# Design, scale-up and characterization of the data acquisition system for the
ANAIS dark matter experiment

Memoria presentada por
Miguel Ángel Oliván Monge
para optar al grado de
Doctor en Física

Laboratorio de Física Nuclear y Astropartículas
Área de Física Atómica, Molecular y Nuclear
Departamento de Física Teórica
UNIVERSIDAD DE ZARAGOZA

(Diciembre 2015)

---

This work is licensed under a Creative Commons Attribution 4.0 International
License except the figures listed below:
[itemize]

& Figure 1.1. From K. Begeman, A. Broeils, and R. Sanders, “Extended rotation
curves of spiral galaxies: Dark haloes and modified dynamics,” Monthly Notices
of the Royal Astronomical Society, vol. 249, no. 3, pp. 523–537, 1991. Figure
1.2. X-ray: NASA/CXC/CfA/M.Markevitch et al.; Optical: NASA/STScI;
Magellan/U.Arizona/D.Clowe et al.; Lensing Map: NASA/STScI; ESO WFI;
Magellan/U.Arizona/D.Clowe et al. Figure 1.3. K.A. Olive et al. (Particle Data
Group), Chin. Phys. C, 38, 090001 (2014). Figure 1.4. © ESA and the Planck
Collaboration. Figure 1.5. P. Gondolo, from https://indico.ibs.re.kr/event/7/
contribution/11/material/slides/0.pdf. Figure 1.6. From R. Bernabei et al.,
“New results from DAMA/LIBRA,” The European Physical Journal C-Particles and
Fields, vol. 67, no. 1, pp. 39–49, 2010. Figure 1.7. From C. Cuesta “ANAIS-0:
Feasibility study for a 250 kg NaI(Tl) dark matter search experiment at the
Canfranc Underground Laboratory”, Universidad de Zaragoza, 2013. Figure 2.8.
From J. Amaré et al. “Status of the ANAIS Dark Matter Project at the Canfranc
Underground Laboratory”. Proceedings of 11th Patras Workshop on Axions, WIMPs
and WISPs. Figure 3.3. From “Photomultiplier Tubes: Basics and Applications”.
Hamamatsu Photonics KK, Iwata City, 2007. Figure 4.13. From D. Breton, E.
Delagnes, and M. Houry, “Very high dynamic range and high sampling rate VME
digitizing boards for physics experiments,” Nuclear Science, IEEE Transactions
on, vol. 52, no. 6, pp. 2853–2860, 2005. Figures 8.2 and 8.3. D. L. Mills,
from https://www.eecis.udel.edu/~mills/ntp/html/warp.html.

###### Contents

  1. 1 Introduction
    1. 1.1 Dark matter evidences
      1. 1.1.1 The galactic scale
      2. 1.1.2 The galaxy cluster scale
      3. 1.1.3 The cosmological scale
      4. 1.1.4 Alternatives to dark matter
    2. 1.2 Dark matter candidates
    3. 1.3 Indirect dark matter detection
    4. 1.4 Direct dark matter detection
      1. 1.4.1 WIMP detection rate
      2. 1.4.2 Background sources
      3. 1.4.3 Direct detection techniques, current status and future prospects
    5. 1.5 NaI(Tl) as target for WIMP searches
  2. 2 The ANAIS experiment
    1. 2.1 ANAIS experimental requirements
      1. 2.1.1 Low energy threshold
      2. 2.1.2 Low background at low energy
      3. 2.1.3 Stability
      4. 2.1.4 Exposure maximization
    2. 2.2 ANAIS experimental set-up
    3. 2.3 ANAIS-25 set-up
    4. 2.4 ANAIS-37 set-up
    5. 2.5 ANAIS sensitivity prospects
    6. 2.6 This work
  3. 3 Optical to electrical conversion
    1. 3.1 Scintillation process in NaI(Tl)
      1. 3.1.1 NaI(Tl) scintillation parameters
    2. 3.2 Photomultipliers
      1. 3.2.1 ANAIS requirements
      2. 3.2.2 Hamamatsu R12669SEL2 PMT
      3. 3.2.3 Voltage divider
      4. 3.2.4 High voltage power supply
    3. 3.3 Photomultiplier radiopurity
    4. 3.4 Low energy signals
    5. 3.5 Photomultiplier response characterization
      1. 3.5.1 Single electron response deconvolution
      2. 3.5.2 PMT test bench
      3. 3.5.3 Deconvolution fit
      4. 3.5.4 Light intensity detection and LED stability
      5. 3.5.5 Mean photoelectrons algorithms and relative quantum efficiency
      6. 3.5.6 Peak-to-valley ratio
      7. 3.5.7 Dark counts
    6. 3.6 Characterization protocol and results
      1. 3.6.1 Parameter extraction automation
      2. 3.6.2 Gain curves
      3. 3.6.3 Peak-to-valley
      4. 3.6.4 Dark counts
      5. 3.6.5 Relative quantum efficiency
      6. 3.6.6 Characterization protocol
    7. 3.7 Operating voltage and trigger level selection
    8. 3.8 Coincidence Trigger
  4. 4 Data acquisition electronic front-end
    1. 4.1 Front-end requirements
    2. 4.2 High Level Description
    3. 4.3 Analog front-end
      1. 4.3.1 Preamplifier
      2. 4.3.2 Trigger Modules
      3. 4.3.3 NIM Modules
    4. 4.4 Digital front-end
      1. 4.4.1 Time scalers
      2. 4.4.2 VME modules
    5. 4.5 Front-end characterization
      1. 4.5.1 Preamplifier
      2. 4.5.2 Delay module
      3. 4.5.3 MATACQ Module
      4. 4.5.4 Trigger modules
      5. 4.5.5 Baseline characterization and improvements
  5. 5 Muon detection system
    1. 5.1 Muon underground interaction
    2. 5.2 Muon detector set-up
    3. 5.3 Plastic scintillator characterization
      1. 5.3.1 Plastic scintillator simulation
      2. 5.3.2 Plastic scintillator test bench
      3. 5.3.3 Homemade plastic scintillators
      4. 5.3.4 Scionix plastic scintillators
    4. 5.4 Electronic front-end design and DAQ
      1. 5.4.1 Pulse shape analysis characterization
    5. 5.5 ANAIS-37 plastic scintillators set-up
      1. 5.5.1 Temporal behavior
      2. 5.5.2 Multiplicity and face coincidences
      3. 5.5.3 Muon related NaI(Tl) events
  6. 6 Data acquisition software
    1. 6.1 DAQ software requirements
    2. 6.2 DAQ software design
      1. 6.2.1 Software Components
      2. 6.2.2 DAQ Program Design
    3. 6.3 DAQ software implementation
      1. 6.3.1 Output file structure and naming conventions
      2. 6.3.2 Run routine and run script
      3. 6.3.3 Run log
  7. 7 Data analysis software
    1. 7.1 Algorithms
      1. 7.1.1 Basic signal characterization
      2. 7.1.2 Peak detection
      3. 7.1.3 Peak based parameters
      4. 7.1.4 Time parameters
    2. 7.2 Baseline algorithms
    3. 7.3 Implementation, configuration and automation
      1. 7.3.1 Algorithm parametrization
      2. 7.3.2 Output file and Naming conventions
      3. 7.3.3 Automation and report notification
      4. 7.3.4 Analysis tools
    4. 7.4 Low energy NaI event selection
  8. 8 Data acquisition characterization
    1. 8.1 Real time clocks
      1. 8.1.1 32-bit latched vs. 64-bit non-latched counter
      2. 8.1.2 NTP system
      3. 8.1.3 Real Time clocks characterization
    2. 8.2 Dead time characterization
      1. 8.2.1 Synchronous vs. asynchronous data storing
      2. 8.2.2 IRQ waiting, board order reading and dead time
      3. 8.2.3 Live time clock versus dead time measured with latched scaler
      4. 8.2.4 Dead time measurements and prospects
    3. 8.3 Live time, dead time and down time
      1. 8.3.1 Live time measurements
    4. 8.4 ANAIS-25 and ANAIS-37 calibration
    5. 8.5 Onsite SER extraction
      1. 8.5.1 SER trigger efficiency
    6. 8.6 Light collection
    7. 8.7 Hardware trigger efficiency
    8. 8.8 Effect of noise reduction with a 100 ns coincidence window
  9. 9 Environmental and data acquisition stability
    1. 9.1 Slow Control
    2. 9.2 Slow Control Data
      1. 9.2.1 Temperatures
      2. 9.2.2 $Rn$ concentration, humidity and pressure
      3. 9.2.3 $N_{2}$ Flux
      4. 9.2.4 PMT power supply monitoring
    3. 9.3 Data taking stability
      1. 9.3.1 Gain stability
      2. 9.3.2 Trigger level stability
      3. 9.3.3 Coincidence window stability
  10. Summary and conclusions
  11. Resumen y conclusiones
  12. Agradecimientos

##  Chapter 1 Introduction

The observation of our universe has been more and more precise and it has
brought many data about its composition and dynamics. As a result, there are
strong evidences supporting the existence of a non-luminous matter known as
dark matter. This matter accounts for the majority of the material that forms
galaxies and clusters of galaxies explaining observational phenomena and it
can not be only composed by particles of the standard model of particle
physics. The evidences of the existence of dark matter come from accurate
measurements of galactic rotation curves, orbital galaxy velocities in
clusters and cluster mass determination with gravitational lensing. In
addition, the precise measurement of the Cosmic Microwave Background (CMB)
combined with the standard cosmological model also gives a big dark matter
proportion ($\sim$ 27% of non-baryonic dark matter and $\sim$ 68% of dark
energy) after the Planck measurements [1].

######

The nature of the hypothetical dark matter remains unknown and the detection
and characterization of this type of matter is an open field in particle
physics that can solve many cosmological questions as well as give answers
beyond the standard model of particle physics [2]. The evidences supporting
the dark matter existence, the possible candidates and the efforts to detect
and characterize the dark matter are covered in this chapter.

######

DAMA/LIBRA stands out among these initiatives because of a positive signal of
annual modulation at low energy attributed to dark matter [3, 4, 5], being the
only experiment with a positive result spanning a long period of time. The
ANAIS project (see Chapter 2) has been a long effort to carry out an
experiment with the same target and technique, which could confirm the
DAMA/LIBRA result.

###  1.1 Dark matter evidences

The measurements of large astrophysical systems from galactic to cosmological
scales show anomalies that can only be explained by assuming the existence of
large amounts of unseen (dark) matter or by assuming deviations from the laws
of gravitation and the theory of general relativity.

######

####  1.1.1 The galactic scale

The most direct and convincing evidences for dark matter existence on galactic
scales are the galactic rotation curves first measured by Vera Rubin [6]. The
rotational velocities of visible stars or gas as a function of the distance to
the galactic center exhibit a flat behavior contrasting with the expected
Newtonian dynamics:

$v(r)=\sqrt{\frac{GM(r)}{r}}$ (1.1)

This velocity should be falling $\propto 1/\sqrt{r}$ outside the optical disk.
The fact that $v(r)$ is almost constant, as seen in Figure 1.1, implies an
halo with $M(r)\propto r$. This observations111The observed zones are inside
and outside the optical disk revealing an important gas contribution in galaxy
composition., usually measured by Doppler shift of 21 cm HI line combined with
optical surface photometry, have been confirmed in many galaxies [7].

Figure 1.1: Example of galactic rotation curve. The dotted, dashed and dash-
dotted lines are the contributions to rotational velocity of gas, disk and
dark matter, respectively. From [7].

There is a larger number of hints at galactic scale such as low surface
brightness (LSB) galaxies, weak modulation of strong lensing around individual
massive elliptical galaxies, velocity dispersion of dwarf spheroidal galaxies
or velocity dispersion of spiral galaxy satellites (see [8] and references
therein).

######

####  1.1.2 The galaxy cluster scale

Historically, the first hint about dark matter existence was at the cluster
scale. Fritz Zwicky inferred the existence of unseen matter examining the Coma
galaxy cluster in 1933 [9] using the virial theorem and he was the first to
refer the unseen matter as _dunkle materie_.

######

Since then, other dark matter evidences such as gravitational lensing effects
have been observed and used to determine cluster mass distribution. This
gravitational lensing involves the distortion of a far galaxy by the
gravitational field from a very massive cluster. The lensing can be used to
estimate the mass profile of the foreground massive object. This is a
especially valuable technique used in combination with other direct
observational data using the visible and the X-ray spectra and it has been
applied to colliding clusters [10, 11, 12].

######

This analysis shows a matter distribution that does not fit with visible and
X-ray patterns. This distribution can be seen in Figure 1.2 in a composite
image showing the first cluster analyzed in this way, the 1E 0657-558 also
known as Bullet Cluster. The hot gas detected by its electromagnetic
interaction and shown in pink, contains the most part of the baryonic matter.
Galaxies are shown in white and orange. The matter profile deduced by
gravitational lensing is shown in blue. Most of the matter, shown in blue,
does not interact which implies that this unseen matter only interacts
gravitationally and/or very weakly. Therefore, this matter can only be
compound of neutrinos or non-baryonic matter. The same result can be reported
from other cluster collision, MACS J0025.4–1222 cluster [11] giving a similar
distribution for every type of mass. However, not all collisions show the same
profile and the Abell 520 galaxy cluster presents a mass distribution with the
cluster center dominated by dark matter [12] being a challenge for theories
and simulations about dark matter interaction properties [13].

Figure 1.2: Bullet cluster composite image. Hot gas detected by Chandra X-ray
telescope is shown in pink. The optical image shows the galaxies in orange and
white from Magellan and Hubble Space Telescope images. The mass distribution
deduced by gravitational lensing is shown in blue. From [14].

####  1.1.3 The cosmological scale

The dark matter is also a fundamental ingredient in the standard cosmological
model. This model, based on general relativity with assumptions about space
geometry and mass distribution and interaction is capable to offer falsifiable
predictions some of them already measured experimentally with high accuracy
like cosmic microwave background (CMB) and CMB anisotropy. This measurements
also characterize the model including the amount of dark matter and dark
energy in the universe.

######

The first fact to take into account in a modern cosmological model is that the
universe is expanding. Edwing Hubble found combining their own measurements
with those of Vesto Slipher and Milton L. Humason that the galaxies velocity
is proportional to their distance [15] in the now known as _Hubble’s law_ :

$v=H_{0}r$ (1.2)

######

Following this empirical measurements describing the average behavior of
distant galaxies a set of solutions to Einstein equations were developed [16]
giving a new era in cosmology: the big bang cosmology [2]. In addition to the
observed expansion, a cosmological model must explain other experimental
evidences such as the accelerated expansion [17, 18] and the CMB [19] among
others.

##### The standard cosmological model

The standard model of cosmology (see [20] for example) is based on the
resolution of the Einstein equations with the isotropic and homogeneous
Friedmann-Lemaître-Robertson-Walker model (or FLRW model) allowing vacuum
energy (via cosmological constant), matter and radiation. It solves the
equations using the perfect fluid model.

######

The FLRW metric emerges from the isotropic and homogeneous conditions. The
FLRW line element should have the form:

$ds^{2}=g_{\mu\nu}dx^{\mu}dx^{\nu}=dt^{2}-a^{2}(t)\left(\frac{dr^{2}}{1-kr^{2}}+r^{2}d\theta+r^{2}sin^{2}\theta
d\phi^{2}\right)$ (1.3)

being $k$ and $a(t)$ the curvature parameter and the time dependent scale
factor respectively. The possible values of $k$ (being $r$ dimensionless) are
+1, 0 or -1 depending on whether the constant curvature is positive, zero or
negative. This model provides a metric $g_{\mu\nu}$ for the Einstein
equations, with the cosmological constant term:

$R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R-\Lambda g_{\mu\nu}=8\pi GT_{\mu\nu}$ (1.4)

being $R_{\mu\nu}$ the Ricci curvature tensor, $R$ ($g^{\mu\nu}R_{\mu\nu}$)
the Ricci scalar, $\Lambda$ the cosmological constant, $G$ the gravitation
constant and $T_{\mu\nu}$ the energy-momentum tensor. This tensor can be
written in the form:

$T_{\mu\nu}=(p+\rho)u_{\mu}u_{\nu}-pg_{\mu\nu}$ (1.5)

for a perfect fluid, a fluid without viscosity or heat flux, with $u_{\mu}$
the four-velocity of the fluid element, $p$ the pressure and $\rho$ the matter
density. All the above equations can be combined to give the Friedmann
equations:

$\left(\frac{\dot{a}}{a}\right)^{2}+\frac{k}{a^{2}}=\frac{8\pi
G}{3}\rho_{tot}\qquad\qquad\frac{\ddot{a}}{a}=\frac{-4\pi
G}{3}(\rho_{tot}+3p)$ (1.6)

being $\rho_{tot}=\rho_{m}+\rho_{rad}+\rho_{vac}$ and
$\rho_{vac}=\rho_{\Lambda}=\frac{\Lambda}{8\pi G}$. This $\rho_{tot}$ takes
into account the density of mass, radiation and vacuum energy.

######

The scale factor temporal behavior can be deduced using again the ideal fluid
model with the state equation $p=\omega\rho$ for every density and assuming a
flat universe $k=0$ (as pointed for WMAP/Planck measurements, see _Cosmic
microwave background experimental results_ subsection). $\rho$ is dominated by
rest mass for non-relativistic matter and the pressure is proportional to
velocity ($v<<c$ for such a type of matter), so $\omega=0$ for non-
relativistic matter. Considering only this matter:

$a(t)\propto t^{2/3}\qquad\text{(matter domination)}$ (1.7)

For radiation, $v=c=1$ and $p=\rho/3$ since pressure is averaged for three
spatial directions, and $\omega=1/3$ gives:

$a(t)\propto\sqrt{t}\qquad\text{(radiation domination)}$ (1.8)

And for vacuum $p=-\rho$, $\omega=-1$:

$a(t)\propto e^{Ht}\qquad\text{(vacuum energy domination)}$ (1.9)

being $H\equiv\frac{\dot{a}}{a}$, the Hubble _constant_ or more properly the
Hubble parameter.

######

These three particular solutions show a simplified set of solutions to
Friedmann equations with an expanding universe. They are useful to understand
the behavior of the universe expansion in special cases illustrating the three
stages in an expanding flat universe: the initial radiation domination, the
subsequent matter domination and the current vacuum energy domination.

######

This above described model can be extended to include perturbations explaining
the universe deviation from homogeneity. In addition, adding a period of
inflationary expansion solves the horizon, the flatness and the lack of
magnetic-monopole problems [21]. Next to this inflationary expansion, the use
of the standard model of particle physics explains how the nuclei of the light
elements were formed in a process called big bang nucleosynthesis [22]. This
cosmological model gives predictions for relative abundances of light elements
and CMB that can be contrasted to measurements. The model is parametrized to
perform such a verification as it can be seen in next section.

#####  $\Lambda CDM$ and the cosmological parameters

One of the first attempts to describe dark matter from a cosmological point of
view included the neutrino as candidate to dark matter in the so-called _hot
dark matter_ models [23]. However, these models were not able to explain the
large scale structure (LSS) and galaxy formation giving more fragmented
structures than the observed [24]. In contrast, the $\Lambda CDM$ (or lambda
cold dark matter) proposes a non-relativistic matter as source of the non-
luminous matter in addition with vacuum energy explaining the accelerating
expansion.

######

In this section, the cosmological parameters that make up the so-called six-
parameter model are described (see [2] and references therein). These six
parameters are used to contrast different cosmological models with
measurements, as it can be seen in the next subsection.

######

The (first) Friedmann equation 1.6 can be used to define critical density
setting $k=0$ and $\Lambda=0$:

$\rho_{c}\equiv\frac{3H^{2}}{8\pi G}$ (1.10)

The scaled Hubble parameter, $h$, is defined as:

$H\equiv 100\,h\,km\,s^{-1}\,Mpc^{-1}$ (1.11)

giving $\rho_{c}=1.88\times 10^{-26}\,h^{2}\,kg\,m^{-3}=1.05\times
h^{2}\,GeV\,cm^{-3}$.

######

The critical density can be used to define adimensional cosmological density
parameter as the energy density relative to critical density:

$\Omega_{tot}\equiv\frac{\rho_{tot}}{\rho_{c}}$ (1.12)

The (first) Friedmann equation 1.6 can be written as:

$\frac{k}{H^{2}a^{2}}=\Omega_{tot}-1$ (1.13)

The overall geometry of the universe is determined by the total energy density
parameter $\Omega_{tot}$: if $k>0$ and $\Omega_{tot}>1$ the universe is closed
(and $a(t)$ can be chosen to be the radius), if $\Omega_{tot}<1$ and $k=-1$
the universe is open and when $\Omega_{tot}=1$ and k=0 the universe is
spatially flat.

######

The $\Lambda CDM$ model breaks down the mass contribution, $\Omega_{m}$, in
components depending of the type of matter
$\Omega_{m}=\Omega_{b}+\Omega_{cdm}$ being $\Omega_{b}$ the baryon density and
$\Omega_{cdm}$ the proposed cold dark matter, i.e. matter moving slowly
compared with the speed of light (cold) that interacts weakly with
electromagnetic radiation (dark). It is necessary to distinguish the different
contributions to the density because of their different dynamics. For non-
relativistic matter, $\Omega_{m}$ is defined as the _present day_ matter
density and critical density ratio, and the same for relativistic matter
$\Omega_{rad}$ using its _present day_ density. It is also possible to write
$\Omega_{\Lambda}\equiv\frac{\Lambda}{3H_{0}^{2}}$ and thus
$\Omega_{tot}=\Omega_{m}+\Omega_{rad}+\Omega_{\Lambda}$. The density of matter
$\Omega_{m}$ includes visible and dark matter.

######

The aforementioned primordial perturbations are usually modeled obeying a
power law parametrized by $n_{s}$ as the density spectral index and $A_{s}$ as
the perturbation amplitude. The last parameter used to the fit of the six-
parameter model is $\tau$ being the Thomson scattering optical depth due to
reionization that alters the pattern of CMB anisotropies as it can be seen in
next subsection.

######

It is worth to mention that other cosmological parameters can be deduced from
the above presented like curvature $k$ (or curvature “density”
$\Omega_{k}\equiv\frac{k}{H^{2}a^{2}}$) from Equation 1.13. A non-complete
list of derived parameters includes the age of the universe, the present
horizon distance, the baryon-to-photon ratio and the baryon to dark matter
density ratio.

##### Cosmic microwave background

The cosmic microwave background (CMB) radiation was first detected in 1964 by
Penzias and Wilson [19] and it was soon identified as relic radiation from the
epoch of recombination or photon decoupling, once the protons and electrons
formed neutral atoms. This background radiation measurement was a landmark for
accepting Big Bang model and later it has been a benchmark to test any
proposed cosmological model. The first measurements by Penzias and Wilson
noted a high isotropy and the study and characterizations of the CMB signal
has been increasingly precise revealing anisotropies at $10^{-5}$ level.

######

This anisotropy is usually expressed by using spherical harmonic expansion.
The temperature can be expressed as:

$T(\theta,\phi)=\sum_{\ell m}{a_{\ell m}{Y_{\ell m}}(\theta,\phi)}$ (1.14)

Given this expansion, it is easier to compare the features of the resultant
power spectrum represented as $\ell(\ell+1)\frac{C_{\ell}}{(2\pi)}$ being
$C_{\ell}=\frac{1}{2\ell+1}\sum_{m}{|a_{\ell m}|^{2}}$. The $\Lambda CDM$
predicted power spectrum, with the above described parameters as input
parameters, can be calculated as it can be seen in Figure 1.3. It is worth to
note that the monopole harmonic takes into account the black body spectrum of
the universe giving the mean temperature and the dipole ($\ell=1$) is
interpreted as the result of the Doppler shift caused by the solar system
motion relative to the nearly isotropic black-body field. The power spectrum
has some peculiar features at higher harmonics such as Sachs-Wolfe plateau and
the acoustic peaks [2] also seen in Figure 1.3.

Figure 1.3: Theoretical $\Lambda CMB$ temperature power spectrum. From [2]
using CAMB software [25].

######

In addition to temperature, different polarization modes can show their own
anisotropies and power spectra $C_{\ell}^{E}$, $C_{\ell}^{B}$ and
$C_{\ell}^{TE}$ for E-modes, B-modes and correlations between density and
velocity perturbations at last scattering surface. The B-mode power spectrum
can reveal signatures of gravitational waves [26].

######

The acoustic oscillations arise from the tight coupling of baryons and photons
in the early Universe: the propagation of sound waves through this medium
gives rise to a characteristic scale in the distribution of perturbations
corresponding to the distance traveled by the wave before recombination. This
signal is imprinted in the distribution of both the matter and the radiation.
The latter are seen as anisotropies in the CMB radiation, featuring the
aforementioned acoustic peaks, while the former are the baryon acoustic
oscillations, measured via astronomical surveys such as Sloan Digital Sky
Survey III [27].

##### Cosmic microwave background experimental results

The COBE (Cosmic background explorer) NASA satellite, launched in 1989, was
the first satellite dedicated to such measurements. It was capable to measure
the universe black body spectrum with an unprecedented accuracy and it was the
first experiment to report a faint anisotropy in CMB [28], compatible with
models of inflationary cosmology.

######

A new spacecraft, WMAP (Wilkinson Microwave Anisotropy Probe), was launched in
2001, again by the NASA, with the aim to characterize the COBE hinted
anisotropy. WMAP has played a key role in establishing the $\Lambda CDM$ model
as current standard model of cosmology. The predicted CMB anisotropies by this
model fits with the WMAP experimental data in the previous presented six-
parameter model. In addition with the values of the direct and derived
parameters such as of baryonic, cold dark matter and dark energy [29] the WMAP
data was used to recalibrate the COBE FIRAS spectrometer giving the more
accurate measurement for the black-body spectrum corresponding to a
temperature of $2.72548\pm 0.00057$ K [30].

######

Figure 1.4: Plank CMB temperature anisotropy data and six-parameter model fit
with $\mathcal{D}_{\ell}\equiv\ell(\ell+1)\frac{C_{\ell}}{(2\pi)}$ (From
[31]).

The Planck satellite was launched in 2009 by the European Space Agency [31].
It was designed to improve the sensitivity and the angular resolution and the
fitted cosmological parameter values are the more accurate at the present
time. The CMB temperature anisotropy data and fit can be seen in Figure 1.4.
It shows the temperature power spectrum in both real data and predicted by
$\Lambda CDM$ model showing a very good fit at high multipoles and determining
the acoustic peaks relative amplitude with an excellent accuracy.

######

The extracted values can be seen in Table 1.1 giving, as stated at the
beginning, a $\sim$ 27% of cold dark matter and a $\sim$ 68% of dark energy
[1]. The Planck results, as seen in Table 1.1, have been presented with two
different combinations. The Planck data only using CMB data combined with
lensing is labeled as _CMB+lensing_. The Planck data, in combination with
polarization measured by WMAP, high-$\ell$ anisotropies from experiments like
ACT [32] and SPT [33] and data by baryon acoustic oscillations, described in
previous section, is labeled as _Planck+WP+highL+BAO_. The ACT and SPT data
help to fix the foreground model at high $\ell$ and the low redshift
measurements provided Baryon Oscillation Spectroscopic Survey (BOSS), which is
part of the Sloan Digital Sky Survey III [27], allow to break some
degenaracies still present in Planck data. The combination of these
experiments provides the best constrains to the six-parameter model.

######

Symbol | Planck (CMB+lensing) | Planck+WP+highL+BAO
---|---|---
Fit Parameters: |  |
$\Omega_{b}h^{2}$ | $0.02217\pm 0.00033$ | $0.02214\pm 0.00024$
$\Omega_{cdm}h^{2}$ | $0.1186\pm 0.0031$ | $0.1187\pm 0.0017$
$100\theta_{MC}$ | $1.04141\pm 0.00067$ | $1.04147\pm 0.00056$
$\tau$ | $0.089\pm 0.032$ | $0.0092\pm 0.0013$
$n_{s}$ | $0.9635\pm 0.0094$ | $0.9608\pm 0.0054$
$ln(10^{10}A_{s})$ | $3.085\pm 0.057$ | $3.091\pm 0.025$
Derived Parameters: |  |
$\Omega_{\Lambda}$ | $0.693\pm 0.019$ | $0.692\pm 0.010$
$H_{0}$ (km s-1 Mpc-1) | $67.9\pm 1.5$ | $67.80\pm 0.77$
$t_{0}$ (Gyr) | $13.796\pm 0.058$ | $13.798\pm 0.037$
$100\Omega_{k}$ | $-4.2^{+4.3}_{-4.8}$ | $-0.10^{+0.62}_{-0.65}$

Parameter | Symbol
---|---
Baryon density today | $\Omega_{b}h^{2}$
Cold dark matter density today | $\Omega_{cdm}h^{2}$
100 $\times$ approximation to $r_{*}/D_{A}$ | $100\theta_{MC}$
Scattering optical depth | $\tau$
Scalar spectrum power-law index | $n_{s}$
Primordial perturbation amplitude | $ln(10^{10}A_{s})$
Dark energy density today | $\Omega_{\Lambda}$
Hubble parameter | $H_{0}$
Age of the universe | $t_{0}$
Curvature “density” | $100\Omega_{k}$

Table 1.1: Cosmological parameters derived from Planck measurements. From [1].

A derived parameter from the fit parameters is the curvature “density”,
$\Omega_{k}$, fully compatible with a flat universe ($k=0$). The Planck
results also establish other constrains for different aspects of the $\Lambda
CDM$ like tensor-to-scalar ratio or inflation models [34]. Tensor-to-scalar
ratio is an important parameter for extensions to $\Lambda CDM$ including
gravitational waves. This parameter has claimed to be measured by BICEP2
collaboration [35] measuring B-mode polarization although an incorrect
foreground estimation could jeopardize the result [36].

#####  $\Lambda CDM$ simulations

A set of simulations based on the $\Lambda CDM$ properties has been performed
taking advantage of the models and data described earlier. These simulations
can be very useful for trying to describe the dark matter distribution in the
clusters and galaxies. At the galactic scale the results of the simulations
hint to clumpsy haloes with streams components [37]. Further gravitationally-
only interacting N-body simulations such as Aquarius [38] or Via Lactea II
[39] increased the resolution of Milky Way sized simulations and they give
hints to indirect dark matter searches [40].

######

These simulations can also be used as a crosscheck of the data of the
observable universe through a post-processing procedure known as semi-analytic
modeling. The modeling involves simple physical prescriptions over the N-body
simulation results to estimate the distribution of galaxies [41, 42].

######

Recent simulations have been carried out using a more complete hydrodynamical
approach taking into account baryonic matter from the beginning trying to
offer self-consistent and predictive approach. The Illustris project has
reproduced in such a way, with a large scale simulation, mixed populations of
elliptical and spiral galaxies [43]. The simulated spiral galaxies agree with
many observational parameters exhibiting an almost flat rotational velocity
profile [44] among other features of real galaxies. However, the simulation
does not reproduce some observational parameters such as the steep slope and
small scatter of the baryonic Tully-Fisher relation found by McGaugh [45] but
it gives more realistic results than previous simulations.

#####  $\Lambda CDM$ challenges

$\Lambda CDM$ model appears to be very successful in predicting the CMB and
large-scale structure but it is fair to note that there are still open
questions. From the astrophysical point of view it is not able to explain the
observed rotation curves of all dwarf and low surface brightness (LSB)
galaxies [46] .

######

Other remarkable issues are the weak agreement at low multipoles with the
$\Lambda CDM$ predictions, the so-called _cold-spot_ (a region of significant
temperature decrement, far from statistic fluctuation) [47] and the primordial
lithium problem [48]: the abundance of 7Li is far below (2-3 factor) of the
predictions of big bang nucleosynthesis together with cosmic baryon density
coming from CMB anisotropy fits. These anomalies, confirmed by WMAP and Planck
measurements, need $\Lambda CDM$ refinement or physics beyond the standard
models.

##### Summary

It can be concluded as a result of the cosmological observation and models
that: [itemize] & The universe is almost homogeneous and it is expanding at an
accelerating rate. The accelerated expansion is “explained” via cosmological
constant and a consequent dark energy ($\sim$ 68%). The universe has a large
amount of non-baryonic, beyond the standard model, cold dark matter ($\sim$
27%).

####  1.1.4 Alternatives to dark matter

The need of dark matter has been questioned by models that have tried to
explain the observed anomalies in an alternative way by modifying gravity
laws. The most promising models have been MOND (modified Newtonian dynamics)
and its relativistic version TeVeS (tensor–vector–scalar gravity) [49]. MOND
was proposed as a correction to Newtonian gravity by modifying the predicted
acceleration at small values of gravitational force giving acceptable fits for
rotational velocity of galaxies [50] and predicting some observational
parameters such as the baryonic Tully-Fisher relation [45].

######

The theory was challenged by the dark matter hints at all scales. TeVeS has
been capable to explain effects such as strong gravitational lensing and some
of the features of the CMB anisotropy but in an incomplete way giving
inaccurate predictions about the weak gravitational lensing effect and the
ratio between acoustic peaks in CMB temperature power spectrum [49, 51]
without the addition of cold dark matter. For these reasons and for its
consistency with general relativity the $\Lambda CDM$ model is the most widely
accepted cosmological model.

###  1.2 Dark matter candidates

Dark matter candidates have to exhibit several properties in order to match
with the models and data described earlier. Candidates for non-baryonic dark
matter have to be weakly interacting with ordinary matter (otherwise they
wouldn’t qualify as _dark_ matter), non-relativistic at the onset of galaxy
formation, massive and stable or very long lived on cosmological time scales
(otherwise they would have decayed by now) [51].

######

The most obvious candidate (partially) fulfilling these conditions is the
neutrino, having “the undisputed virtue of being known to exist” [52] but
cosmological observations and simulations are incompatible with neutrinos as
unique dark matter component, as seen in the previous section. These facts
force the need of candidates beyond the standard model of particle physics
(BSM).

######

Candidates fulfilling the expected properties include axions, sterile
neutrinos and weakly interacting massive particles (WIMPs). These are _well
motivated candidates_ because they are proposed to solve problems in principle
unrelated to dark matter and whose properties can be computed within a well-
defined particle physics model. Primordial black holes, a frequently cited
candidate, have been ruled out as primary dark matter constituent in an
extremely wide range of masses by a variety of searches and constrains [53].

######

Axions were proposed by Peccei and Quinn to resolve the strong CP problem in
quantum chromodynamics explaining the lack of measured broken CP-symmetry in
strong interactions [54]. Several constrains from experiments and
astrophysical observations give an axion mass less than $3\times 10^{-3}$ eV
still enough to be a suitable cold dark matter candidate [55].

######

Sterile neutrinos are proposed neutrinos without any interaction with other
particles except through gravity solving the lack of observed right handed
neutrinos [56]. Due to their predicted collisionless and long lived nature,
they are candidates to dark matter. The Plank data also establish constrains
to their masses [1].

######

Weakly interacting massive particles (WIMPs) are hypothetical particles that
interact with standard model particles via weak nuclear force (or another
interaction similar in strength). The fact that annihilation cross-section at
electroweak scales gives the appropriate relic abundance [57] has been seen as
a major reason to highly consider WIMPs as dark matter candidate. Another
strong reason to consider WIMPs is the natural emergence of this kind of
particles in supersymmetric theories. Supersymmetry (or SUSY) is a
hypothetical space-time symmetry that allows to link matter particles and
force carriers and also link gravity with the other fundamental interaction
solving the hierarchy problem [58]. The introduction of such a symmetry to
extend the particle standard model (SM) predicts the existence of new
particles. The simplest supersymmetry extension to SM, called minimal
supersymmetric standard model (MSSM), gives naturally _superpartners_ for
every SM particle: every fermion has a boson partner and every boson has a
fermion partner. The lightest _superparters_ have properties to be the non-
baryonic dark matter particle such as the neutralino or, including gravity in
the model, the gravitino [59].

######

These WIMPs beyond the standard model (BSM) could be produced at colliders
[60] such Large Hadron Collider (LHC). Other alternative theories, like extra
dimension theories, also predict new particles BSM with distinguishable
features. These alternatives gives different spin or number of _superpartners_
[61] to the expected new particles. These searches have been performed at
accelerators with negative results for the moment. No hints of physics beyond
the standard model have been observed and cross section limits have been
established by Tevatron CDF [62] with $p\overline{p}$ collisions and LHC CMS
[63, 64] and ATLAS [65, 66, 67] experiments with
$pp\rightarrow\chi\tilde{\chi}+X$ being $X$ a hadronic jet, photon or $W$ or
$Z$ bosons.

######

There are many efforts to detect and characterize dark matter. Direct
detection aims to recover information about the WIMPs measuring their
scattering with ordinary matter. Other complementary information about dark
matter can be obtained by detecting secondary products of self-annihilation or
decay of dark matter particles. These by-products are searched by indirect
detection experiments. In the next subsections both indirect and direct
detection techniques are covered.

###  1.3 Indirect dark matter detection

Despite being stable or very long lived particles, dark matter constituents
could decay and despite their weak interacting nature they could self-
annihilate originating ordinary matter (see [68] for an early reference and
[69] for a recent review). Indirect searches try to detect an excess of
ordinary particles not explained by other known physical mechanism.

######

The case of gamma-ray products is particularly interesting because of their
directionality: it can give hints about dark matter decays if diffuse emission
is detected where background is less intense and annihilation should come from
the center of the galaxies, where dark matter density must be higher [70].
These type of products could be detected by Cherenkov telescopes or by space
telescopes. Current data taking Cherenkov telescopes like HESS [71], MAGIC
[72] or VERITAS [73] have not found any excess attributable to self-
annihilation coming from analyzed galaxies. The future CTA (Cherenkov
Telescope Array) could greatly improve the sensitivity in this search [74].
Fermi-LAT space telescope data have been claimed to contain a 130 GeV line
that could be interpreted as a result of WIMP annihilation [75] but further
analyses by Fermi-LAT collaboration disfavor this interpretation [76].

######

Neutrinos can also be used as signature from dark matter annihilation. The
source of this annihilation can be the center of the galaxy or the Sun. The
center of the galaxy has to have a higher density of dark matter and the Sun
could scatter WIMPs and bound them gravitationally giving a signature of high
energy neutrinos [77]. None of these two effects has been detected by IceCube
neutrino telescope [78, 79].

######

The presence of cosmic antimatter could also be a signature of dark matter
annihilation [80]. Unexplained excess in positrons have been observed by
several experiments: PAMELA [81], Fermi-LAT [82], and AMS-01 [83] among
others. The new results for AMS-02 are inconclusive about the end of the
positron spectrum that could be attributed to the total mass of the dark
matter particle in its self-annihilation [84].

###  1.4 Direct dark matter detection

As it has be seen before, the dark matter candidates more suitable for their
direct detection are axions and WIMPs. The detection of the axion has been
proposed to be through the inverse Primakoff effect [85], in which the axion
is converted into a photon in presence of macroscopic magnetic fields. There
have been experiments searching axions with photon regeneration technique
(“shining light through a wall”) [86], from galactic origin [87], and produced
in the Sun [86], all with negative results. A more sensitive helioscope (IAXO)
has been proposed in order to continue the axion searches [88].

######

The Weakly Interacting Massive Particle (WIMP) has been regarded as a very
well-motivated candidate because its existence would give the appropriate
relic abundance as well as its natural emergence from SUSY models as seen
above. The idea of their direct detection relies on the elastic scattering of
the WIMPs with the detector nuclei giving a tiny energy deposition with low
rate of interactions (see [89] and references therein). For this reason, a
detector devoted to these searches has to have very low energy threshold and
low radioactive background.

####  1.4.1 WIMP detection rate

The rate for WIMP elastic scattering off detector nuclei can be expressed as
[90]:

$\frac{dR}{dE_{R}}=N_{N}\frac{\rho_{0}}{m_{W}}\int_{v_{min}}^{v_{max}}f(\textbf{v})\,v\,\frac{d\sigma_{WN}}{dE_{R}}d\textbf{v}$
(1.15)

being $N_{N}$ the number of target nuclei, $m_{W}$ the WIMP mass, $\rho_{0}$
the local WIMP density in the galactic halo, v and $f(\textbf{v})$ the WIMP
velocity and velocity distribution in Earth reference frame and
$d\sigma_{WN}/dE_{R}$ the WIMP-nucleus differential cross-section. The energy
transferred to the recoiling nucleus is:

$E_{R}=\frac{p^{2}}{2m_{N}}=\frac{m_{r}^{2}v^{2}}{m_{N}}(1-cos\theta)$ (1.16)

where $p$ is the momentum transfer, $\theta$ is the scattering angle in WIMP-
nucleus center-of-mass reference frame, $m_{N}$ is the nuclear mass and
$m_{r}$ is the WIMP-nucleus reduced mass
($m_{r}=\frac{m_{N}m_{W}}{m_{N}+m_{W}}$). The minimum velocity needed to
produce a recoil of $E_{R}$ energy is:

$v_{min}=\sqrt{\frac{m_{N}E_{R}}{2m_{r}^{2}}}$ (1.17)

and the maximum velocity is given by the escape WIMP velocity in the Earth’s
reference frame. The rate of detected interactions depends on several
parameters from particle physics and nuclear physics to astrophysics. These
parameters must be investigated in order to recognize patterns for a possible
positive signature of detection.

######

Particle and nuclear physics can give inputs and constrains to some of the
aforementioned parameters. In particular, WIMP mass and interaction strength
can be loosely constrained given the largely different values predicted by
different _beyond the standard model_ theories. The WIMP-nucleus differential
cross-section encodes particle physics inputs (with many uncertainties)
including WIMP interaction properties. It depends on the WIMP-quark
interaction strength, which is calculated from the microscopic description of
the model, and it is later promoted to WIMP-nucleon cross-section. The
calculation of WIMP-nucleus cross-section needs the use of the hadronic matrix
elements, which describe the nucleon content in quarks and gluons, introducing
large uncertainties. In the case of spin-1/2 or spin-1 WIMP field, the WIMP-
nucleus cross-section can be separated as a sum of a spin independent (SI) and
a spin dependent (SD) terms:

$\frac{d\sigma_{WN}}{dE_{R}}=\left(\frac{d\sigma_{WN}}{dE_{R}}\right)_{SI}+\left(\frac{d\sigma_{WN}}{dE_{R}}\right)_{SD}=\frac{m_{N}}{2m^{2}_{r}v^{2}}\left(\sigma^{SI}_{0}F^{2}_{SI}(E_{R})+\sigma^{SD}_{0}F^{2}_{SD}(E_{R})\right)$
(1.18)

where $F(E_{R})$ are the nuclear form factors that encode the momentum
transfer and depend on the recoil energy. $\sigma_{0}^{SI,SD}$ are the WIMP-
nucleon cross-sections in zero momentum transfer limit. They can be expressed
as:

$\displaystyle\begin{split}\sigma^{SI}_{0}=\frac{4m_{rn}^{2}}{\pi}\left(Zf_{p}+(A-Z)f_{n}\right)^{2}\\\
\sigma^{SD}_{0}=\frac{32m_{rn}^{2}}{\pi}G^{2}_{F}\frac{J+1}{J}\left(a_{p}\langle
S_{p}\rangle+a_{n}\langle S_{n}\rangle\right)\end{split}$ (1.19)

with $G_{F}$ being the Fermi coupling constant, $m_{rn}$ the nucleon-WIMP
reduced mass, $f_{p,n}$ and $a_{p,n}$ the effective WIMP coupling to protons
and neutrons in spin-independent and spin dependent, respectively. $\langle
S_{p,n}\rangle$ are the expectation values of proton and neutrons spin
operators in the limit of zero momentum transfer, and it can be determined
using detailed nuclear model calculations.

######

The astrophysics input is also subject to uncertainties [91, 92]. In
particular, WIMP velocity distribution $f(\textbf{v})$ and local dark matter
density $\rho_{0}$ will translate their uncertainties into the predicted event
rate. The velocity distribution is usually modeled with the so-called standard
halo model describing an isotropic, isothermal sphere of collissionless
particles with density profile $\rho_{r}\propto r^{-2}$ and a Maxwellian
velocity distribution. Other halo models use a multivariate Gaussian velocity
distribution that is in better agreement with simulations at galaxy scales
[93] but due to the spatial resolution of this simulations the structure at
local scale is still an open issue. From the experimental point of view, the
GAIA satellite [94] data will largely improve the knowledge of the dark matter
distribution in the Milky Way. For a recent review of the local dark matter
density from simulations to current experimental data and future prospects see
[92].

######

Some signatures in the detected signal can be predicted given the previous
input parameters. In particular, the shape of the recoil energy spectrum
greatly differs with the WIMP and nucleus mass ratio. Taking into account the
Equation 1.16 some extreme scenarios can be explored: $m_{W}<<m_{N}$ gives
$E_{R}\propto m_{W}^{2}$ but $m_{W}>>m_{N}$ shows an energy spectrum
independent of the WIMP mass. The WIMP mass can be more accurately determined
when its mass is comparable with the target nucleus and using different
targets with different nucleus mass can help in providing better constrains on
$m_{W}$ [95]. Anyway, the expected recoil spectrum will have a shape $\propto
e^{-E_{R}}$ for the standard halo model [96].

######

Other very important expected signature is the so-called annual modulation,
i.e. a seasonal variation of the total event rate [97, 98]. This signal arises
because of the Earth’s motion in the galactic rest frame. This motion is a
superposition of Earth’s rotation around the Sun and the Sun’s rotation around
the galactic center. Considering the standard halo model, the amplitude of the
modulation will be small taking into account the ratio between velocities (of
the order of $v_{orb}/v_{c}\simeq 0.07$ being $v_{orb}$ the Earth’s orbital
speed and $v_{c}$ the Sun’s circular speed). Following this model the
differential rate can be approximated to:

$\frac{dR}{dE_{R}}(E_{R},t)\simeq\frac{dR}{dE_{R}}(E_{R})\left[1+\Delta(E_{R})\mathrm{cos}\frac{2\pi(t-t_{0})}{T}\right]$
(1.20)

where the period $T$ = 1 year and the phase is $t_{0}$ = 150 days.
$\Delta(E_{R})$ is positive for high energy recoils and it becomes negative
for small values. This feature implies a modulation phase change: the peak
rate is in winter for small recoil energies and in summer for larger recoils
[99]. The energy at which the phase changes is commonly referred as crossing
energy and it can be used to determine the WIMP mass [100], although this
technique will require an ultra-low energy threshold. The previous analyses
have been performed with the standard halo model. The effect in the annual
modulation for non-standard haloes has been also explored. Introducing the
effect of a dark disk gives a second low energy maximum in the amplitude of
the modulation and a significant phase change [101]. The effect of a dark
matter stream can also affect the shape of the modulation introducing some
non-cosine effects at some energies [102, 103].

######

A stronger signature would come from the ability to detect the axis and
direction of the recoiling nucleus. The direction of the dark matter should
vary in the laboratory reference frame with the motion of the Earth through
the Galaxy and pointing in the direction of the motion of the Sun, to the
Cygnus galaxy. Therefore the recoils should peak in the opposite direction
[104]. The experimental challenge is to build massive enough detectors
sensitive to the direction of the incoming WIMP.

####  1.4.2 Background sources

Minimizing and characterizing the background noise is a necessary and very
challenging task for a WIMP detector due to the expected signal detection
rates [89]. Low background techniques are used in order to achieve as much
sensitivity as possible to the previously described signatures [105]. The main
contributions to this background come from the environmental radioactivity,
the cosmic rays and their secondaries and activation at Earth surface of the
detector materials. Other more subtle but potentially harmful sources are
intrinsic activity of the detector materials and muon induced neutrons. The
ultimate limit in the background will come from the neutrino flux and will
start to play an increasing important role in future experiments because of
its irreducibility.

######

The cosmic rays background can be highly reduced by locating the detector
underground. The hadronic component becomes negligible by tens of meters water
equivalent overburden, but muon flux is more difficult to attenuate producing
high energy fast neutrons. These neutrons can produce keV nuclear recoils in
elastic scatter with detector nuclei [106]. Thus, active veto detectors are
necessary to reduce background by tagging the original muon or its associated
cascade. The muon flux underground also has seasonal variations of amplitude
[107]. To avoid the induced muon signal mimicking a possible WIMP signature is
an additional reason to keep muon flux under control. Other measures such as
passive gamma and neutron shieldings are needed to isolate the detector from
the environmental background. This shielding is typically flushed by boiled-
off $N_{2}$ in order to suppress airborne radon decays.

######

The internal background of the detector materials is a very dangerous
contribution to the sensitivity. The neutron spectra coming from natural
chains can be calculated by measuring the amount of ${}^{238}U$ and
${}^{232}Th$. The signal of these neutrons may be difficult to distinguish
from a potential WIMP signal [108]. Other sources of intrinsic internal
background of some WIMP targets include ${}^{39}Ar$, ${}^{85}Kr$ and
${}^{40}K$. In addition to these contributions, the decay of long lived
isotopes produced by cosmic rays in target and detector materials during their
exposure at Earth’s surface, known as cosmogenic radionuclides, can be a
relevant and harmful fraction of the total background.

######

Additionally to the use of shielding and radiopure detectors the use of
particle discrimination can be very useful to reduce the background. In
particular, the ability of perfectly distinguish nuclear from electronic
recoils could separate all $\gamma/\beta$ background from neutron and WIMPs
contribution, with a great background improvement.

######

####  1.4.3 Direct detection techniques, current status and future prospects

To observe a WIMP-induced spectrum a low energy threshold, an ultra-low
background noise and a large target mass are mandatory. A detector must
convert the scattered nucleus kinetic energy to a mensurable signal such as
ionization, scintillation light or heat. The simultaneous detection of two
different channels of energy conversion gives a powerful discrimination
against background events by determining the nature of the incident particle.

######

The experimental search for the dark matter started in the 1980s profiting the
underground facilities and the low background techniques developed for the
search of the neutrinoless double beta decay. The first relevant experimental
result was to discard heavy standard Dirac neutrinos as candidate to cold dark
matter using $Ge$ detectors [109]. In the 1990s, NaI scintillators started to
be used given its ability to be sensitive to spin-dependent interactions and
the feasibility of growing big mass crystals. More recently, the solid-state
and noble gases detectors have been the most massive and sensitive
experiments, as we will see later. The comparison of the main recent
experimental results in the latest years (solid lines) and prospects (dashed
lines) can be observed in Figure 1.5 in terms of exclusion plots in the cross-
section/WIMP mass space for spin-independent interaction, including the
regions singled out by the DAMA/LIBRA positive signal.

Figure 1.5: Spin independent exclusion plot with current measured better
limits (in pink), current experimental individual results (solid lines) and
prospect projections (dashed lines). From [110].

######

Solid-state cryogenic detectors operated at sub-Kelvin temperatures have been
the most traditional detectors devoted to the direct dark matter detection due
to their low threshold ($<$ 10 keV), excellent resolution ($<$ 1% at 10 keV)
and the ability to discriminate nuclear from electronic recoils [111]. CDMS
collaboration has run several experiments consisting of semiconductors
operated at 40 mK. During 2003-2008 CDMS-II consisted of 4.6 kg of $Ge$
detectors and 1.2 kg of $Si$ detectors reporting an excess of three events in
the $Si$ detectors [112] and no excesses nor modulation in the $Ge$ detectors
[113]. The following experiment upgrade at SOUDAN underground laboratory with
9 kg of new designed $Ge$ detectors, SuperCDMS, has presented data analysis
lowering the previous exclusion limits [114]. The same collaboration has also
run another experiment CDMSLite. It takes advantage of the Luke-Neganov
amplification of the phonon signal but without discrimination between
electronic and nuclear recoils, however it lowers the threshold excluding more
low-mass WIMP parameter space [115]. The next upgrade of SuperCDMS at SNOLAB
will have around 100 Kg of germanium and 10 Kg of silicon detectors [116].

######

The EDELWEISS experiment is also a cryogenic germanium detector measuring
ionization and phonon signal. The EDELWEISS-II upgrade consisted of 4 kg of
$Ge$ detectors finding an excess of five events with an estimate of three
[117]. The same set-up was used to explore the low-mass WIMP parameter space
[118]. The next upgrade called EDELWEISS-III [119] will consist of forty
detectors with improved technology and radiopurity accounting 24 kg of
fiducial mass.

######

The CRESST collaboration has designed and operated several cryogenic detectors
with simultaneous phonon and photon detection. The CRESST-II experiment
consist of eight detector modules of 300 g each reporting sixty-seven events
in the nuclear recoil region [120] not explained by known backgrounds. The
last results of CRESST-II including a new detector design have not confirmed
the aforementioned excess [121]. This collaboration has planned to merge with
EDELWEISS collaboration to perform a high scale cryogenic experiment called
EURECA [122].

######

Germanium ionization detectors operated at 77 K can reach sub-keV energy
threshold and low backgrounds [123] but without the ability of distinguish
electronic from nuclear recoils. This type of experiments includes CoGeNT
[124], TEXONO [125], MALBEK [126] and CEDEX [127]. Unlike the other p-type
point-contact germanium experiments, CoGeNT has reported the presence of an
annual modulation in the event rate [124, 128] but it is worth to mention that
recent analyses result in contradictory conclusions [129, 130, 131].

######

Liquid noble elements can be used for building self-shielding detectors.
Liquid Xenon (LXe) and liquid Argon (LAr) are good scintillators and ionizers
in response to radiation. The simultaneous scintillation and ionization
detection allows to identify the primary interacting particle in the liquid.
In addition, the 3D position of an interaction can be determined in a time
projection chamber (TPC). These features, together with the relative ease of
scale-up to large masses, have contributed to make LXe and LAr powerful
targets for WIMP searches [132] giving the most stringent limits to spin-
independent couplings as it can be seen in Figure 1.5. The LUX experiment, a
double phase liquid/gas $Xe$ TPC experiment at Sanford Underground Research
Facility, has currently set the best limits in the high WIMP masses zone with
data corresponding to 85.3 live days with a fiducial volume of 118 kg [133].
Other $Xe$ TPC with a good experimental limit is XENON100 [134]. Some ton or
multiton-scale Xe TPC experiments have been proposed [89] some of them such as
XENON1T [135] in commissioning stage. In addition to $Xe$ experiments, some
LAr experiment are taking data. DarkSide-50 has presented the first results
[136] reporting the presence of cosmogenic ${}^{39}Ar$ and considering the use
of underground $Ar$ with a factor 150 of ${}^{39}Ar$ below atmospheric argon.
ArDM, a double phase $Ar$ TPC experiment is currently taking data at the
Canfranc Underground Laboratory (LSC) [137].

######

Studying spin-dependent channel requires target nuclei with uneven total
angular momentum. A very favorable candidate is ${}^{19}F$ exhibiting a cross-
section a factor ten above the other used nuclei because of its unpaired
proton. This target is present in WIMP detectors using superheated liquids
composed of $C_{4}F_{12}$, $CF_{3}I$ or $C_{2}ClF_{5}$. An energy deposition
can move the system from its metastable state forming bubbles that can be
detected both acoustically and optically. The temperature and pressure of the
detector can be adjusted to lead to the formation of bubbles only for nuclear
recoils given the fact that the threshold to produce bubbles depends on a
_critical energy_ deposited within a _critical radius_ , both dependent on
pressure and temperature [138]. Additional discrimination of nuclear recoils
from alpha particles has been developed using the acoustic signal [139].
Several low target mass experiments have been carried out. PICASSO [140]
consisted of $C_{4}F_{10}$ droplets in 4.5 liters of polymerized emulsion with
a total mass 0.72 kg of ${}^{19}F$ and an exposure of 114 kg-day without
positive result. COUPP-4 [141] consisted of 4 kg of $CF_{3}$ for an effective
exposure of 437.4 kg-day lowering the exclusion limits except in the low mass
region. Both collaborations joined efforts in a new PICO collaboration.
Results from COUPP-60, a 40 liter $CF_{3}I_{4}$ update of COUP-4, and PICO2L,
a 2-liter $C_{3}F_{8}$ chamber currently running at SNOLAB, are expected in
the short term [142]. PICO-250L [142] will be an experiment in the ton-scale
range of target mass. Another technique being explored for this type of
detectors is the geyser technique [143] that could eventually be applied in
the MOSCAB experiment.

######

Scintillation radiation detectors have been also used in the search of dark
matter from the 1990s as seen earlier. DAMA/LIBRA, a 250 kg Thallium doped
Sodium Iodine experiment, has observed an annual variation of _single-hit_
events with a total exposure of 1.33 ton$\times$year (combining the results
with the previous phase of the experiment, DAMA/NaI), corresponding to 14
annual cycles and a statistical significance of 9.3 $\sigma$ in the 2-6 keV
energy window [3, 4, 5]. In Figure 1.6 it can be seen the seven cycles
corresponding to the DAMA/LIBRA-phase1 set-up. The modulation is not present
at higher energy regions or in coincidence (_multiple-hit_) events.

Figure 1.6: DAMA/LIBRA residual rate of _single hit_ scintillation event in
the 2-6 keV energy window. From [5].

######

The difficulty to find dark matter candidates explaining all experimental
results [144], the dependence on WIMP and halo models considered to compare
different targets [145] along with the uncertainties in nuclear recoil
calibration (see Section 1.5) and the partial understanding of experimental
backgrounds at low energy [146, 147, 148, 149, 150] make highly interesting
confirming the DAMA/LIBRA annual modulation in a model independent way. The
need for this confirmation, with the same target and technique, lead to
several groups to perform large mass NaI(Tl) experiments: ANAIS [151], DM-Ice
[152] and KIMS [153]. KIMS group already carried out an experiment with 103.4
kg of CsI(Tl) scintillators with 25 ton$\times$day exposure and without any
signal of annual modulation [154].

###  1.5 NaI(Tl) as target for WIMP searches

The first feature to be aware for the use of NaI(Tl) for measuring nuclear
recoils is the relative efficiency factor or quenching factor, usually denoted
by Q. The quenching factor is defined as the relative light yield of nuclear
recoils (the expected WIMP interaction, see Section 1.4.1) and electronic
recoils. It is well known that different interacting particles with different
interaction mechanism produce different amount of light for the same recoil
energy. The Q value has been measured giving $\sim$ 0.3 for Na recoils and
$\sim$ 0.1 for I recoils [155, 156]. New measurements pointed Q energy
dependence and a slight increase at low energies [157, 158], however recent
measurements have been presented showing lower values for Na recoils in the
low energy range and a strong energy dependence [159].

######

The NaI(Tl) detectors are usually calibrated with X-ray and gamma sources
using their photopeaks, or peaks in the spectrum created by the total
absorption of the photon energy. In order to not include the aforementioned Q
uncertainties, these calibrations are usually expressed in electron equivalent
energies (keVee or sometimes only keV).

######

These uncertainties have a major impact in the interpretation of a NaI(Tl)
experiment because the energy and the energy threshold are expressed in
electron equivalent energy. The impact of such uncertainties in the expected
rate of WIMPs has been studied [160] as can be seen in Figure 1.7. The
quenching factor also has a key role in the comparison of NaI results with
other experiments with different target and technique.

(a)

(b)

(c)

(d)

Figure 1.7: Expected WIMP rates (left) and modulation amplitude (right) with
NaI target using 10 GeV (top) and 50 GeV (bottom) as WIMP mass and
$\sigma_{SI}=10^{-5}pb$. From [160].

######

As a result of the study seen in Figure 1.7 the expected rate for the
amplitude of the annual modulation is lower than 0.05 count/(keVee kg day)
above 1 keVee. It also illustrates the importance of a threshold as low as
possible and the need for a clean background that does not mask such a subtle
effect.

######

Other NaI(Tl) feature to take into account is the pulse shape discrimination.
Different interacting particles have different pulse shape (see [161] for
example). However, the different shape can not be used as discrimination
technique at low energies [156, 162]. Without discrimination, the background
at low energy must be as clean as possible because of their
indistinguishability from nuclear recoils. Hence, K-shell electron binding
energy following electron capture in 40K (3.2 keV) and 22Na (0.9 keV) adding
counts to low energy are harmful for a NaI(Tl) experiment.

######

Once reviewed the context of the ANAIS experiment, the experiment itself is
presented in the next chapter.

##  Chapter 2 The ANAIS experiment

The ANAIS (Annual modulation with NaI Scintillators) experiment is intended,
as stated in the previous chapter, to search for dark matter annual modulation
with ultrapure NaI(Tl) scintillators in order to provide a model-independent
confirmation of the signal reported by the DAMA/LIBRA collaboration using the
same target and technique. It will consist of more than one hundred kilograms
of NaI(Tl) and it will be conducted at the Canfranc Underground Laboratory
(LSC) in Spain.

######

The ANAIS experiment will be the conclusion of a large series of previous
efforts dating back to the mid-nineties. The NaI32 [163, 164, 165] experiment
searched for dark matter at the LSC with NaI detectors. It used three BICRON
hexagonal detectors operated and stored in underground since the late
eighties. This experiment, amounting 32.1 kg of target mass, accumulated two
years of data taking (1993-94). Bounds of WIMP masses and cross-section were
established given the absence of positive signal, neither in total rate nor in
a pioneer modulation analysis.

######

One of these detectors was modified and it was used to build the ANAIS
prototype I [166], and, after decoupling the photomultiplier and removing the
original encapsulation it was used in ANAIS II [167] and III prototypes. The
main result of the study of these prototypes was the measurements of the
potassium content [168] of the bulk crystal being too high for a dark matter
experiment. A new crystal was tested: a 9.6 kg NaI(Tl) parallelepipedic module
bought to Saint Gobain, with the same shape and size of DAMA/LIBRA crystals
[169], named ANAIS-0. Again, the result of the potassium content was too high
to use it in an experiment devoted to search dark matter annual modulation
[160, 168]. Nevertheless, many technical aspects of the set-up and the study
of these prototypes were used in the set-up, taking data and data analysis of
the next prototypes.

######

Several providers of purified NaI powder were contacted and several samples
were analyzed in order to have a clean starting material [160]. Alpha Spectra
company [170] provided a sample with low potassium content compatible with the
background of the GIFNA HPGe test bench at LSC. Two modules were purchased for
quality assessment in both radiopurity and light collection quality. These
detectors formed the ANAIS-25 set-up described in Section 2.3 featuring an
acceptable content in ${}^{40}K$ but a high ${}^{210}Pb$ contamination. The
origin of such a contamination was identified at purification and growing
processes and a new module was incorporated later to form ANAIS-37 set-up (see
Section 2.4). The reduction of the Pb content was checked in addition to the
reproducibility of the previous properties such as the excellent light
collection and potassium content.

######

Once successfully tested the last module and having good sensitivity prospects
(yet conservative, see Section 2.5) based on the measured backgrounds, the
steps towards the ANAIS full experiment have being started. The phase-I will
consist of nine modules accounting more than 100 kg of ultrapure NaI(Tl) and
it is expected to be fully commissioned along 2016. The ANAIS experimental
set-up is described in Section 2.2.

###  2.1 ANAIS experimental requirements

The expected signal of an annual modulation is subtle and the region of
interest is at very low energies as described in Section 1.5. The rates are
low and the annual modulation is expected to be less than a 10% of the total
rate (of the order of 0.05 count/(keVee kg day) above 1 keVee).

######

For these reasons, a threshold as low as possible is desirable, any noise near
this threshold must be avoided and enough exposure to have statistical
significance is required. Another very important requirement is stability.
Since the experiment must take data for several annual cycles, the conditions
under which these data has been acquired have to be as stable as possible.

######

These requirements, especially a low energy threshold, high exposure and
stability are the framework in which the present work has been developed,
having to fulfill them as a primary goal.

####  2.1.1 Low energy threshold

The energy threshold depends on some experimental aspects like the light
collection efficiency and the hardware triggering strategy. The light
collection efficiency is marked by the optical quality of the crystal and
other optical components such as quartz windows, optical couplings and
photomultiplier (PMT) quantum efficiency. The low energy events and their
conversion into electrical signal throughout PMTs are covered in Chapter 3 and
light collection of the Alpha Spectra modules is analyzed in Section 8.6. The
hardware trigger efficiency at low energy has been studied in Section 8.7.

######

On the other hand, the triggering strategy must ensure the storage of all
relevant events but without a high rate that could increase the dead time.
This is achieved by coupling two PMTs to each crystal and triggering with the
coincidence of the two PMT signals. Due to the nature of the low energy
events, consisting on few separate photons, the trigger must be performed at
photoelectron level. The trigger modules tests are presented in Section 4.5.4
and the trigger at photoelectron level was evaluated in Section 8.5.1. The
trigger can be affected by electric noises at such low level and for this
reason a baseline characterization and improvements were performed and are
described in Section 4.5.5.

####  2.1.2 Low background at low energy

The region of interest for the WIMP annual modulation in our detectors is
below 6 keV. The known background must be kept as low as possible in this
region. Hence, an ultrapure NaI powder must be used, a careful crystal growing
and detector manufacturing and a very thorough selection of external radiopure
materials must be done [160]. In particular, the contamination of 40K and 22Na
can be especially relevant because the K-shell electron binding following an
electron capture are 3.2 keV and 0.9 keV respectively.

######

In addition to internal background, it is important to shield and control the
possible influence of the external background. The passive shielding will
consist of lead, boron-loaded water and polyethylene. An anti-radon box will
keep the system tightly closed and flushed with boil-off Nitrogen. These
techniques to avoid external background are described in Section 2.2.

######

Another relevant external background is the contribution of cosmic rays. For
this reason, an underground experiment is mandatory and ANAIS will be carried
out at the LSC. Anyway, a residual muon flux still survives the rock
shielding. This flux can produce other particles, such as neutrons, in the
shielding or the detector contributing to the low energy region. An active
muon veto system is used to tag muons using plastic scintillators to reject
these potentially harmful events. This system is described and characterized
in Chapter 5.

####  2.1.3 Stability

A very important experimental aspect in an annual modulation search is the
stability of the environmental and experimental parameters. The data will be
taken for several annual cycles and the conditions under which they are taken
must be as stable as possible. It is mandatory to check any seasonal variation
that could affect to any key experimental aspect: gain, threshold or
efficiency for example. Therefore, all relevant environmental and external
parameters must be monitored in order to detect and report any anomaly and
store data to allow correlation with detector data. This slow control system
and the stability of the environmental parameters are described in Chapter 9.
This chapter also covers the test of the stability of the data acquisition
parameters such as the gain, the trigger level and the coincidence window. The
stability of the real time clock and comparisons with the system time via
Internet (NTP system) is reviewed in Section 8.1.

####  2.1.4 Exposure maximization

Another reason to require stability and robustness to the system is to
maximize the exposure (see Section 2.5). When the target mass is fixed, the
exposure is marked by the effective measurement time, or _live time_. Hence,
the system has to maintain the dead time, the time after each event during
which the system is busy and it is not able to record another event due to the
acquisition process; the down time, maintenance or system malfunction time; or
bad experimental conditions, due to ambient radon inside the shielding,
electric noise, etc., as minimum as possible. A study about the dead time of
the experiment and the strategies to keep it controlled can be seen in Section
8.2 and collected statistics of live time, dead time and down time from the
latest prototypes are presented in Section 8.3.

###  2.2 ANAIS experimental set-up

The experimental set-up for the full ANAIS experiment has been designed taking
into account the aforementioned experimental requirements and the experience
of the previous prototypes.

######

The target mass will consist of nine ultrapure 12.5 kg NaI(Tl) detectors
arranged in a $3\times 3$ matrix. These detectors will be enclosed in several
layers of shielding as represented in Figure 2.1, from inner to outer layer:

Figure 2.1: ANAIS experimental set-up artistic view.

[itemize] & 10 cm of ancient very low activity lead plus 20 cm of low activity
lead to attenuate the $\gamma$ background. All lead required for the full
experiment is already available underground at the LSC. A stainless steel
anti-radon box that will tightly close the shielding to avoid the entrance of
airborne radon inside the lead shielding. The box will be continuously flushed
with radon free boil-off nitrogen. Plastic scintillators covering the top and
the lateral faces of the anti-radon box in order to act as active shielding
against muons and muon-related events as described earlier. The most external
layer will consist of a combination of boron-loaded water and polyethylene
blocks acting as neutron shielding.

######

The experimental set-up is completed by the electronic front-end, the data
acquisition and the slow control systems. All of them are the evolution of the
previous prototypes and their scale-up to the full experiment is a nuclear
part of the work described in this thesis.

###  2.3 ANAIS-25 set-up

ANAIS-25 [171, 160] set-up consisted of two modules of 12.5 kg each (named D0
and D1) provided by Alpha Spectra. The main goals for this set-up have been to
measure the crystal internal contamination, determine light collection
efficiency, fine tune the data acquisition and test the filtering and analysis
protocols. The modules are cylindrical, 4.75” diameter and 11.75” length, with
quartz windows for PMTs coupling (see Figure 2.2(a)). A Mylar window in the
lateral face allows for low energy calibrations. Two types of photomultipliers
have been tested (Hamamatsu R12669SEL2 and Hamamatsu R11065SEL) but the model
R12669SEL2 was finally selected. The studies referred as ANAIS-25 in this work
correspond to data taken with four PMTs of this model.

######

The modules have been surrounded by a reduced version of the aforementioned
shielding without boron-loaded water: 10+20 cm of lead, anti-radon box and
plastic scintillators. The introduction of the modules inside the lead
shielding can be observed in Figure 2.2(b) and the anti-radon box in Figure
2.2(c).

(a)

(b)

(c)

Figure 2.2: ANAIS-25 detectors without PMTs (a) and being introduced inside the shielding (b). The anti-radon box (c). 40K (mBq/kg) |  238U (mBq/kg) |  210Pb (mBq/kg) |  232Th (mBq/kg)
---|---|---|---
1.25 $\pm$ 0.11 (41 ppb K) | 0.010 $\pm$ 0.002 |  $\sim$3.15 | 0.002$\pm$ 0.001
Table 2.1: NaI(Tl) crystals internal contamination measured in ANAIS-25
prototype.

######

This set-up was taking data from December 2012 to March 2015. The first
feature to be remarked is the excellent light collection [160], tested again
in this work as it can be seen in Section 8.6. This light collection has a
good impact in both resolution and energy threshold. A preliminary study has
been done with the coincident events in both prototype modules showing two low
energy populations that have been attributed to internal 40K and cosmogenic
22Na as it is shown in Figure 2.3(a). The K-shell electron binding energy
following electron capture in 40K (3.2 keV) and 22Na (0.9 keV) can be tagged
by the coincidence with a high energy $\gamma$ ray (1461 keV and 1274 keV
respectively). Hence, a threshold of the order of 1 keVee seems to be
achievable. The trigger and filtering efficiencies at the threshold level are
currently under study.

(a)

(b)

(c)

Figure 2.3: ANAIS-25 Background. Coincidence scatter plot showing events from
40K and 22Na (a), cosmogenic radionuclide decay at low energy (b) showing the
spectrum for the first month of data taking (black) and fifteen months later
(gray) and filtered and efficiency corrected background 1-6 keV for D0 and D1
modules (c).

######

On the other hand, background contributions have been thoroughly analyzed.
Figure 2.3(b) shows the low energy spectrum at the beginning of the data
taking and fifteen months later, showing a high suppression of most of the
lines except the corresponding to 210Pb, highlighting their cosmogenic origin;
a more detailed study of radionuclide production in NaI(Tl) derived from this
data can be found at reference [172]. Table 2.1 shows the results of the
activities determined for the main crystal contaminations. 40K content has
been measured performing coincidence analysis between 1461 keV and 3.2 keV
lines [160, 168]. The activities from 210Pb and 232Th and 238U chains have
been determined by quantifying Bi/Po sequences and by comparing the total
alpha rate with the low energy depositions attributable to 210Pb, which are
fully compatible.

######

These results give a moderate contamination of 40K, above the initial goal of
ANAIS (20 ppb of K), but acceptable (see Section 2.5); a high suppression of
232Th and 238U chains, but a high activity of 210Pb at the mBq/kg level. The
origin of such contamination was identified as radon contamination at powder
purifying and crystal growing procedures and it was addressed by Alpha
Spectra. A new module, grown following a new protocol, was available for
radiopurity checks at the beginning of 2015. These measurements confirmed the
better background as it can be seen in the next section.

######

Other goals of this set-up were fine tuning the data acquisition and testing
the filtering and analysis protocols. The filtered background of ANAIS-25
modules is shown in Figure 2.3(c). The filtering process removes non-bulk
scintillation based on reference [173]. It was adapted to ANAIS-25 and it is
being improved with the knowledge of PMT only events. This process is
described in Section 7.4.

###  2.4 ANAIS-37 set-up

The origin of ${}^{210}Pb$ contamination was identified and was addressed by
Alpha Spectra. A new 12.5 kg crystal was grown and a new module was
constructed using new improved protocols. This detector, named D2, was
integrated in the ANAIS-25 set-up to form the new ANAIS-37 set-up as it can be
seen in Figure 2.4.

Figure 2.4: The three ANAIS-37 modules.

######

A preliminary determination of the $\alpha$ rate gave a value of $0.58\pm
0.01$ mBq/kg which is five times lower than ANAIS-25 values, concluding that
effective reduction of Rn entrance in the growing or/and purification
processes at Alpha Spectra has been achieved. This reduction can also be
appreciated at low energy (see Figure 2.5) in both peak and continuum in spite
of the still decaying cosmogenic background.

Figure 2.5: Raw background for D0 and D2.

######

The potassium content was also determined with the same technique earlier
mentioned obtaining $44\pm 4$ ppb, compatible with the content of D0 and D1
(see Table 2.1). The contamination measurements were introduced in the
aforementioned background model in order to explain the measured raw
background down to 5 keV [174].

######

In addition to the measurement of the internal contamination and the
understanding of the low energy background, the ANAIS-37 set-up was also used
to test some other improvements for the complete experiment such as the
complete plastic scintillator coverage, the new calibration system and was
also used to the test new approaches to scale up the experiment.

##### Complete plastic scintillator coverage

An almost total plastic scintillator coverage was mounted and put into
operation at the time of the ANAIS-37 set-up with eleven scintillators. This
system and its final extension to sixteen scintillators in order to cover the
total ANAIS experiment are presented in Chapter 5.

(a)

(b)

(c)

Figure 2.6: Calibration system design (a), design detail (b) and its
implementation (c).

Figure 2.7: Blank module assembly.

##### New calibration system

The ANAIS modules have been designed with a Mylar window to allow low energy
calibration as seen previously. The calibration is performed by introducing a
$\gamma$ or X-ray sources inside the shielding and in front of the thin Mylar
window in order to measure the response to known energy depositions. The
introduction of these sources inside the shielding was previously done by
means of an aperture big enough to introduce a tray with a disk shaped source
holder and opening the anti-radon box in the operation. This calibration
system was changed at the end of the ANAIS-25 set-up in order to keep the
system free of radon.

######

The new system consists of flexible wires with ${}^{57}Co$ and ${}^{109}Cd$
customized sources along them. The sources are outside the shielding and they
are introduced inside the shielding facing the Mylar windows during
calibration keeping the system closed and radon free. Mylar windows of
adjacent detectors face each other so that one wire can calibrate two
detectors at a time. The design and implementation of this system can be seen
in Figure 2.6. This system has been tested at the end of the ANAIS-25 set-up
with one wire and a new wire was installed to calibrate the three ANAIS-37
detectors.

##### Blank module testing

A blank module consisting of the D1 PMTs and a copper housing without NaI
crystal or quartz windows was mounted in place of the D1 detector in September
2015. This set-up was conceived to fully understand, characterize and try to
filter and reject all PMT noise. This better filtering will help to understand
the raw background below 1.5 keVee and to lower the energy threshold as much
as possible.

###  2.5 ANAIS sensitivity prospects

The expected sensitivity to annual modulation of the ANAIS full experiment has
been evaluated with the measured background in ANAIS-25 but using the 210Pb
measured in ANAIS-37 D2. The prospects of the sensitivity to the annual
modulation in the WIMP mass-cross-section parameter space are shown in Figure
2.8 using a configuration of 100 kg and 5 years of data taking. The energy
window considered was 1 to 6 keVee. These prospects correspond to a detection
limit at 90% CL with a critical limit at 90% CL, following reference [175]. It
has to be noted that further background reduction from the anticoincidence
pattern is expected. Even with this conservative approach, there is a
considerable discovery potential of dark matter particles within the
DAMA/LIBRA singled-out parameter space regions [176].

Figure 2.8: Sensitivity projection for 1-6 keVee energy window and five years
of data taking (without considering anticoincidence rejection). From [177].

###  2.6 This work

This chapter has been dedicated to give a complete picture of the ANAIS
experiment, its goals, history and status. The complete information and
results have been published in the above referenced articles.

######

This work is devoted to the design and the scale-up of a suitable data
acquisition system for the ANAIS experiment following the experimental
requirements described in Section 2.1. Additionally, the data analysis tools
of previous prototypes have been adapted to the new data structures and an
automation framework has been developed. Finally, the whole system has been
characterized and its stability reviewed.

######

Chapter 3 shows the development of PMTs characterization protocol and the
testing results of the first units. Chapter 4 describes the electronic front-
end and the characterization of the key modules. Chapter 5 presents the design
and first results for the muon detection system. The data acquisition software
design and implementation are covered in Chapter 6 whereas the analysis
software and its use is seen in Chapter 7. Finally, Chapter 8 reviews the
global tests, the performance of the detectors and Chapter 9 the stability of
both the environmental parameters and the full data acquisition system.

##  Chapter 3 Optical to electrical conversion

The scintillation light produced in certain materials is one of the oldest
techniques to detect ionizing radiation and it remains as one of the most
useful available methods for detection and spectroscopy of a wide range of
radiations. This effect is thoroughly covered in references [178] and [179].
The scintillation light is usually detected by photomultiplier tubes (PMTs)
converting photons into electric signal.

######

The processes involved in the light generation and its conversion to
electrical signal are described in this chapter. The characterization of the
ANAIS PMTs is also covered focusing in their critical aspects to ANAIS:
radiopurity, dark counts, gain and quantum efficiency.

###  3.1 Scintillation process in NaI(Tl)

The ideal scintillator material should have some desired properties: convert
kinetic energy of the incident particle into detectable light with high
scintillation efficiency; a linear light yield with deposited energy; the
medium should be transparent to the emitted wavelength; the decay time should
be as short as possible; it has to have good optical quality to produce
practical large size detectors; and its refraction index should be near that
of the glass ($\sim$1.5) to allow efficient photomultiplier coupling.

######

There are two main groups of scintillation materials: inorganic and organic-
based liquids and plastics. The most widely used scintillators include the
inorganic alkali halide crystals (such as NaI), exhibiting the best light
output and good linearity but with a response relatively slow compared to
organic scintillators, which are much faster but have a lower light yield.

######

The scintillation process in organic scintillators arises from transitions in
the energy level structure of a single molecule. A large category of organic
scintillators are based on organic molecules with $\pi$-electron structure
which gives a principal emission path with a decay time of the order of a few
nanoseconds. For example, plastic scintillators are used in ANAIS as a veto
system as described in Chapter 5.

######

Figure 3.1: Energy band structure of an activated crystalline scintillator.

The scintillation mechanism in inorganic materials depends on the energy
states determined by the crystal lattice of the material. As shown in Figure
3.1, electrons only have available discrete bands of energy in insulators or
semiconductor materials. Small amounts of an impurity are commonly added to
inorganic scintillators in order to enhance the probability of visible photon
emission during the de-excitation process. These impurities, called
activators, create special sites in the lattice modifying the normal band
structure of the pure crystal. As a result, new energy states are created
within the forbidden gap through which the electron can de-excite back to the
valence band with the emission of a photon. This de-excitation will occur with
typical half-lives of $\sim$10-7 s and, with a careful selection of the
activator, with a photon in the visible energy range.

######

Competing to the aforementioned scintillation process in inorganic materials
there are other processes: [itemize] & Slow components: the electron can
create an excited configuration at the impurity site whose transition to the
ground state is forbidden. Thermal excitation can give an increment of energy
to raise it to a higher state from which the de-excitation is possible
resulting in a slower component of light called _phosphorescence_. Quenching:
Certain radiationless transitions are possible between some excited states and
the ground state via electron capture, with no visible photons emitted. These
processes are called _quenching_ and account for the loss in the conversion of
particle energy into scintillation light. These effects have an impact in the
efficiency of the scintillation process. Various experimental determinations
have shown that the absolute scintillation efficiency of NaI(Tl) is about 13%.

######

Thallium doped sodium iodide scintillators have been widely used in the gamma
spectroscopy field. The material allows the growing of large mass detectors,
exhibits an excellent light yield and has a close to linear response. For
these reasons, it has been accepted as standard scintillation material for
routine gamma spectroscopy. The disadvantages for some applications are the
long decay time (230 ns), the crystal fragility and its hygroscopic nature
that requires a tight encapsulation. In addition, the phosphorescent effect
can be more evident at high activity creating an “afterglow” effect [180].

######

NaI(Tl) exhibits other features like differences in shape and light yield for
different interaction mechanism. These features are very relevant to the use
of NaI as WIMP-nucleus recoil detector, as described in Section 1.5.

####  3.1.1 NaI(Tl) scintillation parameters

Even taking into account the shape difference between particle interactions,
the time constant of the main scintillation channel only ranges from 200 to
320 ns [161, 180]. This fact, alongside with the response of the light
detector device, will mark the features needed by the front-end electronics in
order to process the signal properly (see Section 3.4). Additionally, the
spectral distribution of the scintillation photons has its maximum around 420
nm [179].

######

Another parameter to take into account is the scintillation yield which is
tens ($\sim$40) of photons per keV for $\gamma$ rays [181]. Given this fact
and considering the light collection efficiency factor, the typical
scintillation constant and the energy range of interest (below 6 keV), a
device sensitive to individual photons of the order of 420 nm is needed in
order to have a threshold as low as possible. High quantum efficiency bialkali
photomultipliers fulfill all the aforementioned requirements and they are
described in the next section.

###  3.2 Photomultipliers

A photomultiplier tube (PMT) is a vacuum tube consisting of an input window, a
photocathode with a photosensitive layer, focusing electrodes, electron
multipliers called dynodes and an anode [179, 182]. The process of converting
light into a measurable electric signal (see Figure 3.2(a)) consists of
several steps involving photoelectric and secondary electron emission effects.
First, the light passes through the input window and excites the photocathode
so that photoelectrons are emitted into the vacuum via photoelectric effect.
The photoelectrons are accelerated in the vacuum and focused by the focusing
electrode onto the first dynode where they are multiplied taking advantage of
the secondary emission effect. This step is repeated at each successive
dynodes. Finally, the electrons emitted by the last dynode are collected by
the anode.

(a)

(b)

Figure 3.2: Schematic of a photomultiplier tube (a) and a usual operating
method (b). From [182]..

######

A PMT needs some peripheral devices for proper operation as seen in Figure
3.2(b): a stable high voltage power supply, a voltage divider circuit, a
housing system to shield the external light and a signal processing set-up.
The high voltage supply is used to provide potential difference to the dynodes
in order to allow the secondary emission effect. The main voltage is
distributed among the dynodes by the voltage divider circuit. The typical high
voltage of a photomultiplier is of the order of one thousand volts.

######

There are several parameters for the photomultiplier characterization:
[itemize] & The spectral response is the ratio between detected and incident
photons as a function of their wavelength. It shows the wavelength range to
which the PMT is sensitive. It has to match the spectrum of the light to be
detected as much as possible. The quantum efficiency is the spectral response
at a given wavelength. It is usually expressed as percentage and given at the
peak of spectral response or at a fixed wavelength. The gain is the number of
electrons coming from the anode for each photoelectron produced in the
photocathode. The rise time of the photomultiplier temporal response to a
single photon quantifies the time to rise from 10% to 90% of the signal peak.
The fall time is defined as the time to fall from the 90% to the 10% of the
signal peak. The transit time is the time interval from the arrival of the
light to the photocathode and the appearance of the output pulse at the anode.
The dark current is the current in the anode not produced by light. The
processes that could be sources of dark current are thermionic emission in the
photocathode and the dynodes, leakage current between anode and other
electrodes, photocurrent produced by scintillation in the glass envelope or
electrode supports, field emission current, ionization current from residual
gases and noise current caused by cosmic rays, radiation from radioisotopes
contained in the glass envelope and environmental gamma rays. The dark counts
are the rate of dark current events that could be accounted as external photon
events. The single electron response (sometimes referred as SER) is the charge
spectrum of the photomultiplier to single photons. It takes account of the
response dispersion of the dynode system and the portion of light events
producing significantly less signal for hitting the second dynode or for
inelastic scattering of the photoelectron [183]. The distribution of these two
type of events is often characterized by the peak-to-valley ratio (see Section
3.5.6).

######

There are several types of PMTs depending on the photocathode type and the
geometric disposition and number of dynodes. The material of the photocathode
determines the spectral response of the photomultiplier in terms of wavelength
and quantum efficiency. The type of the photocathode is selected taking into
account the spectrum of the light to be detected. The type and number of
dynodes will determine the gain of the PMT.

######

In this section the PMTs chosen for the ANAIS experiment and the peripheral
devices are described.

####  3.2.1 ANAIS requirements

A suitable photomultiplier for the ANAIS experiment has to meet certain
requisites coming from the experimental requirements of the ANAIS experiment
(see Section 2.1) in addition to the features of the NaI(Tl) scintillation
(see Section 3.1.1):
[itemize] & High quantum efficiency: The requirement of low energy threshold,
the light yield of the NaI(Tl) and its main scintillation constant demand a
high efficiency in the detection of the light. Low background: The materials
of the photomultiplier must be as radiopure as possible in order to minimize
their contribution to the ANAIS background. Low dark counts: The dark counts
must be as low as possible because they will trigger the acquisition given the
low energy threshold needed by ANAIS producing undesirable high triggering
rate.

######

All these features were considered in the PMT selection and testing [160]. The
model Hamamatsu R12669SEL2 PMT (previously named as R6956MOD) was chosen
fulfilling all requirements. This model is similar to the installed in the
upgrade of the DAMA/LIBRA experiment (DAMA/LIBRA–phase2) [184].

####  3.2.2 Hamamatsu R12669SEL2 PMT

Hamamatsu R12669SEL2 (see Figure 3.3) photomultipliers tubes have bialkali
photocathode with a high quantum efficiency ($>$ 33%) with a maximal response
at 420 nm and dark counts below 500 Hz. They have ten stages and a gain factor
around $10^{6}$. The full technical information can be seen in Table 3.1.

Figure 3.3: Hamamatsu R12669SEL2 photomultipliers. Characteristics |
---|---
Diameter | 3”
Spectral response | 300-650 nm
$\lambda$ of max. response | 420 nm
Photocathode material | Bialkali
Photocathode min. effective | 70 mm
Dynode structure | Box-and-grid + Linear-focused
Number of stages | 10
Operating ambient T | -30/+50 ºC
Max. supply voltage | 1500 V
Max. avg anode current | 0.1 mA
Characteristics at 25 º C |
Cathode luminous sens. | 100 $\mu$A/lm
Quantum efficiency at peak |  $>$ 33%
Anode luminous sens | 100 A/lm
Gain | 106
Anode dark current (max.) | 6 (60) nA
Dark current rate |  $<500$ Hz
Anode pulse rise time | 9.5 ns
Electron transit time | 60 ns
Transit time spread | 13 ns
Pulse linearity | 30 ($\pm$ 2%) mA
Table 3.1: Hamamatsu R12669SEL2 technical data.

######

Forty two high quantum efficiency low background Hamamatsu R12669SEL2 PMTs
were received at the LSC and tested. High purity germanium spectroscopy were
performed at LSC verifying the required radiopurity levels and the homogeneity
among them (see Section 3.3). Operational parameters such as SER, gain,
relative quantum efficiency and dark rate were tested at the University of
Zaragoza test bench. This process is described in the rest of this chapter.

######

First, a set-up to expose PMTs to controlled ultraviolet LED light, data
acquisition chain and algorithms to extract SER parameters and dark rate were
developed and tested as described in Section 3.5. A protocol to characterize
all units was implemented and the results are presented in Section 3.6.

####  3.2.3 Voltage divider

The voltage divider scheme used with these PMTs is the recommended by
Hamamatsu (see Figure 3.4(a)). The construction of such a circuit must be as
radiopure as possible because of the ANAIS experimental requirements (see
Section 2.1). For this reason, CuFlon PCB was designed and manufactured as can
be seen in Figure 3.4(b). CuFlon is a tested radiopure material [185]. All
components in the PCBs are in SMD format to minimize their mass and
consequently their activity and were measured in the HPGe low background test
bench at LSC in order to check their low contribution to the ANAIS background.

(a)

(b)

Figure 3.4: R12669SEL2 voltage divider design recommended by Hamamatsu (a) and
its implementation in CuFlon PCB (b).

####  3.2.4 High voltage power supply

A high voltage power supply with a high density of channels is needed for the
full experiment. For this reason a CAEN SY2527 Universal Multichannel Power
Supply System was acquired. This system offers a high scalability thanks to
its six slots to house High Voltage boards. Two boards were acquired: an
A1833BP with 28 independent channels and an A1535P with 24 independent
channels, accounting a total of 52 channels.

######

The ripple specifications of the aforementioned boards ($<$50 mV pp for
A1833BP and $<$30 mV for A1535P) was not enough for the ANAIS requirements and
a filtering of the output signal was needed. In addition, a crosstalk between
channels was detected risking the coincidence analysis. These effects were
prevented using a proper filter as described in Section 4.5.5.

######

In addition to the high density of channels, the SY2527 system has monitoring
and communication features, very convenient for the ANAIS purposes. The
mainframe can be monitored and controlled, giving the values of current and
voltage and allowing the remote power on and off of the channels. The results
of the monitoring can be seen in Section 9.2.4.

###  3.3 Photomultiplier radiopurity

The measurement of the radioactive isotopes contained in Hamamatsu PMTs was
performed using a of HPGe low background test bench at the LSC (see Figure
3.5).

Figure 3.5: Hamamatsu R12669SEL2 radiopurity screening with a HPGe detector.

######

The test of all PMTs is still ongoing. The result of the already measured
units can be seen in Table 3.2. The first two units, coupled to D0 in
ANAIS-25, are R6956MOD. The rest of the PMTs have a new model reference,
R12669SEL2, due to a Hamamatsu catalog change. The data show a good
homogeneity in contamination levels among units and they are in agreement with
the specifications requested to Hamamatsu. These data have been used as input
for the background model of the ANAIS-0 prototype [186] and the subsequent
refinements for the following prototypes.

PMT | ${}^{232}Th$ | ${}^{238}U$ | ${}^{262}Ra$ | ${}^{40}K$
---|---|---|---|---
| (mBq/PMT) | (mBq/PMT) | (mBq/PMT) | (mBq/PMT)
ZK5902 | 20 $\pm$ 2 | 128 $\pm$ 38 | 84 $\pm$ 3 | 97 $\pm$ 19
ZK5908 | 20 $\pm$ 2 | 150 $\pm$ 34 | 88 $\pm$ 3 | 133 $\pm$ 13
FA0010 | 18 $\pm$ 2 | 77 $\pm$ 42 | 78 $\pm$ 4 | 113 $\pm$ 18
FA0016 | 18 $\pm$ 2 | 179 $\pm$ 51 | 83 $\pm$ 4 | 123 $\pm$ 20
FA0018 | 21 $\pm$ 3 | 161 $\pm$ 58 | 79 $\pm$ 5 | 108 $\pm$ 29
FA0020 | 25 $\pm$ 4 | 260 $\pm$ 84 | 77 $\pm$ 6 | 95 $\pm$ 36
FA0022 | 18 $\pm$ 2 | 158 $\pm$ 53 | 77 $\pm$ 4 | 93 $\pm$ 19
FA0034 | 20 $\pm$ 3 | 144 $\pm$ 33 | 89 $\pm$ 5 | 155 $\pm$ 36
FA0035 | 22 $\pm$ 2 | 148 $\pm$ 29 | 79 $\pm$ 4 | 79 $\pm$ 14
FA0036 | 16 $\pm$ 2 | 139 $\pm$ 31 | 71 $\pm$ 4 | 95 $\pm$ 27
FA0037 | 19 $\pm$ 2 | 170 $\pm$ 37 | 78 $\pm$ 5 | 123 $\pm$ 32
FA0051 | 19 $\pm$ 2 | 133 $\pm$ 52 | 89 $\pm$ 4 | 94 $\pm$ 16
FA0053 | 25 $\pm$ 2 | 114 $\pm$ 29 | 87 $\pm$ 4 | 132 $\pm$ 19
FA0057 | 19 $\pm$ 2 | 153 $\pm$ 25 | 82 $\pm$ 3 | 128 $\pm$ 23
FA0058 | 22 $\pm$ 2 | 168 $\pm$ 31 | 84 $\pm$ 4 | 118 $\pm$ 27
FA0059 | 26 $\pm$ 2 | 171 $\pm$ 32 | 85 $\pm$ 4 | 104 $\pm$ 24
FA0060 | 22 $\pm$ 2 | 145 $\pm$ 29 | 88 $\pm$ 4 | 95 $\pm$ 24
FA0064 | 21 $\pm$ 2 | 180 $\pm$ 34 | 85 $\pm$ 4 | 131 $\pm$ 31
FA0066 | 19 $\pm$ 2 | 156 $\pm$ 31 | 82 $\pm$ 4 | 117 $\pm$ 29
FA0068 | 18 $\pm$ 2 | 185 $\pm$ 29 | 81 $\pm$ 4 | 138 $\pm$ 25
FA0069 | 18 $\pm$ 2 | 159 $\pm$ 29 | 79 $\pm$ 3 | 105 $\pm$ 15
FA0070 | 21 $\pm$ 2 | 127 $\pm$ 30 | 82 $\pm$ 4 | 103 $\pm$ 20
FA0072 | 27 $\pm$ 3 | 172 $\pm$ 35 | 91 $\pm$ 4 | 91 $\pm$ 27
FA0073 | 22 $\pm$ 2 | 181 $\pm$ 31 | 78 $\pm$ 4 | 112 $\pm$ 25
Mean value | 20.7 $\pm$ 0.5 | 157 $\pm$ 8 | 82.5 $\pm$ 0.8 | 111 $\pm$ 5
Standard deviation | 2.8 | 32.3 | 4.9 | 18.2
Table 3.2:  Contamination levels of PMT units from Hamamatsu (R6956MOD and
R12669SEL2) tested at low background HPGe test bench in Canfranc.

###  3.4 Low energy signals

The scintillation light convoluted with the photomultiplier response gives
rise to the electrical signal that will be processed by the ANAIS electronic
front-end (see Chapter 4). The signal features will determine the front-end
requirements, especially in the lower energy region, below 6 keV, the ANAIS
region of interest. The signal of a PMT of one of the ANAIS-25 detectors from
the aforementioned energy region is shown in Figure 3.6 in order to illustrate
the typical shape of the waveform. Taking into account the light yield and the
scintillation constants, an event of few keV consists of some discrete photons
(photoelectrons) following an exponential temporal distribution with a
constant of few hundreds of nanoseconds.

Figure 3.6: Low energy NaI(Tl) scintillation: event of 3.2 keV.

######

This waveform requires a hardware trigger set at the photoelectron level.
Therefore, the study of the response of the photomultiplier to a single
photon, the single electron response or SER, is crucial. This study can be
seen in Section 3.5.

###  3.5 Photomultiplier response characterization

The theory and techniques to characterize the PMTs are described in this
section. A good knowledge of the PMT response at low light intensity is
essential to understand the scintillation signal at very low energies.
Particularly, a characterization of the SER allows to understand the most
elementary PMT signal.

######

In this section an introduction to the Single Electron Response (SER)
deconvolution from PMT spectra is first presented. Next, the actual set-up,
algorithms and procedures are discussed. Finally, in the next section a
summary of the results of the parameter extraction is shown.

####  3.5.1 Single electron response deconvolution

The deconvolution of the PMT charge distribution using a pulsed light as
source is a well-established technique [187, 188, 189, 183]. It is based on
modeling the photomultiplier in two basic steps: photodetection and
amplification.

######

A pulsed source of light produces a flux of photons with a Poisson
distribution in the number of photons per pulse. Photons are converted into
electrons at the photocathode via photoelectric effect as described earlier.
The conversion of photons into electrons and the collection by the dynode
system is a random binary process. So, the photodetection process gives again
a Poisson distribution in the number of detected photons:

$P(n;\mu)=\frac{\mu^{n}e^{-\mu}}{n!}$ (3.1)

where $m$ is the mean photons hitting the photocathode and $\mu$ is defined
as:

$\mu=mq$ (3.2)

where $\mu$ is the mean number of photoelectrons collected by the dynode
system, $P(n;\mu)$ the probability that $n$ photoelectrons will be observed
and $q$ the quantum efficiency.

######

Given a photoelectron coming from the cathode, the amplification process of a
multiplicative dynode system can be approximated by a sum of a Gaussian
distribution (parametrized by $Q_{0}$ and $\sigma_{0}$) and an exponential
component (parametrized by the $\alpha$ constant). The Gaussian part describes
the normal second emission effect in all dynodes and the exponential models
the photoelectron being inelastically back-scattered by the first dynode (with
a probability $w$). The PMT output charge (denoted by $x$) will be:

$SER_{ideal}(x)=\frac{1-w}{\sigma_{0}\sqrt{2\pi}}e^{-\frac{(x-Q_{0})^{2}}{2\sigma_{0}^{2}}}+w\alpha
e^{-\alpha x}$ (3.3)

######

In addition to the response for a photon, other background processes can have
influence in the photomultiplier response. The possible background processes
consist of noise in absence of light signal such as thermoelectron emission in
the photocathode or in the dynodes, electron autoemission by electrodes,
photon and ion feedback and external or internal radioactivity. Additionally,
photon flux can also contribute to this background with photoemission from
focusing electrodes and dynodes or other sources. All these discrete processes
can appear in the measured signal with non-zero probability. The set-up and
analysis described later are designed to avoid such effects as much as
possible. The contribution of these effects, described earlier as dark counts
and usually modeled as an exponential contribution, are considered negligible
for this SER response. This assumption is reviewed later (see Section 3.5.2).
The only contribution to non-photon produced signal to be considered is the
electrical noise, modeled as a Gaussian distribution:

$B(x)=\frac{1}{\sigma_{p}\sqrt{2\pi}}e^{-\frac{(x-Q_{p})^{2}}{2\sigma_{p}^{2}}}$
(3.4)

where $Q_{p}$ and $\sigma_{p}$ determines the electric noise pedestal.

######

A realistic PMT SER response is the convolution of the ideal response (3.3)
and the noise distribution function (3.4):

$\displaystyle\begin{split}SER(x)&=SER_{ideal}\otimes B(x)=\\\ \\\
&=\frac{1-w}{\sqrt{2\pi(\sigma_{p}^{2}+\sigma_{0}^{2})}}e^{-\frac{(x-Q_{p}-Q_{0})^{2}}{2(\sigma_{p}^{2}+\sigma_{0}^{2})}}\\\
&+\frac{w\alpha}{2}e^{\frac{\alpha}{2}(2Q_{p}+\alpha\sigma_{p}^{2}-2x)}\left(1+Erf\left(\frac{Q_{p}+\alpha\sigma_{p}^{2}-x}{\sqrt{2}\sigma_{p}}\right)\right)\end{split}$
(3.5)

$Q_{1}$ is defined as the average charge when an electron is collected in the
first dynode and $\sigma_{1}$ the standard deviation. So, the gain can be
obtained from $Q_{1}=eg$, being $g$ the actual gain and $e$ the electron
charge. These values can be deduced from the SER parameters using an
approximation to low light:

$\displaystyle\begin{split}Q_{1}&\approx(1-w)Q_{0}+w/\alpha\\\
\sigma_{1}^{2}&\approx(1-w)(\sigma_{0}^{2}+Q_{0}^{2})+2w\alpha^{2}-Q_{1}^{2}\end{split}$
(3.6)

######

For a number of photoelectrons $n\geq 2$, the response will be approximately
Gaussian [188] (This approximation is also reviewed later, in Section 3.5.3).
Assuming a linear response, the Gaussian response to $n$ photoelectrons
($G_{n}$) will be:

$\displaystyle\begin{split}G_{n}(x)&=\frac{1}{\sigma_{n}\sqrt{2\pi}}e^{-\frac{(x-Q_{n})^{2}}{2\sigma_{n}^{2}}}\\\
Q_{n}&=Q_{p}+nQ_{1}\\\
\sigma_{n}&=\sqrt{\sigma_{p}+n\sigma_{1}^{2}}\end{split}$ (3.7)

Having all contributions in mind (equations 3.1, 3.4, LABEL:eq:ser_real and
3.7), the function to deconvolute the PMT response will be:

$\displaystyle\begin{split}\begin{aligned} f(x)&=N\left(\vphantom{\int}\
e^{-\mu}B(x)\right.&\text{(0 photons)}\\\ &+\left.\mu
e^{-\mu}SER(x)\right.&\text{(1 photon)}\\\
&+\left.\vphantom{\int}\sum_{n=2}^{\infty}{\frac{\mu^{n}e^{-\mu}}{n!}G_{n}(x)}\right)&\text{(n
photons)}\\\ \end{aligned}\end{split}$ (3.8)

######

where the function has been split in several parts: the pedestal or the
electrical noise contribution to the charge spectrum, the SER and the
components due to higher number of photons.

######

This response function has seven free parameters: $Q_{p}$ and $\sigma_{p}$
define the pedestal, $w$ and $\alpha$ the exponential part of the SER, $Q_{0}$
and $\sigma_{0}$ the Gaussian part and $\mu$ the intensity of the detected
light.

####  3.5.2 PMT test bench

A dedicated set-up was designed and mounted in order to study and characterize
the response of all PMTs using the aforementioned deconvolution. A
periodically pulsed ultraviolet LED [190] was used as light source and as the
trigger for a MATACQ digitizer (see sections 4.4.2 and 4.5.3) as it can be
seen in Figure 3.7.

(a)

(b)

Figure 3.7: Set-up for PMT characterization: scheme (a) and actual set-up (b).

######

This set-up was used to: [itemize] & Deconvolute PMT spectra in order to
obtain fundamental PMT information: gain and single electron response (SER)
parameters [187] and, with reproducible source LED conditions, quantum
efficiency. Study the single and multiple photoelectron distributions and test
the peak detection algorithms with expected distributions. Test all PMTs and
draw their curve gain versus high voltage. Test the dark counts behavior at
different voltages.

######

The light spectrum has been expressed in terms of collected charge while the
described set-up uses digitized waveform. A specific software analysis
configuration was developed to integrate voltage in a fixed window (see
Section 7.3.1) with the same width that the original pulsed signal. The
obtained integrated area is therefore proportional to the collected charge in
the aforementioned time window.

######

A testing of the assumption of a negligible PMT background in this set-up was
performed. The frequency of random coincidences is:

$f_{random}=f_{dark}f_{trigg}\tau_{gate}$ (3.9)

being $f_{dark}$ the dark rate, $f_{trigg}$ the trigger frequency and
$\tau_{gate}$ the integration time. The frequency of real light events at low
light intensity (the worst scenario for the background influence) is:

$f_{events}=(1-P(0))f_{trigg}\simeq\mu f_{trigg}$ (3.10)

$\tau_{gate}$ is 200 ns, the maximum time of LED excitation signal and the
dark count is below 500 Hz (see Section 3.5.7). The minimum amount of light to
have a dark count contribution below 1% is
$\mu\geq\frac{f_{dark}\tau_{gate}}{0.01}=0.01$.

######

A fully opaque layer was used in order to test the above assumptions. The
result can be seen in gray in Figure 3.8. Very few events were in coincidence
with the integration window (with probability $5\sim\times 10^{-5}$) giving a
dark counts result (using equations 3.9 and 3.10) of 260 Hz, fully compatible
with the evolution of the dark current seen later (see Section 3.5.7). A
typical spectrum for the same number of triggers and with light ($\mu\simeq
0.8$) is also shown as reference in black in Figure 3.8.

Figure 3.8: PMT background distribution (in gray) compared with light spectrum
(in black, $\mu\simeq 0.8$).

####  3.5.3 Deconvolution fit

The reproducibility of the deconvolution fit and the light intensity stability
were first studied before establishing a PMT characterization procedure.

######

The result of the data taking with a high density filter (low light intensity,
$\mu<1$) and the data fit with the Equation 3.8 can be observed in Figure
3.9(a). The fit can be seen in red in the figure, the blue left Gaussian line
corresponds to Gaussian pedestal (Gaussian baseline noise), the green line to
the exponential SER component part and the green line to SER Gaussian
component. The terms corresponding to higher number of photons is barely
observed because of their little contribution to the fit.

######

(a)

(b)

(c)

Figure 3.9: Photoelectron distribution fit (a), only SER fit (b) and two
photoelectron Gaussian component (red) compared with SER autoconvolution
(blue) (c) (see text for details).

Two crosschecks were performed in order to study the fit. First, a simplified
fit was performed using the _signal only_ spectrum. This spectrum can be
composed by events with one or more detected peaks using the peak detection
algorithm (see Section 7.1.2). The fit uses the SER equation only
(LABEL:eq:ser_real) assuming two or more photoelectron components negligible
($\mu\simeq$ 0.04). This fit can be seen in Figure 3.9(b) showing both
Gaussian and exponential components, confirming the SER shape and giving hints
to $\alpha$ and $w$ values.

######

The second crosscheck was to test the Gaussian shape for terms corresponding
to more than two photoelectrons. The autoconvolution of the SER extracted with
the peak detection algorithm was performed and compared with the shape of the
Gaussian predicted using Equation 3.7. The result can be seen in Figure 3.9(c)
exhibiting a good general agreement with a little discrepancy at the beginning
of the spectrum.

######

The deconvolution of the PMT spectra at different light intensities was done
at the same high voltage. This test must give a similar value of gain and
standard deviation of the single electron response (SER). The results can be
seen in Figure 3.10 showing the fit with the seven free parameters in the SER
parameters. The contribution of the components of more than one photoelectron
can be observed in the fits (red even number of photoelectrons, blue odd
number of photoelectrons) as described in Equation 3.8.

Figure 3.10: Deconvolution test with increasing light intensity at same
voltage showing the contribution of more than one photoelectron.

######

The parameters extracted from the fits seen in Figure 3.10 exhibit similar
gain results with discrepancies of the order of 5% in $Q_{0}$ for $\mu>0.1$
due to the use of the approximative $Q_{1}$ expression seen in Equation 3.6).

######

As a conclusion, a deconvolution fit was developed to quantify the gain of a
photomultiplier and the light detected from a pulsed light source. In the next
sections the quality, limitations and range of application are studied.

####  3.5.4 Light intensity detection and LED stability

The deconvolution seen in the previous section was studied by trying to
extract the same light intensity at different working PMT voltages, assuming
the same LED emission. This test was not successful and it gave reasons to
examine the LED stability.

######

A very long run of four days at low trigger frequency was performed in order
to see its long term behavior. Some additional parameters were measured in
this run: the voltage in the serial resistor (proportional to LED intensity)
and the temperature in the LED box. The results can be seen in Figure 3.11
showing the LED intensity in black points, the temperature in red and the
light detected ($\mu$ and error) in green. It can be seen a good correlation
among the three magnitudes and a LED instability ($>20$%) correlated with
temperature. The LED stability is crucial for measuring parameters such as
quantum efficiency and a more stable set-up is intended to be designed and
tested. In the meantime, the light characterization runs have been as short as
possible.

Figure 3.11: LED stability study: LED current (black points), extracted light
(green line) and temperature (red).

####  3.5.5 Mean photoelectrons algorithms and relative quantum efficiency

The quantum efficiency of the PMTs is a crucial parameter for their use with
scintillators at very low energy threshold and checking this feature is
important in the ANAIS PMT testing procedure. A direct measurement requires a
well calibrated source of light. However, an easier way to crosscheck the
quantum efficiency is to measure the relative quantum efficiency by detecting
light from a stable source. Once determined $\mu$, the relative quantum
efficiency can be deduced following Equation 3.2:

$\frac{q_{1}}{q_{2}}=\frac{\mu_{1}}{\mu_{2}}$ (3.11)

######

A description of the light measurement procedure and the relative quantum
efficiency determination can be seen in Section 3.6.

######

A study of several algorithms for the extraction of the pulsed LED light
intensity was done in order to compare them and perform PMT relative quantum
efficiency measurements.

######

The mean number of photoelectrons can be extracted from the signal spectral
distribution with several complementary methods [188] in addition to the
deconvolution fit seen earlier. The simplest way is to determine the “non-
photoelectron” part of the Poissonian SER distribution with a low light
intensity. Given this component, the mean photoelectron can be determined with
the expression:

$P(0)=\frac{N_{0}}{N_{trigg}}=e^{-\mu}$ (3.12)

######

where $N_{0}$ is the number of events without signal and $N_{trigg}$ is the
total of events triggered with the external LED trigger. $N_{0}$ can be
determined in several ways: by adjusting the Gaussian pedestal and determining
its area ($\mu_{ped}$) or by counting events with “no signal”. This second
method can be done by subtracting events with signal to the total $N_{trigg}$
events and the events with signal can be quantified with the detection peak
algorithm (see Section 7.1.2) obtaining an estimation $\mu_{peak}$.

######

Two other mean photoelectron estimators were used. $\mu_{fit}$ is obtained in
the deconvolution fit described in the previous subsection. Additionally, a
mixed method correcting the $\mu_{ped}$ by calculating the SER inside the
pedestal from the fit function gives a new estimator: $\mu_{ped\\_fit}$.

######

A comparison of these algorithms was performed at different HV testing $\mu$
stability with the aforementioned estimators. This comparison can be seen in
Figure 3.12. All the PMT data were taken at $\mu\simeq 0.04$. There are some
similar behaviors in the four estimators among PMTs. $\mu_{ped}$ and
$\mu_{ped\\_fit}$ underestimate the light because they do not take into
account the signal inside the pedestal. This effect is corrected for
$\mu_{fit}$ and $\mu_{peak}$. These last estimators have a very good agreement
at low and medium voltage. It has to be noted an increase in all the
estimators except $\mu_{fit}$ at high voltage. This effect may be due to the
increase of the dark counts that affects only at high gain and low light (see
Figures 3.12(b) and 3.12(c)). Every PMT unit has a different dependence of the
dark counts increase as a function of HV as we will see in Section 3.6.4 and
the unit 51 has a very strong increase (see Figure 3.16).

######

As a conclusion, the preferred estimators for $\mu$ are $\mu_{fit}$ and
$\mu_{peak}$ for their agreement. Consequently, the recommended protocol for
measuring light includes low light intensity and a low/medium voltage as we
will see in Section 3.6.6.

(a)

(b)

(c)

(d)

Figure 3.12: Mean photoelectron different extraction methods.

####  3.5.6 Peak-to-valley ratio

The peak-to-valley ratio is defined as the ratio between the peak and the
valley of the SER charge distribution. It is useful to characterize the
discrimination of high charge and low charge peaks. The low charge responses
are caused by the portion of light events producing significantly less signal,
hitting the second dynode or being inelastic scattered in addition to dark
current events.

######

A high peak-to-valley ratio allows to better reject the baseline and dark
noises consisting of low charge events (see Section 3.7). The extraction of
the location and value of the peak and the valley can be seen in Figure 3.13.
The results of the peak-to-valley ratio of all tested PMTs can be seen in
Section 3.6.

Figure 3.13: Peak and valley SER extraction (red triangles).

####  3.5.7 Dark counts

The dark counts (see Section 3.2.2) are a natural source of noise using PMTs.
Therefore, the characterization of the PMT dark counts is needed. It will give
information about the expected rate of dark events and its influence in the
trigger rate and the data.

######

A careful light isolation is required for the PMT in order to avoid external
photon counting. For this reason, the PMT is introduced in a closed cylinder
(as it can be seen in Figure 3.7(b)) in a dark environment. The dark counts
were measured counting the triggers with a scaler at regular time intervals.
The trigger level was set at 2 mV, a value above the electric noise and near
the typical value of the ANAIS trigger level. Two different measurements were
performed: dark counts versus time in order to see the de-activation after the
PMT light exposure and dark counts over HV once these counts were stable.

######

The dark counts over time after light exposure can be observed in Figure
3.14(a). It can be seen a fast decay, but the counts become stable only after
twenty hours. This is the temporal window needed for proper dark counts
characterization, i.e. the time windows used in the systematic measurements
(see Section 3.6.4). In addition to the decay, a more subtle effect can be
observed. A clear correlation with the temperature can be seen in the long run
when the activation effect becomes negligible. An example of such a
correlation can be seen in Figure 3.14(b) showing the end of the activation
and the temperature correlation. The dark counts increase 10% with a
temperature rise of 1 ºC. This is why a good stability in the temperature is
required and its monitoring and control is needed for a long term experiment
such as the ANAIS experiment.

######

The characterization of dark current as a function of high voltage and the
comparison with the vendor data can be seen in Section 3.6.4. The protocol for
subsequent measurements can be seen in Section 3.6.6.

(a)

(b)

Figure 3.14: PMT dark counts decay after light exposure (a) and dark counts
(points) and temperature (line) correlation (b).

###  3.6 Characterization protocol and results

A characterization protocol is needed due to the high number of PMTs to test.
This protocol and associated tools must provide reproducibility and ease of
use in order to be able to extract the parameters of all tested PMTs. In this
section the automation of the characterization process and the obtained
preliminary data for few PMTs are presented.

####  3.6.1 Parameter extraction automation

The first step to define a characterization protocol was to design and
implement a set of tools for the automatic parametrization of the algorithms
described in Section 3.5. This is a critical step taking into account the
difficulty of _a priory_ knowing the initial value of some parameters such as
$Q_{0}$, $\alpha$ or $w$ in the deconvolution fit for all gain range. The
quality of the fit improves with accurate initial values. All this automation
assumes very low light.

######

The steps followed for an appropriate parametrization of the fit are:
[itemize] & Fit the pedestal to a Gaussian, obtaining $Q_{p}$ and
$\sigma_{p}$. Fit the distribution of the events with one or more peak to a
SER distribution, obtaining $\alpha$ and $w$ (as it can be seen in Figure
3.9(b)). Obtain $\mu_{ped}$ from the integral of the pedestal. This will be
the initial value to $\mu$. Obtain peak and valley values. The position of the
peak is used as initial value of $Q_{0}$. Fit the SER fixing $Q_{p}$,
$\sigma_{p}$, $\alpha$ and $w$, obtaining $Q_{0}$, $\sigma_{0}$, $\mu_{fit}$.
Calculate $\mu_{peak}$, $\mu_{ped\\_fit}$ and $Q_{1}$ and $\sigma_{1}$ with
Equation 3.6.

######

This extraction procedure was used in the PMT characterization seen in the
following subsections.

####  3.6.2 Gain curves

The extracted values for $Q_{1}$ were used to plot the gain curve of every PMT
as it can be seen in Figure 3.15(a). The gain is calculated as the charge
collected compared with the elemental incident charge (the electron produced
by photoelectric effect). The charge collected is:

$\displaystyle\begin{split}Q=\int_{t0}^{t1}\frac{V(t)}{R}dt\end{split}$ (3.13)

and for a correct comparison with the electron elementary charge, the input
impedance of the digitizer ($R$) has to be taken into account once the voltage
signal is integrated.

######

It is well known that the behavior of the gain with the voltage approximates
to a power expression $G=AV^{K}$ [182]. The gain curves were fitted to the
previous equation extracting $A$ and $K$ parameters as seen in Table 3.3. The
value is $K=kn$, being $n$ the number of dynodes (9 for the R12699) and $k$ a
constant depending on the dynode structure and the material having a value
from 0.7 to 0.8 [182]. Additionally, $A$ depends on the dynode collection
efficiency. The result table is fully compatible with these facts.

######

(a)

(b)

Figure 3.15: PMTs gain curve (a) and power law fit (b). PMT | A | K
---|---|---
FA0022 | $(1.62\pm 0.08)\times 10^{-20}$ | $6.72\pm 0.01$
FA0034 | $(2.04\pm 0.07)\times 10^{-23}$ | $7.75\pm 0.01$
FA0051 | $(3.73\pm 0.10)\times 10^{-23}$ | $7.74\pm 0.01$
FA0057 | $(3.24\pm 0.04)\times 10^{-23}$ | $7.73\pm 0.02$
FA0087 | $(2.61\pm 0.09)\times 10^{-23}$ | $7.81\pm 0.01$
FA0090 | $(7.67\pm 0.43)\times 10^{-22}$ | $7.18\pm 0.01$
Table 3.3: Hamamatsu R12669SEL2 Gain fit.

Once extracted the gain curves, they are used help the operating voltage
selection (See Section 3.7). The curves describe the dependence of gain and
current with the voltage and they can give the setting for the PMT once
selected the desired gain or the current for the maximum of the energy range
of interest avoiding the non-linear ranges.

####  3.6.3 Peak-to-valley

The data used to calculate the peak-to-valley ratio were the same that the
used to characterize the gain curve and the light detection algorithms (see
Section 3.5.5) and consequently at low light intensity. For this reason, the
statistical significance of the peak and valley zones is limited and the
errors increase. In any case, the results (see Table 3.4) show a good peak-to-
valley ratio, always above 2.0.

PMT | Peak-to-valley ratio
---|---
FA0022 | $2.0\pm 0.1$
FA0034 | $2.5\pm 0.2$
FA0051 | $2.5\pm 0.1$
FA0057 | $2.2\pm 0.1$
FA0087 | $2.1\pm 0.2$
FA0090 | $2.2\pm 0.2$
Table 3.4: Hamamatsu R12669SEL2 peak-to-valley ratio.

######

These peak-to-valley values show the suitability of the photoelectron
triggering (see Section 3.7).

####  3.6.4 Dark counts

The dark counts were measured twenty hours after their last light exposition
in order to wait for their de-excitation following the conclusion seen in
Section 3.5.7. The trigger level was 2 mV.

######

The dark counts behavior with high voltage for five photomultipliers can be
seen in Figure 3.16 showing an exponential growth with a very intrinsic
behavior for every PMT. The comparison of stable dark current at voltage
corresponding to gain $\times 10^{6}$ with the Hamamatsu data-sheet can be