Search for milli-charged particles with the DAMIC experiment

INSTITUTO DE FÍSICA

Search for milli-charged particles with the DAMIC experiment

Victor Barreto Braga Mello

Tese de Doutorado apresentada ao Programa de Pós- Graduação em Física do Instituto de Física da Univer- sidade Federal do Rio de Janeiro - UFRJ, como parte dos requisitos necessários à obtenção do título de Doutor em Ciências (Física).

Orientador:

Rio de Janeiro Junho de 2019

B524s Barreto Braga Mello, Victor

Search for milli-charged particles with the DAMIC exper- iment / Victor Barreto Braga Mello. Rio de Janeiro, 2019.

xxii, 134 f.

Orientador: João Ramos Torres de Mello Neto.

Tese (doutorado) - Universidade Federal do Rio de Janeiro, Instituto de Física, Programa de Pós Graduação em Física, 2019

1. Introduction. 2. Search for mCPs. 3. The DAMIC experiment. 4. Monitoring DAMIC data acquisition parameters. 5.

Search for cosmogenic mCPs with the DAMIC experiment. I. Ramos Torres de Mello Neto, João, orient. II. Título.

Resumo

Procura por partículas de carga fracionária com o experimento DAMIC

Victor Barreto Braga Mello

Orientador: João Ramos Torres de Mello Neto

Resumo da Tese de Doutorado apresentada ao Programa de Pós-Graduação em Física do Instituto de Física da Universidade Federal do Rio de Janeiro - UFRJ, como parte dos requisitos necessários à obtenção do título de Doutor em Ciências (Física).

Palavras-chave: Partículas de carga fracionária, quantização da carga elétrica, matéria escura.

O experimento DAMIC (Dark matter in CCDs) utiliza dispositivos de carga acoplada (CCDs) especializados feitos de silício para detectar a colisão elástica coerente entre WIMPs, candidatos altamente motivados para serem a matéria escura no Universo, e os núcleos de silício. Sendo um detector de baixo ruído eletrônico, sensível à pequenas de- posições de energia, o DAMIC também pode ser utilizado para procurar partículas livres carregadas com uma fração f da carga elementare. Essas partículas, muitas vezes referi- das na literatura como mCPs, são previstas por algumas extensões do Modelo Padrão e estão relacionadas com o problema da quantização de carga. Embora seja bem estabele- cido experimentalmente que todas as partículas elementares observadas têm uma carga elétrica como um múltiplo inteiro do d-quark, este fato permanece inexplicado pelo Mod- elo Padrão. Desde o experimento da gota de óleo de Milikan, o qual trouxe a primeira evidência de que as cargas elétricas na Natureza se apresentam em unidades discretas, muitos outros renaram a medida original de Milikan da carga unitária e procuraram

por partículas livres que violassem essa quantização. Nesta tese, realizamos uma busca por partículas de carga fracionária com o experimento DAMIC. Estabelecemos um limite no uxo cosmogênico dessas partículas exóticas no sítio do experimento competitivo com outros experimentos para partículas com 1/f dentro do intervalo [6-26] e limites mais rigorosos para partículas com carga mais baixa 1/f > 26, sondando um novo espaço de parâmetro para1/f <1000. No contexto da busca por matéria escura, apresentamos dois resultados. O primeiro é o monitoramento dos parâmetros de operação do detector para o experimento durante a última aquisição de dados. A segunda é a simulação do fundo radioativo esperado para a próxima geração do experimento, o chamado DAMIC-M, ex- plorando possíveis projetos para a construção do experimento de acordo com o nível de radioatividade de fundo requerido.

Abstract

Search for milli-charged particles with the DAMIC experiment

Victor Barreto Braga Mello

Orientador: João Ramos Torres de Mello Neto

Abstract da Tese de Doutorado apresentada ao Programa de Pós-Graduação em Física do Instituto de Física da Universidade Federal do Rio de Janeiro - UFRJ, como parte dos requisitos necessários à obtenção do título de Doutor em Ciências (Física).

Keywords: Milli-charged particles, electric charge quantization, dark matter.

The DAMIC (dark matter in CCDs) experiment employs the bulk silicon of scientic- grade charge-coupled devices (CCDs) to detect coherent elastic scattering of weakly inter- acting massive particles (WIMPs), highly motivated candidates for being the dark matter in the Universe. As a low noise detector, sensitive to low energy depositions, it is also adequate to search for free charged particles with a fraction f of the elementary charge e. These particles, often referred in the literature to as milli- or minicharged particles (mCPs), are predicted by some extensions of the Standard Model and related with the charge quantization problem. Although it is well established experimentally that all ele- mentary particles observed has an electric charge as an integer multiple of the d-quark, this fact remains unexplained within the Standard Model. Since the historical Milikan's oil drop experiment brought the rst evidence that electric charges in Nature come in discrete units e, numerous experiments not only have rened Milikan's original determi- nation of the unit charge but also searched for free particles violating this quantization.

In this thesis, we perform a search for millicharged particles with the DAMIC experiment.

We set a limit on the cosmogenic ux of these exotic particles at the experiment site that is competitive with other experiments for particles with 1/f inside the range [6-26] and are the most stringent for lowest charged particles with 1/f >26, probing a new parameter space for 1/f < 1000. In the context of the Dark Matter search we present two results.

The rst is the monitoring of the detector operation parameters for the experiment dur- ing the last science data acquisition run. The second is the simulation of the expected radioactive background on the upgraded version of the experiment, DAMIC-M, exploring possible designs for the construction of the experiment according to our background level requirement.

Agradecimentos

Essa tese é dedicada ao meu avô Wilton de Mello, um exemplo de vida e trabalho que espero seguir. Apesar de não haver palavras para agradecê-lo, tento deixar aqui meu muito obrigado por todos os anos. Igualmente essenciais para mim, exemplos de vida, cuidado e trabalho, deixo meu agradecimento as minhas avós Ilza, Maria da Conceição e Orminda. Aos meus pais Alexandre e Analú, meu agradecimento por todo apoio ao longo desses 10 anos de formação. Nada disso teria sido possível sem vocês, meu exemplo de amor e família.

À minha enorme família composta por tantos membros que ca quase impossível citar nominalmente todos. Pelos risos, festas, viagens, almoços e por principalmente mostrarem a importânica de termos uns aos outro: Vinícius, Andrea, Cláudio, Rafael, Bianca, Vi- viane, George, Lisa, Fabíola, Claudinho, João Paulo, Bianquinha, Guto, Rodolfo, Rafael, Laís e muitos outros (primos e apendiculares somam muito nessa mistura). Aos meus amigos (facilmente alocados no grupo família), sejam os de infância ou graduação ou de vida, só com vocês pra essa loucura de fazer física se tornar algo possível. Gustavo, Bruno, Pedro, Alessandro e Ranieri, muito obrigado.

À uma pessoa muito especial, uma amiga sem igual nesses últimos 3 anos de doutorado.

Minha companhia nas caronas, nas horas felizes (algumas um pouco difíceis), nos docinhos, nas comidas, nas semanas de afastamento e muito essencial na escrita dessa tese. Nunca imaginei minha vida sem você ao meu lado. Ao meu último romance, Tarcilla.

Finalmente, a meu orientador João Torres pelos quase 10 anos de trabalho juntos.

Muito obrigado por me acompanhar ao longo da minha formação. Deixo também, meu agradecimento ao grupo de pesquisa composto por Clara, Diego e Xiaohao, que trabalhou em conjunto nessa linha de pesquisa.

Agradecimento especial a agência de fomento Capes pelo suporte nanceiro que tornou possível essa pesquisa.

Contents

Sumário ix

Lista de Figuras xii

Lista de Tabelas xxii

1 Introduction 1

2 Search for mCPs 7

2.1 Extensions to the Standard Model including mCPs . . . 7

2.1.1 Models with an Extra U(1) hidden symmetry . . . 8

2.1.2 Models with a massive milli-charged fermion . . . 9

2.2 Physical constraints in the mCP mass/charge . . . 11

2.3 Search for violation of the charge quantization principle . . . 18

2.3.1 Millikan Oil Drop Method . . . 18

2.3.2 Accelerators and colliders . . . 19

2.3.3 QED precision measurements . . . 21

2.4 Search for cosmogenic mCPs . . . 22

3 The DAMIC Experiment 26 3.1 Evidences for Dark Matter . . . 26

3.2 Search for Dark Matter . . . 32

3.3 Charge Coupled Devices . . . 36

3.4 Dark Matter in CCDs . . . 44

3.5 DAMIC-M . . . 49

4 Monitoring DAMIC data acquisition parameters 54 4.1 DAMIC Monitoring Shifts . . . 54

4.2 Processing raw images . . . 57

4.3 Measurement of the charge transfer ineciency . . . 62

4.4 Measurement of the dark current . . . 65

5 Search for cosmogenic mCPs with the DAMIC Experiment 69 5.1 Methodology to search for mCP candidates in CCDs . . . 70

5.2 The mCP interaction with matter . . . 71

5.3 Simulation of the mCP track . . . 74

5.3.1 Energy deposition Monte Carlo . . . 74

5.3.2 Diusion code . . . 77

5.4 Data analysis . . . 81

5.4.1 The interaction probability P_ccd and detection eciency . . . 82

5.4.2 Geometric factor . . . 85

5.4.3 Event selection . . . 87

5.4.4 Analysis . . . 91

6 Future and conclusions 98 References 102 A Monitoring analysis gures 113 A.1 Measurement of the charge transfer ineciency . . . 113

A.2 Leakage current as function of the temperature . . . 114

A.3 DAMIC CCD calibration constant . . . 123

B The Photo Absorption Ionization model 124

C Condence interval for the mean Poisson variable 131

List of Figures

1.1 Summary of constraints on fermionic MCPs in the mass/charge plane. The results are divided in models including a massless hidden photon (left) and models without (right). The bounds were derived using CMB, BBN and astrophysical objects (HB, WD, RG stars and supernova 1987A) data, col- lider search at SLAC, LHC and LEP, observation of the positronium decay, Milikan oil drop experiments in bulk matter and meteoritic materials, pro- duction at reactor neutrinos experiments. Figure taken from [6]. . . 3 1.2 Limits at 90% of condence level on the mCP ux at the detector site

derived from Majorana Demonstrator MACRO, Kamiokande-II, LSD, and CDMS data. Figure taken from [35]. . . 4

2.1 Comoving number density evolution as a function of the ratio mass tem- perature ratio m/T in the context of the thermal freeze-out. The size of the annihilation cross section determines the relic abundance. . . 16 2.2 The mCP production cross-section at the LHC simulated assuming a hid-

den sector scenario for processpp→ψ⁺ψ⁻+X as a function of the mCP mass. The total cross section is obtained using Drell-Yan process. Figure taken from [60]. . . 21 2.3 The expected sensitivity for a new search for mCPs propose to be carried

out in LHC. It is sensitive to exploit an unexplored part of the parameter space that is also important for the cosmogenic search. Figure taken from [60]. 22

3.1 Rotation velocity for Andromeda's Galaxy observed by Vera Rubin (black dots). The solid lines represent the expected rotation velocity for dierent spiral galaxy models (Courtesy of the collaborator C. Watanabe). A model of the spiral galaxy only containing luminous matter and the standard gravitation law are not sucient to explain the data. In this framework, the agreement between theory and data is only possible when a halo of invisible matter is added into the system. . . 28

3.2 The bullet cluster event showing the spatial dierence between the bulk of baryonic matter and the bulk of gravitational matter. On top of the optical map of the sky, the X-Rays emitted from the baryonic matter interaction is presented in red. In Blue is the gravitational matter measured using weak lensing technique. Credit: X-ray: NASA/CXC/CfA/ M. Markevitch et al.;

Lensing Map and Optical: NASA/STScI; ESO WFI; Magellan/U.Arizona/

D.Clowe et al. . . 29

3.3 Top: CMB power spectrum measured by the Planck Collaboration and the best t found for the ΛCDM model with the residuals [76]. Bottom:

CMB power spectrum for dierent universe fractional contents taken from [75] showing that this observable is sensitive to changes in the universe composition. . . 31

3.4 Diagram for the three possible interactions between a dark matter particle and SM particles, each observed by distinct experimental approaches. The arrow shows the direction of the interaction. . . 33

3.5 Compilation of WIMP-nucleon spin-independent cross section limits (solid curves) and hints for WIMP signals (shaded closed contours) obtained by dierent experiments. The projected sensitivity for upgraded versions of some experiments are represented by dotted lines. The orange line is called the neutrino oor, a limit for which the experiments will be also sensitive to neutrino coherent scattering, an interaction with signature identical to the one expected for dark matter. Figure taken from [94] . . . 37 3.6 Left: Sketch of a silicon MOS capacitor, the basic unit of a CCD. Applying

a negative bias voltage, drives the electrons way from the Si-SiO2 interface and create a depletion region which acts as a capacitor. Right: The three phase conguration and the voltage manipulation scheme responsible to transfer charge collected at the potential well from MOS capacitor to MOS capacitor and, ultimately, pixel to pixel. . . 39 3.7 Time diagram of a three-phase device. The clock square waveform is shifted

between the phases (1→ 2,2 →3 and 3 →1 of the next pixel) by 1/3 of the period necessary to transfer charge from one pixel to another. . . 39 3.8 CCD structure for the charge transfer mechanism. The physical delimi-

tation of a pixel is done by the channel stop potential barrier and clock electrodes. . . 40 3.9 Absorption length in silicon as function of the incident photon wavelength.

For wavelengths below 500 nm, the absorption length is less than a micron meaning that the photon is immediately absorbed on the material's surface.

Above 900 nm, silicon becomes increasingly transparent to the photon.

Figure taken from [97] . . . 41 3.10 Schematic of a CCD readout node, with the sequence of voltage levels used

for the Correlated Double Sampling technique. . . 43 3.11 Overview of the DAMIC components. . . 46

3.12 Schematics of the lateral diusion (σ_xy) of the collected charge on the pixel array as function of the depth of the interaction. . . 47 3.13 Track identication in DAMIC CCD. The image were taken at sea level. . 47 3.14 Dark matter search performed with a 0.6 kg d exposure of the DAMIC

experiment at the SNOLAB underground laboratory inserted in the current experimental knowledge. . . 48 3.15 Exclusion plot for the hidden-photon kinetic mixing κ as a function of

hidden photon mass derived by the DAMIC experiment. . . 49 3.16 Schematics for the skipper CCD readout system using the oating gate for

non-destructive measurement. H1, H2 and H3 are the horizontal register clock phases as one has in regular CCD . . . 50 3.17 Skipper CCD operating in a single-electron counting regime. Figure taken

from [102] . . . 51 3.18 Top: Skipper CCD image with events coming from the Kapton cable for

a week of operation. Bottom: the corresponding energy spectrum of these events. The concentration of events on the sides of the CCD is an important information to improve the design and reduce the background level. . . 52 4.1 Status of the data acquisition at DAMIC monitoring online platform. In

the color code green is used when the detector is accumulating data, blue for the reading process (appears as thin lines), dark brown to report a crash in the system in which no data are being received, red when the system is not responding to the software and yellow when the system behaves erratically. 55 4.2 Temperature and pressure as function of time displayed at the online plat-

form. On the left side of the plot there is a problematic situation with a sudden increase in the temperature and pressure. On the right side, one can observe the system regular functioning. . . 56

4.3 Monitoring of the radon concentration at DAMIC experiment. In this example, one can see a period with high radon level. The purging system dewar was out of nitrogen at that time. At normal conditions, the DAMIC experiment runs with a radon concentration below 3.0 mBq/m³. . . 57 4.4 DAMIC raw image taken in 1×1 mode with the overscan region and the

real image region identied. . . 58 4.5 Example of a charge histogram of the overscan region taken from DAMIC

CCD. The mean and and standard deviation are a measure of the amplier baseline and noise, respectively. . . 59 4.6 DAMIC raw image taken in 1×100with symmetric patterns on both sides

due to correlated noise. . . 60 4.7 The eect of CTI on the charge packet originally stored by the potential

well. Devices that sizes larger than1k×1k must present CTI values below

<0.00001 in order to function properly. . . 62 4.8 Mean charge in a row as function of the row number. By tting a line, one

obtains the CTI value. Columns closer to the sense node are less aected by the CTI. . . 64 4.9 CTI values for each CCD extension obtained by combining all 343 images.

The values are compatible with the one expected from fabrication. The use of a large number of images reduces the statistical uctuations. . . 64 4.10 CTI values for each CCD extension obtained in each run. The values are

compatible among them and with the one expected from fabrication. Less images increases the statistical uctuations. . . 65 4.11 The mean charge in the row as function of the row number. The dier-

ence between the charge in the image section and the overscan region, is proportional to the leakage current level . . . 67

4.12 All CCD extension leakage current level as function of the temperature.

The linear relation over the temperatures indicates or no extra contribution to the dark current, or at least some irreducible constant contribution.

Extrapolating this line, one may reach the 10⁻³e⁻/d/pixel dark current level from [100] at temperature about 120 K. For temperature of 140K, extension 4 and 12 present higher leakage current level, indicating they are experiencing some extra contribution to the dark current that should be studied. . . 68

5.1 mCP-electron cross section calculated with PAI model considering a inci- dent particle with f = 1 (muon) and βγ = 4interacting with silicon. The peaks are due to the interaction with the atomic shells. . . 73 5.2 Probability and cumulative density function for a energy deposition in a sin-

gle interaction. The application of the transformation method is straight- forward as one can invert the cdf directly. . . 77 5.3 Validation of the mCP simulation. Comparison between the passage of a

muon through the CCD using the developed code and the GEANT4 toolkit showing good agreement in the energy deposition. . . 78 5.4 The mean free path for a mCP inside the silicon calculated via equation

5.13. For some charge fractions, the free mean path is larger than the CCD thickness. . . 79 5.5 An example of a mCP track obtained by our modied clustering algorithm. 80 5.6 The pdf P_k(E;f) for a energy depositionE afterk collisions calculated by

the convolution of the single collision pdf P(E;f). . . 83 5.7 Detection eciency obtained by Monte Carlo. . . 84 5.8 Detection eciency obtained by Monte Carlo. . . 85

5.9 The detection eciency as function of the zenithal angleθ. After a critical value, one for each mCP charge fraction, the eect of the track fragmenta- tion starts to become apparent. . . 86 5.10 Percentual ux of mCP with cosmogenic origin, cosθ² distribution, above

some zenithal angle. . . 87 5.11 Impact of the fragmentation of inclined tracks at the analysis. The dif-

ference in the nal result of the integral in equation 5.4 between the case with the eciency calculated with no fragmented tracks and the eciency including this problem. . . 88 5.12 Illustration of the procedure to calculate the geometric factor. In order to

take advantage of the stacked conguration we should correlate the signal over the CCD (see section 5.4.3). . . 88 5.13 The geometric factor calculated for 3 CCDs following the DAMIC appara-

tus conguration. The left plot shows this function dependence on (θ, φ) angles. The CCD squared geometry reects on the peak structures ob- served on multiples of 45^◦ angles. The right plot shows f_geo(θ) for which the φ dependence is removed by integration. . . 89 5.14 χ² distribution considering an analysis with 4 CCDs. The critical value of

χ²_cut=−3.17was chosen to provide the highest purity for the analysis. The mCP detection eciency is set in 99.994% while having 99.9947% purity in the mCP sample. . . 90 5.15 χ² distribution considering an analysis with 6 CCDs. The critical value

of χ²_cut = −3.35 is chosen to give the highest purity. The mCP detection eciency is set in 99.999% while having no background contamination. . . 91 5.16 Event selection based on the energy deposition for a 4 and 6 CCD analysis.

The purity is computed for each cut proposed as function of the charge fraction f. . . 92

5.17 The background contamination as function of the energy consistency selec- tion criteria. . . 93 5.18 DAMIC sensitivity for a mCP search with τ = 176.7 days of exposure

considering an hypothetical 6 CCD data set. The black curve refers to the rst approach using a theoretical calculation of the interaction probability while the gray curve represents the analysis fully based on Monte Carlo.

The two approaches are compatible showing a sensitivity to a ux above 8 × 10⁻⁹events/s. sr. cm²compatible with CDMS experiment for charge fraction 1/f ≤10. . . 94 5.19 Detection eciency considering a 6 CCDs data analysis and requiring signal

in at least 4 CCD. The result is compared with the case which a signal is required in all CCDs. . . 95 5.20 The DAMIC experiment sensitivity considering that at least 4 CCDs inter-

acts with a mCP obtained by this analysis in comparison with CDMS and MAJORANA constraints. DAMIC shows a sensitivity comparable with CDMS experiment, mainly because of the experiment spatial and energy resolution. Limits from MAJORANA demonstrator are the most stringent ones due to its high active mass and also low energy resolution. . . 96 5.21 Analysis of the DAMIC data set taken between February and November

2017, correspondent to τ = 176.7 live days, searching for mCP candidates.

The χ² and σ_E for the data entire data set together with the cut values established. No mCP candidate was found, conrming the background-only hypothesis. . . 96 5.22 Limits on the cosmogenic mCP ux at the Snolab site placed by the DAMIC

experiment. Limits from previous experiments, CDMS [34] and Majorana demonstrator [35], are presented together for comparison. . . 97

6.1 Dierence between the CCD when the cryocooler is turned on during the readout (left side of the plot) and when it is kept on (right side of the plot).

The increase of the noise is evident when changing this settings. . . 99

A.1 Measurement of the CTI for CCD EXT 1,2 and 3. . . 113

A.2 Measurement of the CTI for CCD EXT 4, 6, 11 and 12. . . 114

A.3 Leakage current in DAMIC CCD for EXT 1 and 2. . . 114

A.4 Leakage current in DAMIC CCD for EXT 3, 4 and 6. . . 115

A.5 Leakage current in DAMIC CCD for EXT 11 and 12. . . 115

A.6 Leakage current in DAMIC CCD for EXT 1, 2 and 3. . . 116

A.7 Leakage current in DAMIC CCD for EXT 4 and 6. . . 116

A.8 Leakage current in DAMIC CCD for EXT 11 and 12. . . 117

A.9 Leakage current in DAMIC CCD for EXT 1, 2 and 3. . . 117

A.10 Leakage current in DAMIC CCD for EXT 4 and 6. . . 118

A.11 Leakage current in DAMIC CCD for EXT 11 and 12. . . 118

A.12 Leakage current in DAMIC CCD for EXT 1, 2 and 3. . . 119

A.13 Leakage current in DAMIC CCD for EXT 4 and 6. . . 119

A.14 Leakage current in DAMIC CCD for EXT 11 and 12. . . 120

A.15 Leakage current in DAMIC CCD for EXT 1, 2 and 3. . . 120

A.16 Leakage current in DAMIC CCD for EXT 4 and 6. . . 121

A.17 Leakage current in DAMIC CCD for EXT 11 and 12. . . 121

A.18 Leakage current in DAMIC CCD for EXT 1, 2 and 3. . . 122

A.19 Leakage current in DAMIC CCD for EXT 4 and 6. . . 122

A.20 Leakage current in DAMIC CCD for EXT 11 and 12. . . 123

B.1 An schematic view of the passage of a particle with electrical chargeq and velocity βc~ in a straight line trajectory through a non-magnetic dielectric material with no net charge. The vector~r label any point P in space such that~r=βct~ is the electrical charge position, source of the elds, in a given time t. . . 124

List of Tables

5.1 Condence belt, at 90% condence level, for a Poissonian variable. . . 82 A.1 Calibration constant for each CCD. . . 123

Chapter 1 Introduction

The electric charge quantization is a fundamental open problem in particle physics arised from the historical Milikan's oil drop experiment in 1909 [1]. This rst evidence that electric charges in Nature come in discrete units e inspired numerous experiments not only to rene Milikan's original determination of the unit charge but also to search for free particles violating this quantization. Within the development of particle physics, the quark model proposed by Gell-Mann and Zweig [2, 3] modied the original charge quantization statement to its modern meaning: all elementary particles observed have an electric charge as an integer multiple of the d-quark. As quarks are conned in color- neutral baryons and mesons that carry integer electric charges, free charge in nature comes in discrete unitse.

No mechanism included in the Standard Model (SM) framework ensures electric charge quantization. In fact, it can be demonstrated that charge may be dequantized in the SM with massless neutrinos and three lepton generations [4], as the SM Lagrangian contains anomaly free global symmetries independent of the standard hypercharge Y. However, as described by Dirac in his seminal work [5], the existence of magnetic monopoles would explain the observed electric charge quantization in a way consistent with the quantum electrodynamics. This solution to the problem motivated an extensive research eld ded- icated to the observation of this new particle. The lack of experimental evidence for monopoles opened the possibility of encountering exotic particles with fractional electro- magnetic charge.

These hypothetical particles which vilolate the charge quantization principle are often referred in the literature to as milli- or minicharged particles (mCPs), fractionally charged particles (FCPs) and lightly ionizing particles (LIPs). The direct observation of a mCP is an undisputed signature of a beyond the Standard Model phenomenon. Unbound quarks, bound states of quarks with noninteger charge or even new leptons are only a few possible mCPs predicted by a great variety of theories. For example, a SU(2)L singlet can always be added to the SM Lagrangian, postulating in this way a new particle with an arbitrary small charge [6]. A hidden sector scenario (new interactions decoupled from the SM particles) with a local unbroken gauge group U(1)h added to the SM groups naturally, includes mCPs [7]. In these theories, the SM photon and the hidden photon has a kinect mixing so that a particle charged under the U(1)h appears to have a small coupling to the photon. Also, as there are four anomaly-free U(1) symmetries in the SM, the hypercharge operator can be redened to give a fractional electric charge _i to the neutrinos without making the theory anomalous [8].

This great diversity of extensions to the Standard Model have been exploited experi- mentally over the years. First, the addition of new exotic particles to the Standard Model can drastically alter well studied physical process depending on the particle's properties.

As a consequence, possible mCP mass and charge should be constrained by the known physics. From the astrophysical point of view, limits on the mCP mass/charge parameter space have been set from red giants (RG) [812], horizontal-branch (HB) [814] stars, white dwarf (WD) [8, 1518], and supernova (SN) 1987A [8, 19, 20] data. For the sun in particular, sound speed proles and neutrino ux data are used to constraint mCP param- eter space [6]. Cosmologically, the existence of a mCP would have an impact at the Early Universe modifying the element abundance predicted by the Big Bang Nucleosinthesis (BBN) theory and the observed Cosmic Microwave Background (CMB) [6,10]. To probe the mass/charge parameter space outside these restrictions, dierent experimental tech- niques were designed. For example, direct production and observation at xed target experiments or colliders [8, 2124], detection of some relic abundance in bulk matter [25]

or in meteoritic materials [26] using modern Milikan oil drop experiments, search for excess of ν−e scattering events at reactor neutrino experiments [27], observation of in- visible ortho-positronium decay [28] and measurement of deviation on the expected Lamb shift [21,29,30] or magnetic moment of the electron [29]. The non observation of a mCP canditate provides more constraints on this particle characteristics. The summary of the observed constraints on fermionic mCPs revised in [6] is presented in gure 1.1.

Figure 1.1: Summary of constraints on fermionic MCPs in the mass/charge plane. The results are divided in models including a massless hidden photon (left) and models without (right). The bounds were derived using CMB, BBN and astrophysical objects (HB, WD, RG stars and supernova 1987A) data, collider search at SLAC, LHC and LEP, observation of the positronium decay, Milikan oil drop experiments in bulk matter and meteoritic materials, production at reactor neutrinos experiments. Figure taken from [6].

As depicted in gure 1.1, there is a signicant part of parameter space allowed for particles characterized by low charge fraction and mass larger than the electron mass. An important channel to directly exploit this region is the cosmogenic search. The interaction between high energy cosmic rays and nuclei in the atmosphere could produce mCPs in the same way they would be produced in accelerators. These particles are expected to have a low energy deposition in matter, proportional to the square of their charges, and a straight line trajectory. With this behavior, it is possible for the mCP to reach

a very specic class of detectors already built underground for science programs that require low natural radiation levels. Using this approach, stringent limits were placed on the mCP ux at the detectors site, including MACRO (Monopole, Astrophysics, Cosmic Ray Observatory) [31], Kamiokande-II [32], and LSD (Liquid Scintillation Detector) [33]

results for particles with charge fraction0.4<1/f <6, the Cryogenic Dark Matter Search (CDMS) experiment [34] in the range with 1/f < 200 and the Majorana Demonstrator for1/f <1000 [35]. The combination of these results found in [35] is shown in gure 1.2.

Figure 1.2: Limits at 90%of condence level on the mCP ux at the detector site derived from Majorana Demonstrator MACRO, Kamiokande-II, LSD, and CDMS data. Figure taken from [35].

The aim of this work is to search for cosmogenic mCPs with data obtained by the Dark Matter in CCDs (DAMIC) experiment [3639]. The existence of dark matter is well established by a variety of observational evidence [4042]. From astrophysical to cosmological scales, there is a discrepancy between the observed universe and the one expected when considering it contains only SM particles. Beside the regular barionic matter, the universe must have a non-luminous cold component interacting gravitationally.

This component, whose nature is still unknown and the subject of many investigations, is called cold dark matter. Hypothesized to be a new particle, there is a great eort to directly detect a dark matter particle. These direct detection experiments search for the scattering signal of a dark matter particle naturally present in our galaxy. They are installed deep underground to reduce the high level of radioactivity produced by cosmic rays and shielded against the natural radioactivity from the surrounding rock. In this context, the DAMIC experiment employs the bulk silicon of scientic-grade charge- coupled devices (CCDs) to detect coherent elastic scattering of weakly interacting massive particles (WIMPs). WIMPs are highly motivated candidates for being the dark matter in the Universe. As silicon is a relatively light element, DAMIC is optimized to search for low mass WIMPs, operating with low noise and at eV scale energy threshold.

This PhD thesis presents the limits on the ux of cosmogenic mCPs derived from DAMIC data. It shows that not only the DAMIC apparatus is adequate to search for free mCPs, being competitive with previous limits (see gure 1.2), but also it is capable of excluding new parameter space due to its unique energy resolution. In parallel to this main analysis, it also presents two results in the context of the dark matter search. First, the monitoring of the detector operation parameters for the experiment during the last science data acquisition run. This service work for the experiment is essencial to ensure good quality data. Second, the simulation of the expected radioactive background on the upgraded version of the experiment, DAMIC-M, exploring possible designs for the construction of the experiment according to our background level requirement. This work serves as guideline to decide the detector design which will be implemented.

The text of the thesis is organized as following: chapter 2 is dedicated to review in details the search for mCPs. Two theoretical models, one with a hidden photon and an- other without, are discussed as examples of the huge variety of models predicting mCPs.

After giving the details of the main techniques to search for these particles and their results, the method to search for cosmogenic mCPs is derived. Chapter 3, presents a brief introduction to the dark matter problem and extensively discusses the CCD operation as

a particle detector. DAMIC scientic goals and results are highlighted. The nal section of this chapter describes the DAMIC-M, an upgraded version of the DAMIC experiment, presenting the rst work of this thesis. Still under development, it is shown the simu- lation of the expected radioactive background of DAMIC-M, exploring possible designs for the construction of the experiment according to the experiment's background level re- quirement. Chapter 4 is dedicated to the application of event reconstruction chain of the DAMIC experiment and the monitoring of the detector operation parameters. The search for cosmogenic mCPs with the DAMIC data is presented in chapter 5. First, a simulation of the interaction between a mCP in the CCDs, including the event reconstruction, is explained. Then, based on this Monte Carlo, selection variables used to characterize a mCP were chosen. The nal analysis presents the limits on the ux of cosmogenic mCPs at the DAMIC site derived after analyzing the data acquired by the experiment. Finally, chapter 6 summarizes all the results, analyzing the future of the experiment and this analysis.

Chapter 2

Search for mCPs

Conrming the existence of an isolatable fractional charged particle is an experimental question. A positive answer to this problem would be an undisputed signature of physics beyond the SM, changing the charge quantization paradigm. The purpose of this chapter is to review the experiments carried out over the years to observe mCPs and discuss the main restrictions imposed on the existence of these particles. First, as two phenomenologies are used to interpret the observations, a brief discussion on these models is presented. Then, after establishing the experimental status of this research eort, the search of cosmogenic mCPs with underground experiment data is motivated as a technique to probe a signicant part of the mCP parameter space unreachable for the other experiments.

2.1 Extensions to the Standard Model including mCPs

Although many extensions to the SM predict mCPs, these theories are separated in only two distinct phenomenologies. One arises from theories with an extraU(1)_h hidden symmetry added to SM. In this case, a particle charged under the new U(1)_h symmetry appears with fractional charge as a result of the SM photon and the hidden photon kinetic mixing. The other is for models in which the mCP is included as a new Dirac fermion with fractional charge quantum number. For some search techniques, the dierences between these two phenomenologies can impact on the data interpretation and restrictions imposed on the mCP characteristics.

2.1.1 Models with an Extra U(1) hidden symmetry

The term Hidden Sector refer to an unobserved set of degrees of freedom added to the SM that are very weakly coupled to SM particles. From the theoretical point of view, models proposing such scenario are highly motivated as a possible explanation for the dark matter problem. The Universe's non-luminous cold component, very weakly coupled to barionic matter, mainly interacting gravitationally, observed as dark matter is easily explained as a hidden particle.

Considering a model with two U(1) gauge groups, one being the electromagnetic U(1)_QED and the other a hidden-sector U(1)_h under which all standard model particles are not charged, the most general kinetic Lagrangian allowed by the symmetries is given by equation 2.1

L=−1

4F^µνF_µν − 1

4B^µνB_µν− 1

2κF^µνB_µν (2.1)

where F_µν is the eld strength tensor for the ordinary electromagnetic QED (Quantum electrodynamics) gauge eld A_µ, B_µν is the eld strength for the hidden-sector eld B_µ and κ is an arbitrary number. In analogy with the standard photon, the latter can be identied as a hidden photon. As the eld strength is gauge invariant, a non-diagonal kinetic term called kinetic mixing is allowed. This term can be diagonalized with the shift B_µ →B˜_µ−κA_µ (and, consequently, B^µν →B˜^µν−κA^µν).

L=−1

4(1−κ²)F^µνF_µν −1 4

B˜^µνB˜_µν (2.2)

With a multiplicative renormalization of the gauge coupling e² → e²/(1−κ²), the visible elds are unaected by the shift. On the other hand, for a hidden-sector fermion h charged under B_µ, it induces a coupling to the SM photon.

e_h¯h /Bh→e_h¯h /Bh−κe_h¯h /Ah (2.3) It can be directly identied that the hidden-sector fermion has an eective electric

chargeq =κe_h which does not follow the charge quantization principle sinceκ is an arbi- trary number. Of course it is possible to haveκ equal to zero, destroying the appearance of the mCP. An important point emphasized in [7, 43] is that κ would be a completely arbitrary parameter from a low-energy eective Lagrangian point of view. Inside a more fundamental theory, it is plausible to have κ = 0 at a high energy scale related to the fundamental theory. However, integrating out the quantum uctuations below this scale generally tends to generate non-vanishing κ.

This simple model has considered the case of an unbroken U(1)_h symmetry to exem- plify how the hidden sector fermion h manifestly becomes a mCP when the equations of motion of the photons are diagonalized. The eects of adding a mass term to the Lagragian can be found in [43]. By insertingL_µ = ¹₂µ²B^µB_µ, a new term mixing photons with hidden photons appears when applying the shift. It was shown that for a massless on shell external photon, the mCP is undone due to a cancellation between the charge contribution arised from the shift and the non-diagonal mass term. O shell, in a plasma for example, this is not the case. Other models can be found in the literature (example with more than one hidden photon [44]) based on the idea presented by [7] where the mCP naturally arises from an extraU(1)_h.

2.1.2 Models with a massive milli-charged fermion

The charge quantization observed among elementary particles is not a requirement of the SM. The theoretical basis for this problem is that the description of electroweak interactions, based on the SU(2)_L×U(1)_Y gauge group, has an Abelian factor U(1)_Y related to the weak hypercharge. Since an Abelian theory has no nontrivial commutation relations between the group generators, there is no algebraic quantization of its charge eigenvalues. In other words, the electrical charges of elementary particles, related to SU(2)L and U(1)_Y eigenvalues viaQ_em =T3 +Y /2, are not quantized due to the lack of quantization of the weak hypercharge Y. Constraints on the hypercharge values derived by requiring the Lagrangian to be invariant under the gauge symmetry and also gauge

anomaly cancellation are not sucient to guarantee the electric charge quantization [4].

Within the SM framework, nothing prevents the addition of new particles with ar- bitrary mass and charge into the theory. A Dirac fermion can be added to the SM Lagrangian as described in equation 2.4, an extra SU(2)_L singlet with gauge invariant mass term and coupled to the photons.

L=L_SM+ ¯f(i /∂ −m_f)f +ef /¯Af (2.4) where A_µ is the SM photon's vector potential and f denotes the new fermion with mass m_f and chargee. The charge quantum number of the mCP can be arbitrarily small, reg- ulating the intensity of its coupling with the photon. This new term in the SM Lagrangian would not contribute to local or global anomalies because of its vectorlike coupling.

Although this modication is straightforward, it is not simple if the hyperchargeU(1)_Y is embedded in a grand unied gauge group [45]. It can be shown that such models contain a large number of particles and therefore are unrealizable in nature. Another possible mechanism to induce mCP into the theory which avoids this problem is to allow the neutrinos to have small electric charges [4]. By a redenition of the Standard Model hypercharge operator Y_SM to Y =Y_SM+ 2P

i_i(B/3−L_i), the neutrinos acquire small electric charges _i, also preserving anomaly cancellation.

The approach to include mCP into the theory directly as a new particle relates with a variety of models found in the literature. In this phenomenology, the small charge is a property of the particle itself. This is the main contrast with mCP models with an extra U(1) hidden symmetry, in which the particle's small charge arise from an eective small coupling between a hidden sector fermion and the ordinary photon. In the next sections, one can nd experiments devised to observe mCPs and restrictions imposed on the existence of such particles due to known and well studied physical process in which the presence of a mCP may impact. For the latter, there are some processes where the dierences between these two phenomenologies can modify the limits on the mCP characteristics obtained.

2.2 Physical constraints in the mCP mass/charge

The Standard Model of particle physics [40] is the theory describing all known ele- mentary particles and their possible interactions. It is known to be incomplete as it does not explain problems such as the neutrinos masses or matter-antimatter asymmetry, for example. However, being the base to correctly explain a vast number of natural phenom- ena, the addition of new particles within its framework or modications of any kind at the theory is very restricted. Expanding the SM usually have consequences incompatible with the experimental knowledge in well studied physical process. This argument can be directly applied to the mCP, a new fermion inserted into the theory, whose characteristics such as mass and charge should be constrained by the known physics. Some examples of experimental limits imposed to the mCP mass and charge derived from this idea are given below. Most of them are related with physics at early stages of the Universe or stellar physics, systems with sucient energy density to create mCPs. The combination of the latest constraints imposed in the mCP parameters space (not only the ones discussed in details here) is shown in gure 1.1

I. Big Bang Nucleosynthesis

In Cosmology, Big Bang nucleosynthesis (BBN) [46] refers to the production of light chemical elements (atomic masses lighter or equal than⁷Li) during the early stages of the Universe. One of the greatest success of the big bang theory, it predicts the abundance of these elements as function of the barion-photon ratio η= ⁿ_n^B

γ based on the SM.

The nucleosynthesis happens in radiation dominated era of the Universe when the energy density was given by:

ρ_rad = π² 30

X

i

g_ibosons+ 7

8g_ifermions

T⁴ (2.5)

where the index i runs over all possible particles, bosons or fermions with respectively g_ibosons and g_ifermions degrees of freedom, contributing for the energy density and T is the

Universe temperature. The nucleosynthesis starts when the temperature falls to MeV scale and the only relativistic species are photons, electrons, positrons, neutrinos and anti-neutrinos, yielding a energy density ρ_rad = ^π₃₀² 2 + ⁷₄ +⁷₄Nν

T⁴. The number of neutrino avors N_ν were left as a variable on purpose for further discussions. In the standard BBN calculation,N_ν = 3is used. The important weak interactions for BBN are

n+e⁺ ↔p+ ¯ν_e n+ν_e ↔p+e⁻

n ↔p+e⁻+ ¯ν_e

(2.6)

For temperatures T 1 MeV, these reactions are in thermodynamical equilibrium with an equal number of protons and neutrons. Due to the temperature drop with the Universe expansion, at some point the weak interaction rates will no longer be fast enough to sustain the equilibrium, a process known as freeze-out. This condition is reached at T = 0.8 MeV, when the reaction rate Γ ∼ G_FT⁵ falls below the expansion rate H² ∼ ^8πG₃^Nρ. The proton and neutron number densities after the freeze-out can be calculated the using Maxwell-Boltzmann distribution. So, for T = 0.8MeV, the neutron- proton ratio is ⁿ_nⁿ_p =

mn

mp

3/2

exp ∆m/T ∼ 1/6, where ∆m is the neutron-proton mass dierence. This value goes to1/7if ones consider neutrons decaying before nucleosynthesis begins.

The elements formation chain starts with the Deuterium production p+n ↔ D+ γ. Because of the large number of photons relative to nucleons (η⁻¹ ∼ 10¹⁰), with a signicative fraction of them carrying energy above the Deuterium binding energy E_D = 2.2 MeV, the formation of Deuterium is delayed until the temperature reaches T = 0.1 MeV. At this point the production rate overcomes the destruction. Then, the chain continues with the Helium formation through D+D → ⁴He. Using a crude estimation which assumes that all neutrons are converted in Helium, the expected abundance of this

element is given by equation 2.7

Y_He ≈ 2n

n+p = 2 (n/p)

1 + (n/p) ≈0.25 (2.7)

The other light elements are produced in less abundance: D and ³He at ∼ 10⁻⁵ level and ⁷Li at ∼ 10⁻¹⁰ level. The BBN predictions are compatible with experimental observations and the addition of the mCP into the theory must not change this fact.

New components in the Universe content with masses below the MeV scale are relativis- tic just before BBN starts, contributing in equation 2.5 and modifying the abundances.

This argument was rst applied to constraint the number of possible neutrino avors. It can be shown that the abundances of light elements are still compatible with observations for N_ν < 3.3 Majorana neutrino avors [4749]. In this way, BBN allows for 0.3 extra two-component neutrinos or their equivalent in other relativistic particles at MeV mass scale. For a model without a hidden photon, this argument rules out mCP withM_mCP <1 MeV. As this constraint is predicated on the assumption that these particles are in ther- mal equilibrium with the electrons and photons, it is valid for charges withε >10⁻⁸ [21].

In order to reach the equilibrium at BBN, their interaction cross section must fall below the expansion rate before temperatures ofT = 5MeV. If one consider models including a massless hidden photonγ⁰, the exclusion is even more stringent. As a massless boson, the hidden photon would contribute as 8/7 of a neutrino and, for this reason, they are not allowed to be in thermal equilibrium with the ordinary photons. Instead, they are only allowed to exist if ⁸₇T_γ⁴0 = 0.3T_γ. The photons must therefore be heated by annihilation after the hidden photon decouple. It can be shown that this implies the photons and hidden photons must be out of equilibrium at QCD phase transition (T ∼200 MeV) [21].

This fact can be used to constraint the mCP masses below7 + 0.4 lnε GeV scale [50].

II. Flatness of the Universe

Another physical constraint that bounds the mCP parameter space is the requirement of a particle density below the critical density ρ_c. In Cosmology, the expansion of the

Universe is governed by the Friedmann equations [51, 52]. Within the context of general relativity, the Cosmological Principle, the notion of a spatially homogeneous and isotropic Universe at large scales (justied at scales larger than ∼ 100 Mpc), leads to a generic metric in the form:

ds² =a(t)dr₃²−c²dt² (2.8) where, dr₃² is a three-dimensional spatial metric and a(t) is a scale factor. This is called the Friedmann-Lemaître-Robertson-Walker metric. Einstein's eld equations relates the evolution of the scale factor to the pressurep and energy densityρ of the matter content in the Universe as:

H₀²a˙

a =H² = 8πG 3 ρ+Λ

3 − kc²

a² (2.9a)

H₀²¨a

a =−4πG 3

ρ+ 3p c²

=−4πGρ

3 (1 + 3ω) (2.9b)

where G is gravitational constant. The energy density and the pressure term are related by a perfect uid equation of state p = ρc²ω (dierent values of the constant ω for each Universe component). The actual Universe's energy content, a crucial parameter to determine the Universe evolution, is one of the biggest open questions of the century.

A large number of astronomical observations [5355] indicate that the regular baryonic matter represents only a small fractional, 4.9%, of the energetic content of the universe.

About 26.8% is in the form of the so called dark matter (introduced in chapter 1 and described in more details in chapter 3). The remaining 68.3% is called dark energy, a negative pressure term inserted in Friedmann equation via a cosmological constant Λ, is responsible for the accelerate expansion of the universe. The great open question resides in what is the composition or physical phenomena responsible for these last two terms, the major content of the Universe.

In this context, the critical densityρ_cwas rst introduced as a means to determine the spatial geometry of the universe, representing the density for which the spatial geometry

is at. By settingΛ = 0andk = 0, one nds the expression for the critical density to be:

ρc= 3H₀²

8πG (2.10)

where is usual to dene the density parameter as Ω ≡ _ρ^ρ

c. If Ω is larger than unity, the space sections of the universe are closed and the universe will eventually stop expanding, then collapse. IfΩis less than unity, they are open and the universe expands forever. So, by requiring the mCP particle density below the critical densityρc, one assure that they will not overclose the Universe.

The abundance observed today of any thermally produced particle (including mCPs) in the Universe can be obtained via the Boltzmann equation [56]:

dn

dt + 3Hn=< σ_av >(n−n_eq) (2.11) where the second term includes the density dilution due to the Universe expansion and the last is an interaction term taking into account the particle annihilation. The annihilation rate is given by the thermally averaged annihilation cross section< σ_av >and the particle number density.

It is assumed that the particles were created in thermal equilibrium between the cre- ation and annihilation. As the Universe expands, it also cools down, stopping the particle creation and reducing exponentially the particle number density due to annihilation. Fi- nally, for a rate of expansion higher than the interaction rate, the particle number density freezes in a certain value. This value is controlled by the annihilation cross-section. This process is shown in gure 2.1 taken from [57]. In the case of mCPs, dierent masses and charge fraction leads to dierent number density that are constrained requiringρ_mCP < ρ_c.

III. Stellar physics

The stellar evolution and supernova theory is well described by the standard model.

In a simplied picture, a star is the result of the dynamics between the gravitational collapse and the pressure of the stellar material. In this thermodynamical system, fusion

Figure 2.1: Comoving number density evolution as a function of the ratio mass tempera- ture ratiom/T in the context of the thermal freeze-out. The size of the annihilation cross section determines the relic abundance.

reactions driven by the gravitational collapse and high temperatures liberate energy while creating heavy elements. In parallel, neutrinos carry energy from the star as they are produced in the photo-neutrino process γe⁻ → e⁻νν¯, the bremsstrahlung process e⁻ + (A, Z) → (A, Z) +e⁻ +νν¯ and the plasmon decay γ → νν¯. Plasmons are excitations of the dense electron-proton plasma in which the photons obtain non-trivial dispersion relation. In other words, they acquire an eective mass while propagating through this medium, allowing them to decay without violating gauge invariance or conservation of energy and momentum. The stellar theory based on the standard model is in good agreement with experimental data. New particles that could carry extra energy from the star, such as mCPs with small couplingε (or other weakly interacting particle), may lead to observational modications on the standard course of its evolution depending on its properties [58]. In general, the hot dense medium inside a star has sucient energy to produce mCPs and stellar physics can also be used to constraint these particles parameter

space.

The dominant mechanism that would produce mCPs in the stellar medium is the plasmon decay γ^∗ → ff¯. Other possible mCP production channels are negligible in comparison with the plasmon decay. The small number of positrons suppresses the mCP production via the annihilatione⁺e⁻ →ff¯. The fusion of two photonsγγ →ff¯is in high order of the small coupling ε. Also, the fusion of two hidden photons γ⁰γ⁰ → ff¯would be suppressed by the small number of these particle. Based on this energy loss argument, red giants (RG), horizontal-branch (HB) stars, white dwarf (WD), supernova (SN) 1987A and sun data were used to derive constraints on the mCP parameter space. A red giant is a luminous giant star, of roughly 0.3 to 8 solar masses M, in a late phase of stellar evolution. In this stage, the star is still fusing hydrogen into helium, with a hydrogen shell surrounding an inert helium core. Changes in the electron density and temperature, that occurs in the presence of a new energy loss channel, would reect in the brightness at the tip of the red-giant branch in globular clusters and therefore could be observed [812].

The horizontal branch is a stage of stellar evolution that immediately follows the red giant for stars with masses similar to the Sun's. They are powered by helium fusion in the core and hydrogen fusion in a shell surrounding the core. New energy loss mechanisms means an accelerated consumption of nuclear fuel for these stars. This can be measured by number counts of HB stars in globular clusters [814]. The population of White Dwarfs can also be used to limit the mCPs characteristics. The present theory explaining the cooling for these stars by surface emission of photons and volume emission of neutrinos produced in plasmon decay via Standard Model interactions, seems to agree with the observed luminosity distribution of their population. This observable would be changed with a new decay channel for the plasmon [8, 1518]. For supernovas, the number of neutrinos detected at Earth after the SN 1987A event agrees roughly with theoretical expectations. Other particles contributing to the cooling of the proto neutron star would imply in a reduced neutrino ux and in short duration of the neutrino signal [8,19,20]. In the case of the Sun, the proximity of the star allow the same study using observables such

as neutrino ux and sound speed prole. Solar models with exotic energy loss mechanism, lead to measurable changes on these observables and this is also used to limit the mCP parameter space [6].

2.3 Search for violation of the charge quantization prin- ciple

Outside the restrictions imposed by known physical process, experiments sensitive to the passage of this kind of particle can be elaborated to verify the existence of a particle violating the charge quantization principle. In case of no hint of mCP found in these analysis, more limits are imposed on its mass and charge.

2.3.1 Millikan Oil Drop Method

The pioneer experiment to state the charge quantization principle can also be used to search for particles with fractional charge. Assuming these particles were produced in the early universe and some abundance remains today, one can search for them in bulk matter [25] or meteoritic materials [26] using the Milikan's oil drop method.

This experiment is based on the classical equations of motion of a spherical oil drop with some net charge. The drop is moving in a air tube subjected to an electric eld that can oppose or be in the same direction of the gravity. These equations describing the drop falling or going up are given, respectively, by

−ρ_oilgV_drop+mg+E↑Q= 6πηrv↓ (2.12)

−ρ_oilgV_drop+mg−E↓Q= 6πηrv↑ (2.13) where η is the viscosity of air and the drop parameters are its mass m, charge Q, radius r, volume V_drop = ⁴₃πr³, measured terminal velocities v↑ and v↓. These equation can be

combined to obtain the drop's radius and charge via:

r= 3 r

v_g η

2g(ρ_oil−ρ_air) (2.14)

q= 18π e

r

v_g 2 ρ_oil−ρ_air

1 E↑+E↓

η^3/2v_e (2.15)

Using a CCD camera, the experiment is able to image the positions of the falling drops and track its position. The charge of the drop is calculated by nding the best t to the sequence of the drop's position measurements.

Using this method, a single drop measurement consistent with non-integer charge was found in bulk matter among 4.17×10⁷ sample [25]. No claim of discovery was made though, as this result could be adressed to some extra background that begins to appear at the one in the 10⁷ level. Further searches with meteoritic material found no evidence for non-integer charge [26].

2.3.2 Accelerators and colliders

Perhaps the most natural method to look for new particles is in high-energy collision experiments. In the case of mCPs, there are two possible approaches to be followed in order to observe them. One, more indirect, is in the so called missing energy analysis.

The mCPs are weakly coupled to photons, interacting only rarely while traveling through matter. For this reason, the mCP production in collision experiments would appear as a missing energy at the detectors such as it happens for neutrinos and may be for other exotic weakly interacting particles. This method could be regarded in some sense as a physical constraints in the mCP mass/charge based on the known physics. The other is directly observe a particle signature compatible with a mCP in a setup outside the accelerators main detectors (far from the collision center), in a region only accessible for this kind of particles.

Both searches can be conducted in a e⁺e⁻ annihilation beams. In this search, the interactions are electromagnetic or weak, in such way that the mCP production cross

sections are known. In the case where mCPs interact via the weak force, its coupling to the Z₀ boson is suppressed by εtanθ_W. A dedicated search for mCPs carried out at SLAC [23] excluded part of the mCP mass/charge, electric charge of 4.1 × 10⁻⁵e for mCPs of mass 1 MeV and 5.8×10⁻⁴e for mass 100 MeV, by not observing events consistent with these particles. The experiment main detector consisted of a 2×2array of blocks of 21×21×130 plastic scintillator located way from the beam. The short duration pulses with high intensity of the beam were a powerful tool for background reduction, as the signal is expected to occur within a narrow time window. The Anomalous Single Photon (ASP), also at SLAC, was an experiment designed to search for events like e⁺e⁻ →γ+ weakly interacting particles [59]. A missing energy experiment, the expected signature for this process was a single photon observed with a transverse momentum unexplained by particles lost at the beam pipe. Their limits on this process can be readily translated to limits for mCPs [21].

Hadronic beams colliders can also be used on the searches for isolatable fractional charge particles. If these particles interact through the strong interaction, for example if they are free quarks, then there is an advantage to search for them using hadron-hadron collisions. Another advantage is that a highest mass region can be explored using a proton collider. Of course, the main disadvantage is not knowing the cross-section for the mCP production through the strong interaction, in contrast to the e⁺e⁻ beam.

There is a proposal for a new experiment at the Large Hadron Collider (LHC) aiming to be sensitive to charges in the range 10⁻¹ −10⁻³e for masses in the range 0.1−100 GeV [60]. This is an interesting region because it is the least constrained part of the mCP parameter space. In the context of this work, it is also the region exploited by the cosmogenic search. The experiment propose the implementation of a telescope design (stacked detectors acting in coincidence) mounted apart from the LHC main detectors to search for the passage of a fractionally charged particle produced on the beam. The mCP production cross section via a s-channel γ or Z₀ is simulated assuming a hidden photon scenario. Figure 2.2 shows the total cross section simulated.

Figure 2.2: The mCP production cross-section at the LHC simulated assuming a hidden sector scenario for process pp → ψ⁺ψ⁻+X as a function of the mCP mass. The total cross section is obtained using Drell-Yan process. Figure taken from [60].

The expected sensitivity for this proposed search is shown in gure 2.3. As it will be clear latter in the text, the cosmogenic search for mCPs will be able to probe the same region on this parameter space and it will be interesting to compare both results in the future.

2.3.3 QED precision measurements

Precision QED experiments are a powerful tool to probe directly the existence of mCPs [29]. These particles enter into the theory adding loop corrections in the QED calculation.

For this reason, the existence of mCPs can be tested in the ortho-positronium (o-Ps) decay, measurement of the Lamb-shift or the electron anomalous magnetic moment.

The lightest known atom is a positron-electron bound state called positronium. It is a system fully described by a pure electromagnetic process, as it is bounded and self- annihilates via this interaction only. Such feature made positronium an ideal system for testing the accuracy of the QED calculations. There are two experimental signatures that could indicate the existence of the mCP in the o-Ps (triplet state). One is a missing energy of the expected 1.022 MeV decay. The other is dierences between the observed

Figure 2.3: The expected sensitivity for a new search for mCPs propose to be carried out in LHC. It is sensitive to exploit an unexplored part of the parameter space that is also important for the cosmogenic search. Figure taken from [60].

o-Ps decay rate and the QED predictions [28,61].

The Lamb shift is a dierence between the energy levels 2S_1/2 and 2P_1/2 due to the interaction between vacuum energy uctuations and the hydrogen electron. It can be visualized as a perturbation in the nuclear electric potential caused by QED vacuum uctuations. The presence of the mCP alter the QED calculation of these uctuations, impacting at the measured value of the Lamb-shift [8,30]. For the same reason, the mCP would add corrections in the QED calculation of the anomalous magnetic moment of the electron [29].

The current experimental knowledge agrees with QED calculations, imposing con- straints at the mCP existence.

2.4 Search for cosmogenic mCPs

As shown in gure 1.1, there is part of parameter space relative to particles with small charge fraction (f ∼10up to 10⁻³) and masses much larger than the electron mass