIGURE 3.18: Resonance light effect exploited using different polarization angles of the incident light on an elliptical cluster from a 100keV C-ion sample. On the left are reported the dx and dy displacements of the cluster barycenter versus the polarization angle. On the right is reported the barycenter shift in the xy−plane. Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 66

3.4.3 Optical microscope for LSPRs analysis Optical microscopes for automatic scanning of nuclear emulsions based on the ESS framework consist of a computer driven mechanical stage, an appropriate optical system, a photo-detector (typically a CMOS camera) and its associated readout. During the acquisition, the whole emulsion is scanned view by view by the camera and the images are sent to the frame grabber located in a computer. The latter is also devoted to control the light intensity and the stages displacements. The readout is performed by moving the best focus plane of the objective lens inside the emulsion layer with constant speed and, for each field of view, a vertical sequence of images is taken by the camera. A motor driven scanning table for horizontal (XY) movements and a granite arm are fixed to a high quality table, which provides a virtually rigid and vibration-free working surface, holding the components in a fixed position. Vertical movements (Z) are obtained by a motor driven stage, which is fixed to the granite arm. The optics and the digital camera for image grabbing are mounted on the vertical stage. The emulsion support is provided with a vacuum system to avoid unwanted movements during the data taking. The ESS hardware is interfaced with the LASSO (Large Angle Scanning System for OPERA) [163, 164] software which improves the performance of the ESS by increasing the scanning speed, the angular acceptance and the efficiency in microtrack reconstruction. In the last years the upgrading of the ESS to the New Generation Scanning System (NGSS) [165] and the development of the Continuous Motion (CM) technique [166] led to a further scanning speed improvement up to ∼ 200 cm2 h−1. The ESS framework has been upgraded to reach the optical resolution required for the detection of sub-micron tracks and to exploit the LSPRs effect. In Fig. 3.19 is shown a picture of the prototype designed by the Napoli group, with the main differences from the ESS microscope being listed below:

• UPM-160 precision stages equipped with a center-mounted direct-metrology linear scale encoder for minimum Abbe error;

• Bonito CL/CMC-4000 is a high speed camera with excellent image quality and with a very sensitive CMOS sensor with global shutter. This high speed camera runs at up to 386 fps with 4 Megapixel resolution (2320 × 1726), providing a resolution of ∼ 27 nm pixel and a view size of ∼ 64 × 41 µm2;

• Epi-illumination mode, providing the illumination and detection from one side of the sample (by reﬂection) in order to further decrease the amount of illumination Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 67

light entering the objective lens and increase the contrast. The illumination source is a UV LED with λ = 406 nm; • high magnification objective lens Nikon Oil Objective 100X, 1.45 N.A., Plan. Apo. providing a good image flatness over the entire field of view, with chromatic aberra- tion corrected throughout the entire visible spectrum. The larger numerical aperture and magnification are used to optimize the response near the optical limit (∼ 190 nm); • Pneumatic vibrational dumper used to isolate the vibrations due to working component; • Liquid Crystal Polarization Rotator (LPR-200-0405-C) coupled with a linear polarizer filter used to rotate the polarization state of a linearly polarized input beam through more than 180◦ without involving any movement.

FIGURE 3.19: Optical microscope for dark matter search assembled in Napoli University.

The optical microscope for the dark matter search is still in a dynamic development stage where several upgrades are currently under test on a second prototype. An example is the Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 68 possibility to exploit the LSPRs wavelength dependency on the grain size, thus adding a new source of information to the Plasmon analysis. Indeed, different nanometric grain size correspond to different wavelengths in the plasmon resonance response. A Color Camera (Mikroton EoSens 4CXP MC-4087) was mounted for the acquisition of images analyzed with different polarization angles illuminated with white light. In Fig. 3.20 the different color response corresponding to two nano-rods with different size, 80 nm and 120 respectively. In particular, longer nano-rods (120 nm) show a red-shift of the resonant wavelength. Since larger energy losses are expected to produce larger and longer grains, we expect that a grain at the end of a track trajectory shows a red nuance, being the ionization higher. The application of the LSPRs technique could therefore pave the way for the head-tail discrimination in NIT emulsions. The data will be analyzed by machine learning techniques. Finally, an innovative method to achieve a 3D track reconstruction with nanometric accuracy was developed and recently patented within INFN [167]. The concept is based on the simultaneous use of two cameras: the ﬁrst takes the projection of the cluster in the horizontal (XY) plane and the second in a vertical plane. After determining the orientation of the cluster in the XY plane, the vertical plane is rotated around the Z-axis to get a focused view of the cluster. The analysis with polarized light is then performed in the vertical plane, thus achieving a position accuracy of the order of 10 nm also in the Z coordinate.

3.5 Sensitivity

The discovery potential of an nanometric-emulsion-based detector to distinguish a WIMP signal from the background, profiting of the signal anisotropy over an isotropic background has been recently studied in the SHM case [168], where a spherical and pseudo- isothermal halo permeating the Milky Way is assumed (see Eq. 1.18) . The capability of measuring track lengths above 100 nm without sense recognition was assumed. The angular distribution of WIMP-induced recoils is expected to have a Gaussian shape peaked at zero, with a sigma depending on the WIMP mass. The lighter the WIMP, the stronger the angular anisotropy. Indeed, for low WIMP masses the recoil energy is rather low and the track length threshold selects only a small fraction of the spectrum, characterised by the largest fractional energy transfer to the recoiled nucleus. This makes the sigma of the angular distribution narrower, thus enhancing the directional feature. The estimate of the expected significance for a Dark Matter search with a directional detection in emulsions was performed following a frequentist approach with the profile likelihood ratio Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 69

FIGURE 3.20: Optical microscope with color camera (top) and TEM (bottom) images of nano-rods of 45 × 80 nm2 (left) and 45 × 120 nm2 (right). test [169]. The power of the directionality was evaluated in absence of a signal assuming 100 kg year exposure and 100 background events. The upper limit evaluation was performed ﬁxing the CL at 90% and applying the CLs correction [170]. The curve is obtained by plotting the exclusion limits for different WIMP masses and it is reported in Fig. 3.21 (a) using both the Likelihood Ratio (red) and Poisson methods (blue). The gain obtained exploiting the directional information with respect to the Poisson method ranges from 10% to 20%. In Fig. 3.21 (b) the NEWSdm exclusion limit assuming zero background is compared with the curve representing the neutrino bound for a Xe/Ge target (gray dotted curve), as evaluated in [171]. The neutrino limit is reached with a 10 (100) ton × year exposure if a 30 (50) nm threshold is achieved. The resonance effect of polarised light even now allows to reach an accuracy in the position of the grains less then 10 nm in both X and Y coordinates (see Sec. 5.4). Besides, nano-metric grains of ∼ 20 nm of size are already developed in Nagoya University paving the way for a reduction of the detector threshold. On the other side, the scanning speed performances of fully automated optical microscopes is rapidly increasing in the last years allowing in the near future the design of a ton-scale detector-based on NIT emulsions. Chapter 3. Nuclear Emulsions for WIMP Search with directional measurement 70

FIGURE 3.21: Left: Exclusion curve at 90% conﬁdence for WIMP in the (mass,cross-section) plane for 100 expected background events and 100 kg year exposure. Right: Exclusion limits for the NEWSdm detector with 10 ton × year exposure and 30 nm threshold (solid blue curve) and with 100 ton × year exposure and 50 nm threshold (dashed red curve). 71

Chapter 4

Background simulation

Dark matter is a very complex paradigma and its intrinsic nature is still far from being revealed. Therefore, the identiﬁcation of such signal is very laborious and a clear under- standing of all the background sources is needed. We cannot foresee whether and how WIMP particles interact with the detector, but it is possible to predict the behavior of the known particles in the detector during the whole exposure. In this Chapter I will describe the simulation studies based on the GEANT4 toolkit [172] for the technical test of 10 g × month, planned for the beginning of 2019, and for the pilot experiment of 10 kg × y exposure. The aim of these studies is to predict the rate of events induced by the background sources at LNGS, to provide indications about materials and thickness needed to shield or considerably reduce the interactions induced by external sources. Physical processes and cross-sections for each kind of propagated particles refer to the Physics Lists validated in the GEANT4 framework. I have adopted different Phyisics Lists depending on the particle under study: (i) QGSP_BERT_HP for detailed neutron transport, high-energy muons interactions and nuclear recoils; (ii) Livermore for detailed low- energy electron physics [173, 174].

4.1 Input parameters

As mentioned in Sec. 3.2, several physical sources can act as background for dark matter experiments. They can be categorized as external, if they can be shielded before interacting with the detector, and internal, if they depend on the purity of the detector materials. These sources may be very dangerous as the exposure time and the detector mass increase since they can give rise to false positive WIMP-nucleus interactions. Since track lengths Chapter 4. Background simulation 72 of WIMP-induced recoils are expected to be a few hundred nanometers long, a signal region (SR) from 100 nm to 1 µm has been defined. According to their flux and their energy spectrum and angular distributions, simulation studies have been performed in order to quantify their contribution to the overall rate of background events in the signal region. For each source a specific number of incoming particles, corresponding to a specific exposure, has been propagated according to the distributions reported in the following subsections. In Fig. 4.1a it is shown an example with 100 events propagated in the GEANT4 framework while in 4.1b and 4.1c are reported typical nuclear (blue) and electron (yellow) recoils, respectively. In Tab. 4.1 it is recalled the expected flux at LNGS

(A) (B) (C)

FIGURE 4.1: Event display of 100 primary particles with secondaries (A) and nuclear (B) and electron (C) recoil in GEANT4. of each source (see Sec. 3.2), while the angular distributions in terms of the cosine of the zenith angle, deﬁned as the angle with respect to the local zenith, and energy spectrum are reported in the following.

4.1.1 Neutron sources Neutrons lose kinetic energy along their paths mainly because of elastic or inelastic scattering and neutron capture. Neutrons coming from external sources as environmental and cosmogenic neutrons can be moderated or absorbed by an appropriate shielding. Never- theless, a fraction of them can survive after the shielding and induce nuclear recoils in the detector. Furthermore, radiogenic neutrons originated by impurity of detector materials increase the nuclear recoils amount. A neutron-induced recoil can mimic the signal and Chapter 4. Background simulation 73

Source Flux Environmental gammas 0.35 cm−2 s−1 Environmental neutrons 8.7 × 10−7 cm−2 s−1 Cosmogenic neutrons 7.3 × 10−10 cm−2 s−1 Cosmic Muons 0.3 × 10−7 cm−2 s−1 Radiogenic neutrons 1.2 kg−1 y−1 Intinsic β-rays 7.3 × 108 kg−1 y−1

TABLE 4.1: Flux of external and internal sources at LNGS. therefore constitute a background source when its tracks is fully contained in a NIT emulsion layer and the corresponding length lies in the SR. Radiogenic and environmental neutrons are isotropically distributed inside and outside the detector, respectively, and their energy spectra extend up to 10 MeV. On the other hand, the cosmogenic neutrons induced by high-energy cosmic muons show a peculiar angular distribution, which depends on the Gran Sasso mountain proﬁle, and the energy spectrum extends up to 10 GeV. The energy spectrum and angular distribution used in the simulation study are reported in Fig. 4.2, 4.3 and 4.4 for environmental neutrons, cosmogenic neutrons and radiogenic neutrons, respectively.

4.1.2 Cosmic muons

Cosmic muons at LNGS are very energetic (< Eµ >∼ 270 GeV) since they have to cross several kilometers throught the rock. Muons entering in the detector volume do not constitute a background source by themselves since NIT emulsions are not sensitive to MIPs. However, they can produce neutrons along their path. Muon-induced neutrons can induce WIMP-like nuclear recoils if produced in the NIT emulsion stack or the most inner shielding layers, where there is no enough material for them to be absorbed. Unlike electronic detectors, nuclear emulsions do not record the time information, thus making it impossible to veto this category of events if associated to the passage of a muon track. Muons have been simulated at LNGS using two Monte Carlo codes: MUSIC (MUon SImulation Code) for the propagation of muon through large rock thicknesses; MUSUN (MUon Sim- ulation UNderground) which uses the results provided by MUSIC to generate muons in the underground site [175]. Finally, the results obtained by MUSUN have been interfaced with GEANT4 using the HepMC package [176]. Chapter 4. Background simulation 74

(A) Energy spectrum (B) Cosine of Zenith angle

FIGURE 4.2: Monte Carlo simulation of environmental neutrons.

(A) Energy spectrum (B) Cosine of Zenith angle

FIGURE 4.3: Monte Carlo simulation of cosmogenic neutrons. Chapter 4. Background simulation 75

(A) Energy spectrum (B) Cosine of Zenith angle

FIGURE 4.4: Monte Carlo simulation of radiogenic neutrons.

In Fig. 4.5, 4.6a and 4.6b are reported the energy spectrum, the cosine of zenith angle and the azimuthal angle of generated muons, respectively. Neutrons produced by cosmic muons either in the rock, in the shielding or in the detector will be referred to as cosmogenic neutrons.

4.1.3 Environmental gammas and electrons from 14C Environmental gammas passing through the emulsions lose their energy producing electrons. In addition, NIT emulsions contain the 14C isotope which undergoes β−decay thus producing electrons. The electrons, in turn, lose their energy via ionization and Bremssthralung processes. Electrons mainly produce one grain at the end of their range. In order to evaluate the minimum energy needed for the electrons to sensitize a crystal and the chance coincidence of two grains produced by two electrons at the ﬁnal range, all the electrons stopped in NIT emulsions are taken into account and clusterised as described in Sec. 4.2. In ﬁg. 4.7 and 4.8 are reported the energy spectrum and the angular distribution used in the simulation study for environmental gammas and electrons from 14C, respectively. Chapter 4. Background simulation 76

FIGURE 4.5: Monte Carlo simulation of the energy spectrum of cosmic muons at LNGS.

(A) Azimuthal angle (B) Cosine of Zenith angle

FIGURE 4.6: Monte Carlo simulation of the angular distributions of cosmic muons at LNGS. Chapter 4. Background simulation 77

(A) Energy spectrum (B) Cosine of Zenith angle

FIGURE 4.7: Monte Carlo simulation of environmental gammas.

(A) Energy spectrum (B) Cosine of Zenith angle

FIGURE 4.8: Monte Carlo simulation of electrons from 14C. Chapter 4. Background simulation 78

4.2 Simulation of NIT response to electrons

The simulation software deals with sets of particles. A track is the path the particle takes in matter until it is absorbed. Although the passage of the particles through the matter is a continuous process, the transportation has to be done in steps due to computing constraints. Each particle track is therefore composed of a sequence of steps, the length of which is related to the energy deposit and depends on the physical undergoing process. The particles under study in the present analysis can be divided in two categories: nuclear recoils and electrons. Having energies O(100 keV), the former lose their energy in a few steps (see Fig. 4.1b) and their trajectory can be treated as straight lines. Electrons, on the contrary, show a large number of steps and their trajectory is far from being straight since they undergo elastic scattering in the material (see Fig. 4.1c). The description of an event induced by a photon interaction in the emulsion is therefore rather complex. It can be schematised as shown in Fig. 4.9a: the photon undergoes photoelectric effect generating a primary electron. Depending on the initial energy of the primary electron, a number of secondary electrons is produced in the proximity of the initial interaction point via ionization processes. Both primary and secondary electrons lose most of their energy in the last step, as shown in Fig. 4.9b, where dE/dx per step is reported as a function of the fraction of total track length. Therefore only the position and the energy release in the last step is considered for electrons stopping in NIT emulsions. As the secondary electrons can be created and absorbed in a volume with dimensions comparable to those of the AgBr crystal, they can be indistinguishable from each other. The process can effectively be described by using the probability distribution of the number of electrons directly or indirectly liber- ated during a primary interaction. This distribution is known as cluster size distribution. The calculation of the cluster size distribution requires knowledge of the atomic structure of the target and is non-trivial. In order to evaluate the number of grains produced in NIT by electrons, a clusterisation algorithm was introduced: the Density-based Spatial Clus- tering of Applications with Noise (DBSCAN) [177]. It is based on two main principles: (i) each point is characterized by a local density; (ii) a set of point in a cluster is spatially connected. The local density can be expressed as:

Ne(x) = {y ∈ D | dist(x, y) ≤ e} (4.1) where N is the number of points (x) which have a distance less than e from at least one point (y) belonging to the cluster D. The algorithm requires in the simplest form two parameters: Chapter 4. Background simulation 79

(A) (B)

FIGURE 4.9: (A) Schematic representation of gamma interaction in GEANT4. (B) dE/dx versus the fraction of the total track length for primary (blue) and secondary (red) electrons.

1. e the maximum distance for the local density;

2. nmin the minimum number required to form a dense region.

In Fig. 4.10a is reported a schematic illustration of the DBSCAN algorithm with nmin = 4. Red points are called core-points since they are connected within e with at least 4 points, while yellow points are called border-points since they belong to the cluster but do not stay in a dense region. Finally, the blue point is called noise-point because is not connected with other points. In Fig. 4.10b it is reported the DSBCAN method applied on a gamma event simulated in GEANT4. The different colors represent the different clusters formed by the last step of gamma-induced electrons. The DBSCAN algorithm has been used to evaluate the minimum energy deposit required to form a grain in NIT emulsions. A test beam exposure to a gamma source of 241Am has been performed at LNGS with an NIT ﬁlm to calibrate the algorithm by measuring the electron density after the fog subtraction. In Fig. 4.11a it is shown the plastic support used to place the source and the NIT ﬁlm. The sample was developed and scanned in two different small region of 5 × 103 × [10 µm]3 at the Nagoya University. The measured electron density was estimated to be ∼ 1.15 × [10 µm]−3. This value was used as a reference for the simulation study to gammas from 241Am; the simulation of the experimental setup and the gamma energy spectrum is reported in Fig. 4.11b and 4.11c, respectively. Chapter 4. Background simulation 80

(A) (B)

FIGURE 4.10: Schematic representation of DBSCAN method (A) and its application on an electron track (B).

The analysis strategy is based on four steps and consists of two iterations of the DBSCAN algorithm with nmin = 1: 1. small clusters are obtained event by event with all the stopped electrons using e = 100 nm which is the average size of AgBr crystal plus gelatine;

2. an energy threshold is set and only the small clusters with a total energy deposit larger than the threshold are considered;

3. big clusters are obtained over all the events from the small clusters survived to the energy cut. The maximum distance for the local density is set to 450 nm which is the minimum recognition distance in the Japanese optical microscope;

4. the grain density is evaluated as the number of big clusters in ten cubic micrometer.

Small clusters and big clusters represent the schematization of two effects: the former de- picts the AgBr crystals in NIT emulsions; the latter, instead, describe grains observed at optical microscope after taking into account its spatial resolution. In Fig. 4.12 is reported the grain density, normalized to [10µm]−3, versus the energy deposit threshold adopted for all the small clusters. The two curves, which refer to two different regions scanned by Chapter 4. Background simulation 81

(A) (B) (C)

FIGURE 4.11: (A) Box for radioactive source exposure of NIT sample. Event display of NIT exposure to 241Am (B) and its energy spectrum (C). the optical microscope, reach the measured grain density induced by electrons if an energy deposit larger than 3.5 keV is contained in a small cluster. Therefore, in the following simulations it is assumed that an energy threshold equal to Ethr = 3.5 keV is necessary in order to sensitize AgBr crystals.

4.3 Intrinsic neutron and electrons from 14C background

Intrinsic neutrons and electrons from 14C have been isotropically generated in a cube made of NIT emulsions, as shown in Fig. 4.13. Given the intrinsic neutron yield reported in Tab. 4.1, the induced nuclear recoils can be neglected for an exposure of 10 g per month while for 10 kg per year it is important to evaluate the corresponding rate of neutron-induced recoils in the SR. In Ref. [152] is shown that neutrons interact via elastic scattering in 97% of cases and the ∼ 10% of nuclear induced recoils have a track length within the SR. This result corresponds to a rate of ∼ 0.1 kg−1 year−1 nuclear recoils which could be further reduced down to ∼ 0.06 kg−1 year−1 exploiting directional information. Electrons from 14C have been analyzed using the DBSCAN algorithm over all the last energy deposit inside NIT cube. Small clusters with an energy deposit Edep >= 3.5 keV have been considered to form big clusters. The number of grains estimated from the analysis is (33.7 ± 1.8) per gram per month. In Tab. 4.2 are summarized the results described above. Chapter 4. Background simulation 82

FIGURE 4.12: Electron density versus energy deposit in small clusters. Red and blue circles refer to two different scanned regions. The horizontal green dotted-line represents the measured electron density.

FIGURE 4.13: Event display of 1 kg of NIT emulsion exposed to radiogenic neutrons. Chapter 4. Background simulation 83

Source Rate [g−1month−1] Rate [kg−1y−1] Radiogenic neutrons (5.0 ± 1.7) × 10−6 0.06 ± 0.02 Intinsic β-rays 33.7 ± 1.8 (4.04 ± 0.02) × 106

TABLE 4.2: Background rate from intrinsic neutrons and electrons from 14C.

4.4 Technical test simulation

The NEWSdm Collaboration is preparing a technical test in order to evaluate the detectable background in Gran Sasso underground laboratory. The exposure will be performed with 10 gram of NIT emulsion films. Having a size of 12 × 10 cm2, a single emulsion film has a sensitive mass of 2 grams. Five one-side coated films will therefore be used for the test; they will be disposed in a stack and surrounded by a shielding. The technical test will last one month. In this phase, the presence of the equatorial telescope is not needed. As reported in Fig. 3.13, the shielding for the technical test was installed in February 2017 in the Hall B. Before the installation a simulation study was performed to optimize the choice of all the materials and their thickness, and the configuration of the experimental setup. The main goal was the design of a shielding able to reduce the background from external neutrons down to less than one nuclear recoil in SR and that from environmental photons lower than the contribution from 14C. In Fig. 4.14 it is shown the experimental setup simulated by GEANT4 with the NIT emulsions (yellow) and the contours of polyethylene slabs (cyan), lead sheets (white) and the cryostat (brown). As mentioned in Sec. 3.3, the final configuration is composed by 10 cm of Lead and 40 cm of Polyethylene. The generation surface is a 2 m-radius sphere for photons and neutrons, a 2.5 m-wide box for muons, both centered in the geometrical centre of the NIT stack. The rate evaluated for nuclear recoils in the SR producing false positive signal events is negligible for all the external neutron sources and the grain density induced by electrons is comparable to the yield that would be induced by 14C. Details about the simulated total exposure, the number of events in the SR and the corresponding rate per gram per month are reported in Tab. 4.3. Chapter 4. Background simulation 84

(A) (B) (C)

FIGURE 4.14: Shielding for 10g × month: lateral view (A), axonometric view (B) and top view (C).

Source Exposure [10 g month]−1 SR events Rate [10 g month]−1 Environmental gammas 0.1 31 310 ± 56 Environmental neutrons 50 0 < 4.7 × 10−2 (90% C.L.) Cosmogenic neutrons 8832 6 (6.8 ± 2.8) × 10−4

TABLE 4.3: Estimation of the background rate, normalized to [10 g month]−1, induced by the external sources for the technical test. Chapter 4. Background simulation 85

4.5 Simulation of the pilot experiment

The NEWSdm Collaboration aims at achieving a pilot experiment with a mass of 10 kg scale. This experiment would act as a demonstrator of the directional approach for direct dark matter search with a solid state detector. The pilot experiment is mainly devoted to prove the directionality potential using NIT emulsions and to explore the parameter space delimited by the DAMA experiment. The project basically consists of three components: (i) NIT emulsions at low temperature; (ii) a shielding; (iii) an equatorial telescope. Simulation studies have been performed in order to evaluate the thicknesses and the materials needed to realize an appropriate shielding which should ensure a mass exposure up to 10 kg × y. Furthermore, this study will drive the design of the equatorial telescope. Several simulation campaigns have been performed to evaluate the rate of nuclear recoils induced by external neutrons and muons interacting inside the shielding. A simple geometry based on a sequence of concentric shells allowed to test combinations of materials with different sorting and thickness (see Fig. 4.15). The inner shell is a vacuum chamber with 50 cm radius where the detector is placed; the external shells are filled with shielding materials as polyethylene, copper and polyborate. Double-side coated NIT films are simulated with a surface of 30 × 25 cm2 and a 50 µm thickness; the base is made of PMMA and is 280 µm thick. They have been disposed in a stack of 389 films with a total height of ∼ 15 cm and mass of 10 kg. The generation surfaces for the different background sources are the same reported in the Sec. 4.4. Firstly, the effectiveness of a shielding made of polyethylene or water has been tested. In Fig. 4.16 it is reported the rate of background events in the SR, normalized to 10 kg × y, versus the shielding thickness. Background events induced by environmental neutrons are strongly reduced after a few tens of centimeters, while those from cosmogenic neutrons shows a saturation above 100 cm. The contribution from muons interacting in the shielding cannot be further reduced since it increases with the amount of the material crossed. Moreover, the polyethylene shows a lower background rate with respect to water shielding. I therefore focused on a shielding made of 100 cm of polyethylene that is enough thick to guarantee a total rate of background event of about 1.4 for an exposure of 10 kg yr. In Tab. 4.4 are reported the rate of false positive recoils for each source and the electron density, estimated using the DBSCAN method induced by environmental gammas. Hydrogenous materials have an higher capture cross section for thermal neutron and an high neutron elastic scattering cross section. Nevertheless, having muon-induced neutrons energies up Chapter 4. Background simulation 86

(A) (B)

FIGURE 4.15: Event display of NIT stack with emulsion ﬁlms in yellow and the base in white (A), of the inner shell (red) with the detector (B), of the outer shells (green and blue) ﬁlled with shielding materials as Polyethylene and Copper (C and D). Chapter 4. Background simulation 87

Source Rate [10 kg × y]−1 Environmental gammas (1.97 ± 0.17) × 104 Environmental neutrons O(10−2) Cosmogenic neutrons 1.41 ± 0.14

TABLE 4.4: Background rate estimation induced by external gamma and neutron sources for 10 kg yr exposure with a shielding made of 100 cm of polyethilene. to the GeV, the elastic scattering is less effective to moderate and absorb neutrons. On the other side, inelastic scattering in materials with high atomic number (Z) gives a larger contribution in the reduction of the neutron energy. Typically shieldings are made of a sequence of an high Z material followed by an hydrogeneous material. In this way, high energy neutrons are firstly moderated by high Z materials down to thermal energies and then absorbed in hydrogeneous material. In addition, a copper layer before polyethylene drastically reduce the environmental gammas. In order to study the effectiveness of high Z materials for the shielding, several configurations have been simulated with copper outside of the polyethylene shell. Although the background rate induced by cosmogenic neutrons produced in the surrounding rock can be reduced of a 20% with 10 cm of copper and 50 cm of polyethylene, muons cross-section increases with high Z materials thus producing high energy secondaries which result in a total background rate a factor two larger than the only polyethylene configuration. Hence, configurations with the addition of copper have been discarded. Finally, since hydrogenous materials quickly slow down neutrons until thermal energies, boron-doped polyethylene might be used in the last part of the shielding since Boron has a large cross-section for thermalised neutron absorption. Several configurations have been simulated with a shielding made by standard polyethylene in the outer part and polyety- lene containing 25% Boron in the inner part; nevertheless, it was not observed a significant gain both for cosmogenic neutrons and muon induced background.

4.5.1 Opera emulsion as a veto To further reduce the rate of background events induced by muons, OPERA-like emulsions [178], which are sensitive to MIPs, could be added as a veto between two NIT ﬁlms. A background event may be further rejected if a charged particle, reconstructed in the Chapter 4. Background simulation 88

FIGURE 4.16: Rate of background events, normalized to 10 kg yr exposure, induced by external neutron sources versus the shielding thickness for the polyethylene and water options. adjacent OPERA ﬁlms, is pointing to the recoiled nucleus in NIT emulsions. In Fig. 4.17a it is reported a GEANT4 representation of the stack composed by a sandwich of OPERA- like emulsions in blue and NIT emulsions in yellow. In Fig. 4.17b is reported for a NIT layer the XY scatter plot of all steps simulated by charged particles (with Z < 3) in 2.6 year of exposure. Assuming a ﬁducial area of (100µm)2 for each step and given the total number of entries, the sensible area that would be discarded is less than 0.1%. In order to evaluate the reduction that can be achieved using OPERA emulsions as a veto, a preliminary analysis, based on visual inspection, it has been performed on an ensemble of 32 background events induced by muons crossing the shielding. Eight recoils result linked to some charged particle (or anti-particle) like (p, d, µ, τ, π, κ), thus corresponding to a reduction of ∼ 25%. In Fig. 4.18 are reported two false positive events (red triangles) for which a link with charged particles it was found. The effectiveness of OPERA emulsion as a veto for NIT will be widely studied in the near future since it could represent an important solution to decrease the muon-induced background for larger mass exposure. Chapter 4. Background simulation 89

(A) (B)

FIGURE 4.17: (A) Event display of NIT ﬁlms (yellow) among OPERA ﬁlms (blue). (B) Scatter plot of charged particle positions in a layer of NIT emulsion.

(A) (B)

FIGURE 4.18: Event display of false positive recoils (red triangles) linked to charged particles as µ (A) and d and p (B). Chapter 4. Background simulation 90

4.6 Discussion on simulation results

The results obtained by simulation studies have shown that the total rate of the background events induced by nuclear recoils can be kept at about 1 for exposures up to ten kilogram per year. Muons interacting in the shielding seem to be the most dangerous source in the perspective to extend the mass-scale of the detector. The use of OPERA- like emulsions can reduce of a factor four the muon-induced background rate and other strategies to further decrease such amount will be considered in the near future. The density of electron-induced grains is lower than the expected level (see Fig. 3.10 and Tab. 4.5) to produce dangerous chance coincidence which can mimic signal events. More-

Exposure 10 g × month 10 kg × y Source Rate [10 µm]−3 Rate [10 µm]−3 Environmental gammas O(10−7) O(10−9) Intrinsic β−rays O(10−7) O(10−5)

TABLE 4.5: Density of electron-induced grains in NIT emulsions for the technical test and the pilot experiment. over, as reported in Fig. 3.7, keeping the detector at cryogenic temperature (. 100 K) provides a discrimination power of the electron grains up to 108. In addition, the analysis of the emulsion with polarized light can further improve the discrimination power. Instrumental background represented by fog-grains and dust is actually the true challenge in order to perform a free background experiment. As remarked in Sec. 3.2.3, it is crucial to reduce of a factor 102 the current fog-level in order to reduce the chance coincidence less than 1. In this perspective, considerable efforts are going towards a new procedure for puriﬁed gelatine, the use of a clean room and cryogenic temperature, and, as for electron-induced grains, analysis with polarized light. 91

Chapter 5

Resonance effect of polarised light in NIT emulsions

The directionality is the most promising approach to have an unambiguous proof of the intrinsic nature of WIMP dark matter. The kinematics of nuclear recoils in a solid-based detector presents us with a huge challenge since the expected signature is represented by a few hundred nanometers-long tracks. NIT emulsions are the best tracking detector since they allow to reconstruct tracks down to 100 nm and optical microscopes, although limited by the optical resolution, are currently the best scanning devices both in terms of speed and feasibility. The observation of track lengths shorter than the diffraction limit is therefore crucial for the NEWSdm experiment. This challenging requirement can be achieved by exploiting the resonance effect of polarized light: nanometric metallic grains behave differently when illuminated by light with different polarization angles. In this chapter the analysis with polarized light is described and the most relevant results obtained on NIT samples are reported.

5.1 Scanning and analysis processes

The NEWSdm experiment adopts a two-step strategy for the analysis of NIT emulsions, as mentioned in Sec. 3.4. In the former, the analysis of the elliptical shape is used to select signal-like clusters. In the latter, the validation of candidates by using the effect of LSPRs is performed. The optical microscope assembled in Napoli University (see Sec. 3.4.3) is mainly devoted to the development of the plasmon analysis which looks at the cluster properties when observed with different polarization of incident light. Chapter 5. Resonance effect of polarised light in NIT emulsions 92

The reference system used in the following description has the X and Y axes parallel to the emulsion surface. The scanning procedure is performed in ﬁve steps:

1. the scanned area is divided in 60 µm × 45 µm-wide ﬁeld of views; the pixel size is ∼ 27 nm;

2. for each view the whole emulsion thickness is scanned as a vertical sequence of layers by moving the focal plane with a 250 nm step;

3. each layer is scanned by using 8 different polarization angles of the incident light with a step of 22.5°;

4. the grabbed images, appearing as white pixels over a dark ﬁeld, for each polarization angle are sent to a dedicated image processor and reconstructed as 2D clusters from pixels above the brightness threshold;

5. clusters reconstructed in all the layers of the same view are stored before moving to the adjacent one.

The scanning is then followed by an analysis process consisting of two main steps: (i) the reconstruction of 3D grains from 2D clusters (grain reconstruction) and (ii) the characterization of reconstructed grains by exploiting the polarization information (plasmon analysis). Reconstructed 3D grains represent the physical grains formed by the latent images and made visible by chemical treatments1. The grain reconstruction is performed as follows:

a) for each layer 2D clusters closer than ∼ 300 nm are grouped in the so-called 2D merged cluster;

b) 2D merged clusters in consecutive layers are linked together if located within an angular and position acceptance deﬁned by a truncated cone, thus forming the 3D grain;

c) the brightest 2D merged cluster is referred to as best focus cluster and the corresponding layer is called best focus layer;

d) the polarized clusters reconstructed in the best focus layer are deﬁned as best focus polarized clusters (BFPCs).

1The term grain will only refer to the reconstructed 3D objects from now on. Chapter 5. Resonance effect of polarised light in NIT emulsions 93

In Fig. 5.1 is reported a schematic representation of the grain reconstruction process. The polarization information for each reconstructed grain is retrieved from its best focus cluster. The 3D position of the grain is reconstructed as the barycenter of the positions of the merged clusters it is made of, each weighted for its brightness. The data can be divided into two main categories: (i) micro-tracks produced by two or more adjacent but distinct grains, (ii) isolated grains. In turn, isolated grains can be made by a single grain (background-like) or by more than two non-resolved grains (signal-like). In order to distinguish these two categories the plasmon analysis is used.

FIGURE 5.1: Schematic illustration of the grain reconstruction process. 2D merged clusters are represented in red and the best-focus cluster in blue. 2D merged clusters are linked to form the reconstructed grain represented in green.

5.2 Plasmon variables

WIMP-induced recoils are supposed to produce tracks a few hundred nanometers long (nano-tracks) in the NIT emulsions (see Fig. 5.2). Nano-tracks appearing as isolated grains could be identiﬁed using the best focus polarized clusters. The application of the plasmon analysis allows to overcome the diffraction limit, thus exploring for the ﬁrst time the Chapter 5. Resonance effect of polarised light in NIT emulsions 94

FIGURE 5.2: Track length distributions of WIMP-induced recoils in the NEWSdm detector obtained by SRIM simulation. Different colors represent different WIMP masses. nanometer scale Universe with the optical microscope. The subject of the analysis therefore moves from grains to the best focus polarized clusters. Several variables have been taken into account and the most relevant ones are reported in the following list:

• Ncopy: total number of BFPCs stored for each grain and ranges from 1 to 8 which is the maximum number of polarization angles used;

• α: polarization angle of the BFPCs;

• xα, yα: coordinates of the BFPCs;

• xb f c, yb f c: coordinates of the barycenter of BFPCs;

• ∆sb f c: maximum distance between two BFPCs belonging to the same grain and representing for each grain the maximum barycenter displacement of its BFPCs;

• φb f c: track direction in the xy plane, obtained from the line connecting the two ex- treme displacements of the BFPCs; Chapter 5. Resonance effect of polarised light in NIT emulsions 95

• < ∆φ >: average of the mutual angular distance over all the BFPCs, providing an estimate about the kind of motion of the best focus cluster (rotational or transla- tional).

In Fig. 5.3 are shown the eight BFPCs plus the merged best focus cluster of two isolated grains. On the axes are reported the X and Y coordinates in pixel size units in the same reference system. The blue dot represents the barycenter position of the cluster while the black (white) line is the major (minor) axis of an ellipse defined by the variances of a bidimensional gaussian distribution. The event display in Fig. 5.3a shows an almost spherical cluster for eight different polarizations: the barycenter position is not moving (static grain). On the contrary, the event display in Fig. 5.3b shows an elliptical cluster with its barycenter moving as the polarization angle rotates (moving grain). The position in the XY plane of the BFPCs barycenter for different polarization angles is reported in Fig. 5.4: background-like grains show a circular movement of the barycenter within 15 nm (see Fig. 5.4a) while for the signal-like grain (see Fig. 5.4b) the displacement of the barycenter occurs in a preferred direction with a maximum distance between α = 67.5° and α = 157.5° corresponding to ∆sb f c = 56 nm and φb f c ∼ 136°. Plasmon analysis is useful for the identification of micro-tracks with lengths very close to the optical resolution limit (∼ 200 nm). When studying the BFPCs of an isolated grain for some polarization it appears as two or more clusters (npeaks grains). In such cases, the length and the direction of grains are measured by the largest distance between the clusters. In Fig. 5.5 is shown an example of a micro-track identified by the presence of two separated clusters in the first three polarizations. The length and the direction of the grain, measured from the largest distance between the two clusters over the three polarizations, corresponds to ∼ 195 nm and ∼ 79°, respectively. The study of the LSRPs is therefore a powerful tool to investigate the properties of nanotracks allowing through the barycenter displacement the reconstruction of the shape anisotropy when clusters are formed by two or more physical grains.

5.3 Test beam with Carbon ions

In order to benchmark with real data the capability to reconstruct nuclear recoils induced by WIMPs, the Collaboration is analysing NIT emulsion samples implanted with low energy Carbon ions with an inclination of ∼ 10° with respect to the emulsion surface. I analyzed samples exposed to 100, 60 and 30 keV, whose average range calculated by SRIM software [179] is estimated to be 240, 150 and 80 nm, respectively (see Fig. 5.6). The ﬁrst Chapter 5. Resonance effect of polarised light in NIT emulsions 96

(A)

(B)

FIGURE 5.3: Event displays of BFPCs for two isolated grains. Chapter 5. Resonance effect of polarised light in NIT emulsions 97

(A) (B)

FIGURE 5.4: XY scatter plot of BFPCs positions for a static grain (5.4a) and a moving grain (5.4b).

FIGURE 5.5: Event display of BFPCs for a npeak grain. Chapter 5. Resonance effect of polarised light in NIT emulsions 98 two samples act as a signal-like samples since Carbon ions are expected to sensitise on average more than one crystal, thus resulting in a cluster with elliptical shape and a signiﬁcant barycenter shift . I also analyzed a NIT sample exposed to a 10 keV Carbon ion beam impinging at ∼ 90° with respect to the emulsion plane. It acts as a background-like sample since such low energy C ions are expected to sensitize one crystal thus resulting in clusters with a spherical shape and a barycenter shift compatible with the statistical ﬂuctuations. The sample exposed to 30 keV, representing an intermediate case between background- like sample and the signal-like samples. It therefore plays an important role in this analysis since it could be used to determine the threshold both in energy per nucleon and in track length achieved by the NEWSdm experiment using the plasmon analysis.

5.3.1 Simulation of the test beam A simulation of the test beam has been performed for a comparison with data. As shown in Fig. 5.6, the SRIM software has been used to generate the nuclear recoils induced by Carbon ions in NIT emulsion. The 3D hit positions of each produced track is recorded by SRIM and the projection in the emulsion plane (XY) of the last hit is reported in Fig. 5.7 each Carbon beam energy. Scattering hides the directional information for low energy ions thus making the directional measurement a challenging task. The track length has been deﬁned as the length of the line connecting the two marginal hits belonging the track. It is worth noting that SRIM assumes an inﬁnite resolution and does not take into account the granularity of the detector. A Monte Carlo study was therefore performed to simulate the 3D crystal structure of NIT emulsions in ∼ 1 µm3. Crystals have been generated as spheres with a radius following a gaussian distribution and a volume density according to the values reported in Ref. [137]. An illustration of the generated crystals is shown in Fig. 5.8 and the distributions of the radius and the position for each coordinate are reported in Fig. 5.9. The crystal simulation is useful to take into account the effect of the granularity in the track length reconstruction.

Tracks generated by SRIM have been randomly translated in the 3D crystal pattern and for each event the number of sensitized crystals, i.e. crossed by C ion, was retrieved. Three categories of tracks can be identiﬁed:

• zero crystals: ions which do not sensitize any crystal represent the detector inefﬁciency and their fraction increases as the ion energy decreases; Chapter 5. Resonance effect of polarised light in NIT emulsions 99

(A) (B)

FIGURE 5.6: Track length distribution obtained by SRIM simulation for 100 keV (A), 60 keV (B), 30 keV (C), 10 keV (D) Carbon ion beams. Chapter 5. Resonance effect of polarised light in NIT emulsions 100

(A) (B)

FIGURE 5.7: Last hit positions, as provideed by SRIM simulation, in the emulsion plane (XY) for 100 keV (A), 60 keV (B), 30 keV (C), 10 keV (D) Car- bon ion beams. Chapter 5. Resonance effect of polarised light in NIT emulsions 101

FIGURE 5.8: Monte Carlo simulation of the crystals dispersed in a NIT emulsion.

FIGURE 5.9: Coordinates (x, y, z) and radius of the simulated crystals. Chapter 5. Resonance effect of polarised light in NIT emulsions 102

• one crystal: recoils which sensitize only one crystal can be detected by the optical microscope but neither the shape or the barycenter shift of the grain can identify them as signal. They represent background-like clusters;

• n-crystals: recoils which sensitize more than one crystals represent the signal-like clusters since they have an elliptical shape and plasmon effect could be observed by varying the polarization of the incident light.

In Fig. 5.10a it is reported a schematic illustration of the model for a track (black dotted line) passing through the crystals (circles). All the crystals crossed by the blue line which represents the track length calculated by SRIM, are considered as sensitized (grey circles). In Fig. 5.10b, 5.10c and 5.10d are reported the zero crystals, one crystal and n-crystals, respectively. In Tab. 5.1 are reported for each sample the fraction of events belonging to the three categories. In order to take into account the granularity of the NEWSdm detector

Energy [keV] zero crystals [%] one crystal [%] n-crystals [%] 100 9.8 17.0 73.2 60 12.2 22.9 64.9 30 18.4 35.3 46.3 10 18.0 47.5 34.5

TABLE 5.1: Event fraction of the three categories for each sample. and the fact that the latent images are formed on a random point on the crystal surface, the length for n-grains crystals has been constructed as the distance between two randoms points nearby of the furthest crystals sensitized. Signal-like clusters can be identiﬁed by the optical microscope if their lengths are longer than the track length threshold that can be achieved using plasmon analysis. In Fig. 5.11 the track length distribution of n-grains crystals and the corresponding cumulative distribution function obtained considering the SRIM+Crystal model (red) are compared with the only SRIM simulation (blue). The difference between the two distributions is larger for higher energies samples. Granularity therefore affects track length reconstruction when marginal points of a track are outside the crystals thus providing an underestimation in the total length, as shown in Fig. 5.12. The probability that marginal points are outside the crystals is larger for longer tracks as in the 100 keV sample, while track lengths comparable to the linear density of crystals, as in the 30 keV sample, are mainly contained inside the crystals (see Tab. 5.2). Chapter 5. Resonance effect of polarised light in NIT emulsions 103

(A)

(B) (C) (D)

FIGURE 5.10: (A) Schematic illustration of a track passing through the crystal pattern. Representation of zero crystal (B), one crystal (C) and n-crystals (D) categories.

Energy [keV] zero marginals [%] one marginal [%] two marginals [%] 100 4.9 40.6 54.5 60 2.1 26.5 71.4 30 0.1 6.2 93.7

TABLE 5.2: Event fraction with marginal points inside or outside the crystals. Chapter 5. Resonance effect of polarised light in NIT emulsions 104

(A) (B)

(E) (F)

FIGURE 5.11: Track length distributions and related cumulative functions for the n-crystals category of 100 keV (A,B), 60 keV (C,D) and 30 keV (E,F) C ion samples. Chapter 5. Resonance effect of polarised light in NIT emulsions 105

FIGURE 5.12: Schematic illustration of marginal points outside (left) and inside (right) the crystals.

5.3.2 Scanning of the data The aim of the analysis is to reconstruct the direction of nuclear recoils induced by Carbon ions. In order to evaluate the gain of the plasmon analysis in addition to the shape analysis, each sample was scanned by the optical microscope in two modes: with polarized light to exploit plasmon variables; without polarized light for the shape analysis, since the polarization can modify the shape of the clusters. Then, the two datasets have been aligned and only grains having both information were selected. In Fig. 5.13a and 5.13b the grain positions before and after the alignment process is shown. The distribution of the residuals is reported in Fig. 5.14. Signal-like clusters can be therefore identiﬁed from their shape or barycenter shift over a ﬁxed threshold.

5.4 Position accuracy

The NIT film vertically exposed to 10 keV can be used as a reference sample for two main reasons: (i) the angular distribution of nuclear induced recoil is expected to be flat; (ii) the barycenter shift for n-crystals is expected to be small and comparable with the expected fluctuation in the cluster position. It is therefore useful to evaluate the position accuracy achieved in the emulsion plane (XY) by the optical microscope assembled in Napoli University in order to determine the threshold for the barycentre shift to be used for the Chapter 5. Resonance effect of polarised light in NIT emulsions 106

(A) (B)

FIGURE 5.13: (x, y) grain positions measured with (black) and without (red) polarized light before (A) and after (B) the alignment process.

FIGURE 5.14: Residual distribution of the aligned grains. Chapter 5. Resonance effect of polarised light in NIT emulsions 107 candidate selection with plasmon analysis. The position accuracy is deﬁned for each coordinate as the standard deviation of xα(yα) coordinates from xb f c(yb f c) and is reported in Fig. 5.15 where an accuracy of ∼ 8.4 nm and ∼ 5.7 nm is obtained for the x and y coordinates. Then, the threshold on the barycenter shift ∆sthr has been deﬁned as follows: q 2 2 ∆sthr = 3σxy = 3 σx + σy ' 30 nm. (5.1)

Hence, clusters having a barycentre shift larger then ∆s > ∆sthr are considered signal-like events.

(A) (B)

FIGURE 5.15: Position accuracy for the x (A) and y (B) coordinate.

5.5 Shape analysis

The first step of the analysis is focused on the elliptical shape of the isolated grains which are fitted with a bidimensional gaussian distribution. The parameters obtained by the fit are used to reconstruct the minor and major axes and, consequently, the ellipticity and the direction of all the grains. In Fig. 5.16 are reported the 2D angular distributions obtained by the SRIM+Crystals simulation (blue) and the data (red) with the shape analysis for the reference sample: both distributions are isotropic as expected. Chapter 5. Resonance effect of polarised light in NIT emulsions 108

In Fig. 5.17a, 5.17b, 5.17c are reported the 2D angular distribution obtained by the SRIM+Crystals (blue) and data (red) for the samples exposed to 100, 60 and 30 keV Carbon ions, respectively. The distributions can be ﬁtted by the sum of a gaussian plus a constant (p3).

FIGURE 5.16: 2D angular distribution obtained by the data (red) and the SRIM+Crystals simulation (blue) for the 10 keV C ion sample.

The plateau is populated by the one grain component. The discrepancy by the expected and observed plateau levels is due to the inability of the shape analysis to reconstruct the direction of tracks smaller than the optical resolution limit. The lower is the energy of the Carbon beam, the smaller is the capability of reconstructing the elliptical shape and therefore the incoming direction of the beam. The directionality is well reconstructed for 100 keV and 60 keV samples while for 30 keV is barely visible since less than 1% of tracks are longer than the optical resolution limit ∼ 200 nm (see Fig. 5.7c). The 100 keV and 60 keV samples can be used to evaluate the efﬁciency of directional events esh that is deﬁned as the ratio between the area of the gaussian and the total area:

Ngaus esh = (5.2) Ngaus + Nf lat where Ngaus and Nf lat represent the number of events with a preferred direction and a random direction, respectively. The directional efﬁciency amounts to ∼ 43.6% for 100 keV sample and ∼ 23.6% for 60 keV. Since clusters with elliptical shape hide more than one grain, they represent the n-crystals Chapter 5. Resonance effect of polarised light in NIT emulsions 109

(A) (B) (C)

FIGURE 5.17: 2D angular distribution obtained by the data (red) and the SRIM+Crystals simulation (blue) for the 100 keV (A), 60 keV (B), 30 keV (C) C ion sample. fraction in the SRIM+Crystals simulation. By using the CDF curve obtained by the simulated model, it is possible to retrieve the track length threshold corresponding to the measured inefﬁciency (1 − esh). In Fig. 5.18 the estimation of the threshold with 1σ (dark teal) and 2σ (light teal) error bands is reported of both samples and ranges around 190 nm. A cross-check was performed to test the reliability of the SRIM+Crystal model by using the resolution limit achieved by the shape analysis. Tracks with length smaller than 190 nm have been reconstructed with a random direction and the comparison between simulation (blue) and data (red) of the 2D angular distributions is reported in Fig. 5.19 for each sample. Simulation and data are in good agreement.

5.6 Plasmon analysis

Elliptical shape analysis makes it possible to perform a directional measurement of nuclear recoils with track length down to ∼ 190 nm, as reported in the previous section. The use of the plasmon analysis allows to further decrease the threshold in the track length reconstruction by exploiting at the barycenter shift of the clusters. Carbon ion samples, as mentioned in Sec. 5.1 can be divided in two categories: micro-tracks and isolated grains, which in turn can be categorized in static grains (∆s < ∆sthr) and moving grains (∆s > ∆sthr). In Tab. 5.3 are reported the fraction of all categories for each scanned sample. Chapter 5. Resonance effect of polarised light in NIT emulsions 110

(A) (B)

FIGURE 5.18: Track length threshold achieved with shape analysis with 1σ (dark teal) and 2σ (light teal) error bands for the 100 keV (A) and 60 keV (B) C ion samples.

(A) (B) (C)

FIGURE 5.19: 2D angular distribution obtained by the data (red) and the SRIM+Crystals simulation, with a track length threshold at 190 nm (blue) for the 100 keV (A), 60 keV (B), 30 keV (C) C ion sample. Chapter 5. Resonance effect of polarised light in NIT emulsions 111

Data Sample C100 [%] C60 [%] C30 [%] C10 [%] Microtracks 5.1 5.1 5.0 5.5 Npeaks 5.7 2.7 2.0 1.7 Isolated grains 89.2 92.2 93.0 92.8 Moving grains 42.6 37.1 29.4 20.3 Static grains 46.6 55.1 63.6 72.5

TABLE 5.3: Event fraction for each category of grains in the dataset.

5.6.1 Microtracks and Npeaks Microtracks and Npeaks in principle identify the same category of events since they are made of aligned grains. However, the former are longer and are reconstructed without the help of polarized light; the latter are shorter (≤ 350 nm) and can be identiﬁed only by the plasmon analysis. Although the npeaks fraction decrease as the energy of the Car- bon ion decreases, and the tracks are shorter, the fraction of mictrotracks is constant for all the samples. The track length versus the φ angle for micro-tracks and npeaks is reported in Fig. 5.20 for each sample. A clear peak is observed in the beam direction for all the samples horizontally exposed in the npeaks region, i.e. track length smaller than 350 nm; while for larger track length it is not observed any angular correlation. This result suggests that npeaks grains are linked to the same Carbon ion representing a fraction of signal-like event, while microtracks are related to different Carbon ions. Therefore, for these samples dominated by track lengths of few hundred nanomenter, micro-tracks fraction represents the level of chanche coincidence which is linked to the density of Carbon ion and to the fog level. The 2D angular distributions of npeaks, measured with the elliptical shape (blue dotted) and with plasmon (red line) are reported in Fig. 5.21 for each sample. The angular resolution is lower using plasmon information since the elliptical ﬁt is optimized for nanotracks and it is unstable for npeaks grains where the brightness peaks are completely separated.

5.6.2 Isolated grains Isolated grains represent the main fraction of the dataset (∼ 90%) for each sample since track length distributions are mainly formed by nano-tracks. Furthermore, larger is the Chapter 5. Resonance effect of polarised light in NIT emulsions 112

(A) (B)

FIGURE 5.20: Track length versus the φ angle of micro-tracks and npeaks grains for 100 keV (A), 60 keV (B), 30 keV (C) and 10 keV (D). Chapter 5. Resonance effect of polarised light in NIT emulsions 113

(A) (B)

FIGURE 5.21: 2D angular distribution of npeaks grains obtained by shape (blue) and plasmon (red) analysis for the 100 keV (A), 60 keV (B), 30 keV (C) and 10 keV (D). Chapter 5. Resonance effect of polarised light in NIT emulsions 114 energy of the Carbon ion beam, higher is the fraction of the moving grains showing the resonance effect of polarized light (see Tab. 5.3). The barycenter displacement is reported for each sample in Fig. 5.22. The 2D angular distribution obtained by the direction of the barycenter shift is reported for moving grains (red) and static grains (blue) in Fig. 5.23. Moving grains have a clear peak in the direction of the incoming Carbon ions, while static grains show a ﬂat angular distribution. In Fig. 5.24 the 2D angular distribution of moving grains is reported using both plasmon (red) and shape (blue) information. Shape analysis looks more precise in the directional reconstruction of moving grains, in particular in the case of 100 keV and 60 keV samples.

5.7 Efﬁciency and track length threshold with plasmon analysis

Npeaks and moving grains represent signal-like events identified by using the plasmon analysis and correspond to n-crystals grains in the SRIM+Crystals model. The efficiency of plasmon analysis epl can be therefore defined as follows:

Nnpeaks + Nmoving epl = (5.3) Ntot where Nnpeaks and Nmoving are the fraction of Npeaks and moving grains, respectively, and Ntot the total number of events in the dataset. The plasmon efficiency amounts to ∼ 48.3% for 100 keV, ∼ 39.8% for 60 keV and ∼ 31.4% for 30 keV samples. It is worth noting that for the 30 keV Carbon ion sample only the plasmon analysis contribute to n-crystal grains. Therefore, using this sample, it is possible to evaluate the track length threshold achieved with plasmon analysis by comparing the efficiency obtained by the data with the CDF obtained by the model. The estimation of the threshold with 1σ (dark teal) and 2σ (light teal) error bands is reported in Fig. 5.25. The track length threshold amounts to ∼ 120 nm. A comparison with higher energy samples can be performed bearing in mind the fact that the plasmon effect does not provide a significant barshift for all the elliptical clusters pop- ulating the n-crystals component. In Fig. 5.26 it is reported the 2D angular distribution for static grains as measured by the shape analysis. Static grains still show a directional peak in the case of 100 keV and 60 keV samples. Given that, it is crucial to recover the fraction lost with the cut on the barycenter displacement by taking into account the events in the gaussian peak. The estimated track length threshold amounts to ∼ 134 nm and ∼ 125 nm Chapter 5. Resonance effect of polarised light in NIT emulsions 115

(A) (B)

FIGURE 5.22: Distributions of the barycenter displacement for the 100 keV (A), 60 keV (B), 30 keV (C) and 10 keV (D). Chapter 5. Resonance effect of polarised light in NIT emulsions 116

(A) (B)

FIGURE 5.23: 2D angular distribution of moving grains (red) and static grains (blue) for the 100 keV (A), 60 keV (B), 30 keV (C) and 10 keV (D). Chapter 5. Resonance effect of polarised light in NIT emulsions 117

(A) (B)

FIGURE 5.24: 2D angular distribution of moving grains obtained by shape (blue) and plasmon (red) analysis for the 100 keV (A), 60 keV (B), 30 keV (C) and 10 keV (D). Chapter 5. Resonance effect of polarised light in NIT emulsions 118 for 100 keV and 60 keV C ion samples, respectively. The 1σ (dark teal) and 2σ (light teal) error bands are reported in Fig. 5.27: they are compatible with the result obtained for the 30 keV Carbon ion sample.

FIGURE 5.25: Track length threshold achieved with plasmon analysis with 1σ (dark teal) and 2σ (light teal) error bands for the 30 keV C ion sample.

5.8 Summary

The directional dark matter search with a solid target requires the use of detectors capable to reconstruct tracks of few hundred nanometers, as expected from WIMP-induced nuclear recoils. NIT emulsions with nanometric-scale crystals make it possible to detect an eventual WIMP signal by using new generation optical microscopes: the elliptical shape analysis allows to reach ∼ 185 nm threshold and the subsequent use of polarized light can further reduce the limit imposed by the optical resolution. The state-of-art threshold was measured by analysing NIT emulsion samples exposed to Carbon ion beams and containing a few hundred nanometers long tracks. The plasmon analysis allowed to achieve a 120 nm threshold in NIT samples made of ∼ 44 nm AgBr crystals. Improvements in the optical system are envisaged to further lower the threshold Chapter 5. Resonance effect of polarised light in NIT emulsions 119

(A) (B)

FIGURE 5.26: 2D angular distribution of static grains obtained by shape (blue) and plasmon (red) analysis for the 100 keV (A), 60 keV (B), 30 keV (C) and 10 keV (D). Chapter 5. Resonance effect of polarised light in NIT emulsions 120

(A) (B)

FIGURE 5.27: Track length threshold achieved by adding the plasmon analysis with 1σ (dark teal) and 2σ (light teal) error bands for the 100 keV (A) and 60 keV (B) C ion samples. Chapter 5. Resonance effect of polarised light in NIT emulsions 121 down to the physical limit imposed by the crystal dimension. In Fig. 5.28 the state-of-art threshold was used to construct the NEWSdm sensitivity curve, for the pilot experiment with an exposure of 10 kg per year assuming zero background: the black dotted-line represents the sensitivity region with 120 nm as threshold while the solid dark and light teal lines the 1σ and 2σ bands. It is worth noting that with mass detector of 10 kg and assuming a spin-indipendent interaction and the SHM for the local WIMP density, it is possible to cover a wide region of the DAMA/LIBRA signal by using a completely different approach.

FIGURE 5.28: Sensitivity curve of NEWSdm experiment assuming zero background and a track length threshold of 120 nm. 122

Chapter 6

Neutrino studies with NEWSdm detector

The new generation of direct dark matter detection experiments based on ultra-pure ton- scale detectors will soon reach the so called neutrino ﬂoor being sensitive to coherent elastic neutrino-nucleus scattering (CEνNS) [180]. Neutrinos of ∼ 10 MeV interacting coherently with target materials can produce recoils of O(10 keV) energies which are indistinguishable from WIMP-nucleus scattering events. Neutrinos are elusive particles capable of crossing the whole Earth without interacting; it is therefore impossible to build any shield from astrophysical sources. CEνNS is therefore considered an irreducible background unless the direction of neutrino-induced recoils is measured. On the other hand, the observation of CEνNS events represent a great scientiﬁc result since the only available measurement was performed by the COHERENT experiment with 6.7σ C.L. at Oak Ridge National Laboratory in 2017 [181]. CEνNS observation allows to extend our knowledge of neutrino properties within the Standard Model, but could also provide some constraints on the non-standard neutrino interactions (NSI), new NC medi- ators and neutrino magnetic moment [182]. From the astrophysical point of view, it gives the opportunity to measure neutrinos from the CNO cycle [183, 184] thus evaluating the solar metallicity [183], and it could provide a more complete picture of some phenomena like supernova neutrino emissions where neutral-current events are free from the uncertainties that currently affect the description of neutrino oscillations. This latter property is used to search for sterile neutrinos through the disappearance of neutral-current neutrinos which cannot be related to the standard oscillation [185]. Chapter 6. Neutrino studies with NEWSdm detector 123

In this framework, a directional detector as NEWSdm not only could give the unique possibility to overcome the neutrino ﬂoor but could also be an ideal detector for CEνNS. In this chapter, I will describe several neutrino studies performed using a detector based on NIT emulsions: (i) study of the neutrino ﬂoor for the NEWSdm experiment; (ii) observation of supernova neutrinos; (iii) studies of reactor and spallation neutron source (SNS) neutrinos.

6.1 Coherent elastic neutrino-nucleus scattering

Coherent elastic neutrino-nucleus scattering refers to a neutral-current neutrino interaction with an entire nucleus. The Feynmann diagram of this process, mediated by the Z0 boson, is reported in Fig. 6.1. The differential cross-section in the solid angle Ω can be

FIGURE 6.1: Feynman diagram of the CENNS process. written as [186]: dσ G2 Q2 = F W E2(1 + cos θ)F2(q) (6.1) dΩ (2π)2 4 ν 2 where GF the Fermi constant, Eν the neutrino energy, Qw the weak charge, θ the neutrino scattering angle and F(q) the form factor assuming the Helm’s model and depending from the momentum transfer q. The number of neutrinos interacting in a detector depends on the number of targets, the min energy threshold Ethr which constraints the minimum detectable neutrino energy Eν , Chapter 6. Neutrino studies with NEWSdm detector 124

the cross-section σ(E) and the energy spectrum dΦ/dEν of the incoming neutrinos:

dR M Z dσ dΦ = dEν (6.2) min dEν Amuma Eν dEr dEν where M is the detector mass, A is the atomic mass number, muma is the atomic mass unit. Altough the cross-section enhances heavier targets more than lighter ones (see Fig. 6.2), the kinematics makes lighter targets easier to detect since for equal momentum transfer the energy recoil of the nucleus is larger, as can be derived from the following relation:

q2 Er = (6.3) 2mN The dependence between the track length of neutrino-induced recoils and the neutrino energy for NIT emulsions is reported in Fig. 6.3. Only neutrinos with energies larger than 10 MeV are capable to produce tracks larger than 50 nm.

FIGURE 6.2: Energy dependent cross-section for CEνNS after integrating the differential cross-section (Eq. 6.1) over the solid angle. Chapter 6. Neutrino studies with NEWSdm detector 125

FIGURE 6.3: Dependence of the track length of neutrino-induced recoils from the neutrino energy.

6.2 Neutrino ﬂoor for the NEWSdm detector

The expression Neutrino Floor indicates a boundary in the WIMP mass cross-section plane below which an experiment is sensitive to the Solar, atmospheric, and diffuse supernovae neutrinos background. Since it depends on the target nuclei the detector is made of, the neutrino ﬂoor is peculiar for each experiment and it is constructed as follows:

1. for a given threshold, the number of neutrino-induced recoils above the threshold is evaluated;

2. the exposure is adjusted in such a way that the expected number of CEνNS events amounts to 1 for the considered threshold;

3. the upper limit at 90% C.L. on the WIMP-nucleus scattering cross- section as a function of the WIMP mass is evaluated for the exposure obtained in the step 2;

4. the neutrino ﬂoor represent the minimum of all the isocurves obtained with different thresholds. Chapter 6. Neutrino studies with NEWSdm detector 126

Given the neutrino energy spectra shown in Fig. 3.6, Ref. [171] reported the curve representing the neutrino ﬂoor for a Xe/Ge target (see Fig. 6.4).

FIGURE 6.4: The neutrino ﬂoor (orange-dotted) for a Xe/Ge target in the WIMP-mass cross-section plane.

A preliminary study of the neutrino floor for the NEWSdm case has been performed considering track length thresholds ranging from 30 nm to 900 nm. The exposure providing an expectation of 1 neutrino-induced event is reported in Tab. 6.1. A Xenon target has been studied in order to validate the reported estimations and the event rate obtained from ν(8B) has been compared with the event rate induced by a WIMP with a mass of 6 GeV. As shown in Fig. 6.5 and similarly with what reported in Ref. [146], the two spectra overlap thus showing why the CEνNS limit the WIMP discovery. The neutrino floor (black-dotted line) obtained for the NEWSdm targets is shown in Fig. 6.6, where colored lines represent the isocurves for different thresholds and the grey-filled area the neutrino floor as shown in Fig. 6.4. It is worth noting that the neutrino floor curve reported in Ref. [171] is evaluated using a Profile Likelihood test taking into account systematic uncertainties on neutrino fluxes. That curve represents the discovery limit reachable for a Xe/Ge detector: beyond that line systematic errors from high neutrino contaminations dominate. On the other hand, the neutrino floor for the NEWSdm detector refers to the so called Chapter 6. Neutrino studies with NEWSdm detector 127

Threshold [nm] Exposure [ton × yr] 30 0.8 40 2.3 50 5.3 60 16.8 70 57.4 80 140.5 90 308.3 100 391.1 200 531.1 300 604.9 400 675.9 500 756.0 600 845.3 700 944.7 800 1070.2 900 1213.0

TABLE 6.1: Ton per year exposure required in order to expect one neutrino- induced event for different track length thresholds.

8 FIGURE 6.5: Event rate induced by ν( B) (red) and Mχ = 6 GeV (blue) as a function of the recoil energy for a Xenon target. Chapter 6. Neutrino studies with NEWSdm detector 128

FIGURE 6.6: Neutrino floor (black-dotted line) for the NEWSdm detector. one-neutrino event line and represents the level where the neutrino background begin to be observable. The definition for the neutrino floor used in this work is therefore more stringent and largely explains the gap between the two curves. In addition we also underline that the curve obtained for the NEWSdm detector does not represent a final discovery limit. The long term goal of the experiment is indeed to overcome the neutrino floor through a statistical analysis of the direction of the events.

6.3 Supernova neutrinos with the NEWSdm detector

The explosion of a Supernova, due to the collapse of a star at the end of its life is one of the most energetic observable phenomena in the Universe. Neutrinos are powerful mes- sengers of a supernova explosion since they carry almost the total energy emitted by the source and are weakly interacting [187]. Therefore, they could directly explain the under- lying processes inside a star leading to the the violent explosion. The energy spectrum of emitted neutrinos can be parametrized by a quasi-thermal distribution [188] with the mean energies for each type of neutrinos provided by several models [189–191]. The total energy released by the supernova is the neutron star gravitational binding energy that is about 3 × 1053 erg [189, 190, 192] corresponding to ∼ 1057 emitted neutrinos. Since the Chapter 6. Neutrino studies with NEWSdm detector 129 main processes leading to the neutrino emission are mediated by neutral current interactions we can assume the energy equipartition for each neutrinos and antineutrinos, as predicted also by several simulations [188, 193, 194]. I have evaluated quantitatively and for the ﬁrst time the possibility of detecting and identifying coherent elastic neutrino nucleus scattering with NEWSdm detector exploiting directional information. The results here reported have been recently published in Ref. [195].

6.3.1 Supernova neutrino source Supernova neutrinos emission is a transient phenomenon whose detection does not depend on the exposure time. The assumed ﬂuence can be derived from the quasi-thermal parameterisation ﬁrstly proposed in Ref. [188]

α dF E E i e−Eν/Ti F ( ) = i = i ν = i Eν 2 α +2 with i νe, ν¯e, νµ, ν¯µ, ντ, ν¯τ (6.4) dEν 4πD i Ti Γ (αi + 2) where Γ(x) is the Euler gamma function and Ti is the temperature, linked to the mean energy (hEii) by the relation: Ti = hEii/(αi + 1). (6.5) The so-called pinching parameter α parametrises the deviation from the thermal Maxwell- Boltzmann distribution, reproduced by α = 2. In the calculations we have adopted the value αi = 2.5 and for the mean energies we have used the values proposed in Ref. [192]

hEνe i = 9.5 MeV, hEν¯e i = 12 MeV, hEνx i = 15.6 MeV (6.6) where the notation νx stands for one among the four non-electronic species. Assuming D = 8 kpc as a case of study, in Fig. 6.7a are reported the ﬂuences for each neutrino specie as a function of the above deﬁned parameters while Fig. 6.7b shows the total number of expected events summed over all the neutrino species as a function of the nucleus recoil energy threshold, for a ton of active mass. The elements considered are the constituents of NIT emulsions and are reported in different colors. Chapter 6. Neutrino studies with NEWSdm detector 130

(A) (B)

FIGURE 6.7: (A) Fluences for the three neutrino species as deﬁned in Eq. 6.4. (B) Total number of events (from Eq. 6.2) of supernova neutrino induced recoils per ton of active mass, as a function of the threshold on the recoiling nucleus energy.

6.3.2 Supernova neutrino signal According to Eqs. 6.2 and 6.4 the number of expected recoils induced by supernova neutrinos depends on the detector threshold, the exposed mass and the distance of the source from the Earth. The energy threshold corresponds to the minimum detectable track length in NIT emulsions and only energies corresponding to recoil track lengths equal or larger than 50 nm have been considered in this study. Given the ﬂuences in Eq. 6.4, the strong dependence on the inverse of the squared distance D is shown in Fig. 6.8 assuming a 50 nm threshold. In the galactic centre the density of stars is very high and a supernova explosion is more likely to occur; therefore a distance D = 8 kpc, which is the conventional value adopted for this type of calculation was assumed. From this assumption, the total number of expected events obtained for a detector made of NIT emulsions is 0.30 ton−1. The track length L of nuclear recoils induced by supernova neutrino scattering versus the transferred energy is reported in Fig. 6.9a for each target nucleus. In Fig. 6.9b is shown the track length distribution in NIT emulsions, normalized to the number of expected events in the [0.05, 1] µm range. The contribution of each element is weighted for the element mass fraction reported in Tab. 3.1. The scattering angle θsc is deﬁned as the angle between the incoming neutrino direction Chapter 6. Neutrino studies with NEWSdm detector 131

FIGURE 6.8: Number of expected events per ton of active mass as a function of the distance D of the supernova explosion.

(A) Track lengths (B) Number of events

FIGURE 6.9: (A) Track length versus transferred energy for the target nuclei of NIT emulsions. (B) Track length distribution in NIT emulsions of supernova neutrino induced recoils in the range [0.05, 1] µm. Chapter 6. Neutrino studies with NEWSdm detector 132 and that of the scattered nucleus. Its value can be obtained by the following relation: r Eν + M K cos θsc = , (6.7) Eν 2M √ where K is the transferred kinetic energy in the non-relativistic limit (|~vrec| = 2K/M). Assuming a supernova explosion from the direction of the Galactic Centre, the scattering angles of neutrino induced recoils are generated and the angular distributions of θe and φe derived as reported in ﬁgure 6.10a and 6.10b. More details about the reference system are reported in the Appendix A of the Ref. [195]. In this study it is assumed that the incom-

(A) θe distribution (B) φe distribution

FIGURE 6.10: Distributions of the emulsion angles θe (a) and φe (b) of supernova neutrino induced recoils in the NEWSdm detector. ing neutrino direction points to the Galactic Centre, since it is the region where the stellar mass density is higher and therefore there is a higher probability for a supernova explosion. The θe and φe angle distributions are peaked at zero and −π/2 rad, respectively, corresponding to the direction opposite to the Galactic Centre, since induced recoils are mostly diffused around the neutrino incoming direction. Chapter 6. Neutrino studies with NEWSdm detector 133

6.3.3 Background sources Assuming to make the external background negligible by employing an appropriate shielding, the background sources for the supernova neutrino study come from the radiogenic neutrons and solar neutrinos from 8B. As far as intrinsic background is concerned, ultra-low radioactivity materials are used in current ton-mass dark matter detectors. As a result of this effort the radiogenic neutrons are typically reduced down to the level of ∼ 1 neutron ton−1 yr−1. In this study we assume that NEWSdm will reach the same high-purity standards. The number of neutron- induced recoils with track lengths in the [0.05, 1] µm range amounts to ∼ 0.33 ton−1 yr−1, where fiducial volume effects have been accounted for. The energy spectrum of solar neutrinos from 8B extend up to ∼ 16 MeV as shown in figure 3.6. Note that the 8B solar neutrino flux has been measured by SNO with neutral SNO 6 −2 −1 currents [196] and the result ΦB = (5.25 ± 0.21) × 10 cm s is more precise than the theoretical predictions and it is independent upon neutrino oscillations. The direction of incoming neutrinos from 8B has been simulated using the projection of the Earth velocity around the Sun onto galactic axes [197]. The Earth revolution orbit is assumed to be circular. The Mollweide projection in a Galactic-like coordinate system of the induced recoils, assuming one ton per year exposure, is reported in figure 6.11 where the magenta line represents the revolution of the Earth around the Sun. The number of expected induced recoils with track lengths in the [0.05, 1] µm range amounts to ∼ 0.18 ton−1 yr−1. The observation of 8B neutrinos would be relevant as a control sample.

6.3.4 Results The potentiality of supernova neutrino observation was studied assuming a signal region ranging from 50 nm to 1 µm, for a detector mass of 30 ton and a distance D = 8 kpc. The corresponding number of expected events is:

N (ν|SN) = 9.0. (6.8)

On the other hand, the rate due to 8B neutrinos and background neutrons from intrinsic contamination (IC) for a 30 tons detector mass amounts to:

N(ν, 8B) = 5.4 yr−1; (6.9) N (n, IC) = 9.9 yr−1. (6.10) Chapter 6. Neutrino studies with NEWSdm detector 134

FIGURE 6.11: Mollweide projection in a Galactic-like coordinate system of the induced recoils from 8B solar neutrinos: the latitude corresponds to θe while the longitude to φe − π/2. The magenta line marks the neutrino arrival direction, i.e. from the Sun to the Earth.

A likelihood ratio test [169] was performed to discriminate the supernova neutrino signal from background sources: the null hypothesis H0 (background only) has been tested against the alternative hypothesis H1 (signal plus background). Three kinematical variables have been taken into account: track length L, θe and φe angles of the induced recoils. The PDFs of the three variables for supernova neutrinos, solar neutrinos from 8B and intrinsic neutrons are reported in Fig. 6.12. The significance of the test statistics for the signal plus background hypothesis (S+B) has been studied using the ROOFIT toolkit [198]. All the three above mentioned variables have been used in the Profile Likelihood function. Figure 6.13a shows the mean significance as a function of the exposure time assuming 30 ton detector mass and a distance D = 8 kpc. The median expectation for the supernova neutrino signal is represented by the blue dotted line with the green (68% CL) and yellow (95% CL) solid color regions. The shorter the exposure time the larger the significance of S+B hypothesis, since the background increases with the time while the supernova explosion is a transient event. An observation of supernova neutrinos with a confidence level larger than 3σ requires that the detector has been operated — i.e., that background events has been collected — for a time shorter than 4 years. In the assumption that the background will be a factor two (four) larger than the expected one we would obtain a 3σ significance for exposures shorter than 2 (1) years. Chapter 6. Neutrino studies with NEWSdm detector 135

(A) L (B) θe (C) φe

FIGURE 6.12: PDFs of recoiled nuclei, normalized to 1, induced by supernova neutrinos (blue), solar neutrinos from 8B (green) and radiogenic neutrons (red). The track length, θe and φe distributions are shown in panels (a), (b) and (c), respectively.

In addition to the signal observation, the directionality can be exploited to retrieve important information on the supernova. The likelihood ratio test can indeed be used to derive the distance of the supernova explosion which is proportional to the inverse square root of the number of observed signal events. One thousand of pseudo-experiments were simulated for different distances and a fit of maximum likelihood was used to extract the number of signal events (µs) and therefore the measured distance D after two years of detector operation. The residual between the measured and expected distance is reported in Fig. 6.14 with 68% and 95% C.L. intervals. The expected median is centered at zero and the measurement is more precise for shorter distances where the signal is expected to be larger. It is worth pointing out that this result does not take into account uncertainties about the total energy released by the supernova explosion. The capability of the NEWSdm detector to identify nuclear recoils induced by solar neutrinos from 8B has been also studied. Figure 6.13b shows the mean significance as a function of the exposure for 30 ton mass detector. The median expectation for solar neutrinos from 8B signal is represented by the blue dotted line with the green (68% CL) and yellow (95% CL) solid colour regions. The longer the exposure time the larger the significance of S+B hypothesis, since the signal-to-background ratio increases with time. After one year, an observation of the signal from 8B solar neutrinos can be achieved with a confidence level of 3σ. Chapter 6. Neutrino studies with NEWSdm detector 136

8 (A) SN signal (B) B neutrinos

FIGURE 6.13: Mean signiﬁcance as a function of the exposure time for a 30 ton mass detector (blue dotted line), for the supernova neutrino signal (a) and the 8B neutrinos (b)

FIGURE 6.14: Residuals between the measured and expected distance. Chapter 6. Neutrino studies with NEWSdm detector 137

6.4 Neutrinos from nuclear reactors

Nuclear fission reactors are the most intense source of low energy electron anti-neutrinos. They are emitted when an heavy fissile atomic nucleus as 235U or 239Pu splits into two or more lighter nuclei. Since high-Z elements have a large number of neutrons to contrast the Coulomb repulsion between protons into the nucleus, the products of the fission have instead an excess of neutrons thus being generally unstable and undergoing β−decays. Assuming the energy released to be ∼ 200 MeV per fission with 6 ν¯e produced along the β−decay chains of the daughter nuclei, one expects ∼ 2 × 1020 neutrinos emitted from a 1 GW reactor over the whole solid angle [199]. The typical neutrino energy spectrum for each fissile isotope is reported in Fig. 6.15. Since the maximum energy of neutrinos does

FIGURE 6.15: Neutrino spectrum for each isotope in nuclear reactors according to the Huber and Mueller parametrization [199]. not exceed 10 MeV, they cannot produce recoils with track length larger than 50 nm, as already showed in Fig. 6.3. Indeed, in Fig. 6.16a it is reported the track length distribution due to reactor neutrinos: in the 97% of cases the recoiled nucleus is a Carbon ion with a track length ranging from 25 to 45 nm. Nevertheless, a preliminary study was performed assuming that in the near future a track length threshold as low as 30 nm will be achieved. As a case of a short base-line experiment [200], the nominal ﬂux of 1019ν/s and a distance of 10 m between the reactor and the detector was used. The latter has to be as short as Chapter 6. Neutrino studies with NEWSdm detector 138 possible thus increasing the geometrical acceptance. The ratio between neutrinos hitting the detector and simulated ones (dispersion factor) was calculated using GEANT4. The rate per year of nuclear recoils induced by the electron anti-neutrinos (red circles) and the dispersion factor (black squares) are reported in Fig. 6.16b for different detector masses. If the exposed mass increases of a factor 102 the dispersion factor decreases of a factor 10 and the rate of neutrino-induced recoils per year is larger of a factor 103. Assuming an exposure of 1 ton yr 9230 signal events per year are expected to be observed.

(A) (B)

FIGURE 6.16: (A) Track length distribution in NIT emulsions of reactor neutrinos induced recoils. (B) Dispersion factor (black squares) and neutrino induced recoil rate (red circles) versus the NIT exposed mass.

6.5 Neutrinos from spallation neutron source

The Spallation Neutron Source (SNS) is an accelerator-based facility at Oak Ridge Na- tional Laboratory (ORNL) which provides an alternative way with respect to nuclear reactors to produce high-ﬂux neutron beams. The working principle is based on the production of neutrons from high energy proton beams (∼ 1 GeV) impinging on heavy metal target. Due to their interaction length, GeV scale protons interact directly with nucleons within Chapter 6. Neutrino studies with NEWSdm detector 139 the nucleus producing an intra-nuclear cascade. Some nucleons can escape from the nucleus thus giving rise to similar cascade processes in the neighbors nuclei. After the cascade, the excited nucleus returns to the ground state by evaporating low energy neutrons which are then moderated to thermal or epi-thermal velocities. The number of neutrons produced depends on the target geometry and material and on the incoming proton energy [201]. The SNS is safer than nuclear reactors since the released energy is lower than the one (O(GeV)) required to trigger the reaction of high-energy protons off target and ∼ 60% of initial proton energy is deposited in the target as heat. The SNS operates with a liquid mercury target surrounded by hydrogenous and helium moderators to thermalize the produced neutrons; 1 GeV protons are used to initiate the cascade. Not only neutrons are produced during the interactions but also π-mesons + quickly stopped inside the target. Stopped π decay in mono-energetic 30 MeV νµ which in turn decay producing a spectrum of νe and ν¯µ with energies up 52.6 MeV (see Fig. 6.17a); pions and muons with negative charge are instead quickly absorbed in the target [202]. The integrated neutrino ﬂux over all the three species is 4.3 × 107ν cm−2 s−1 at a distance of 20 m [181]. A preliminary study on the observation of neutrino-induced recoils was performed assuming an exposure of 10 kg yr. In Fig. 6.17b is reported the track length distribution of the recoiled nuclei in NIT emulsions: assuming a threshold of 100 nm 137 signal events per year are expected to be observed.

6.6 Conclusions on neutrino studies

A detector using nanometric nuclear emulsions is sensitive to the coherent elastic neutrino- nucleus scattering. Neutrino sources could represent an ultimate discovery limit, the neutrino floor, for many experiments unless they exploit the directional information. The neutrino floor expected for the NEWSdm experiment has been evaluated for the first time. The presence of light nuclei in NIT compound results in a higher sensitivity to neutrinos with respect to a Xe/Ge target. On the other hand, the observation of a signal due to neutrino neutral-current interactions is a challenging task. Assuming a track length threshold equal to 50 nm, a 30 ton detector with an exposure shorter than 4 years is able to detect supernova neutrino interactions with 3σ C.L. and measure the direction and the distance of the supernova explosion. So- lar neutrinos from ν(8B) can also be detected with 3σ C.L for exposures larger than one year. Chapter 6. Neutrino studies with NEWSdm detector 140

(A)

(B)

FIGURE 6.17: (A) Energy spectrum for prompt and delayed neutrinos at SNS. (B) Track length distribution in NIT emulsions of nuclear recoils induced by neutrinos from the spallation neutron source. An exposure of 10 kg yr it has been assumed.

Finally, a preliminary study was performed on neutrinos produced by reactors and spallation neutron source. The former can be observed only by lowering the track length threshold at least down to 30 nm and increasing the geometrical acceptance of the detector to the neutrino source. The latter is currently the most promising source for the neutrino observation since with ∼ 10 kg and ∼ 100 nm track threshold more than one hundred neutrino-induced recoils are expected. 141

Conclusions

NEWSdm is meant to be the first experiment with a solid target for directional dark matter searches: the use of a nuclear emulsion based detector, acting both as target and tracking device, would allow to extend dark matter searches beyond the neutrino floor and provide an unambiguous signature of the detection of Galactic dark matter. The novel emulsion technology, based on the use of nuclear emulsion with nanometric AgBr crystals (NIT), makes it possible to record the sub-micrometric tracks produced by the WIMP scattering off a target nucleus. The presence, in the emulsion components, of light and heavy nuclei results in an enhanced sensitivity to both light and heavy WIMP masses. The final signal confirmation is obtained with powerful optical microscope equipped with a light polarizer: exploiting the different response of non spherical grain clusters to different polarization angles, the unprecedented position accuracy less than 10 nm is obtained. My PhD work was focused on several tasks concerning different aspects of the NEWSdm experiment: chemical treatments and handling of nanometric nuclear emulsions, exposures of NIT films to α, β and γ-rays at LNGS underground facility, scanning of emulsion samples with the optical microscope at Napoli University. I performed simulation studies on background sources as environmental gamma and neutrons, radiogenic and cosmogenic neutrons, cosmic muons and electrons from 14C for the technical test of 10 g month planned in the beginning of 2019 and the pilot experiment of 10 kg yr. In the first case, I simulated the shield installed at LNGS and made of 40 cm of polyethylene and 10 cm of lead. The total rate of nuclear-induced recoils is expected to be less than 0.01. In the second case, I found that the best compromise to reduce the total rate of nuclear-induced recoils to about 1.4 is obtained by using a 100 cm thick polyethylene shield. A preliminary investigation of simulated events showed that OPERA-like emulsions interleaved with NIT films can be used as an active veto to reject ∼ 25% of nuclear recoils induced by muons interacting inside the detector. This results will be accounted for in the Technical Design Report. Conclusions 142

I developed new analysis tools to exploit the resonance effect of polarized light occurring on nanometric metallic grains and a simulation of the AgBr crystals dispersed in NIT emulsions for a comparison with the data from samples exposed to Carbon ion beams. I have evaluated that the track length threshold achieved with the optical microscope using the shape analysis amounts to ∼ 190 nm while the gain introduced by the plasmon analysis makes it possible to further reduce the threshold down to ∼ 120 nm. I performed neutrino simulation studies with nanometric nuclear emulsions exploring the possibility to observe coherent elastic neutrino-nucleus scattering. The observation of neutrinos from a supernova exploded at 8 kpc can be obtained assuming both an hypothetical threshold at 50 nm and 30 ton detector with a 3σ of confidence level if the explosion occurs within four year exposure, while recoils induced by 8B solar neutrinos after one year exposure. I performed also preliminary studies on neutrinos from reactors and neutron spallation source: the former source can be detected only achieving a threshold at 30 nm; the latter is very promising since more than one hundred events can be observed with an exposure of 10 kg yr and a track length threshold at 100 nm. Finally, I performed the first estimation of the neutrino floor for the NEWSdm experiment. 143

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