DAMIC-M Collaboration

# First Constraints from DAMIC-M on Sub-GeV Dark-Matter Particles Interacting
with Electrons

I. Arnquist  Pacific Northwest National Laboratory (PNNL), Richland, WA,
United States  N. Avalos  Centro Atómico Bariloche and Instituto Balseiro,
Comisión Nacional de Energía Atómica (CNEA), Consejo Nacional de
Investigaciones Científicas y Técnicas (CONICET), Universidad Nacional de Cuyo
(UNCUYO), San Carlos de Bariloche, Argentina  D. Baxter  Kavli Institute for
Cosmological Physics and The Enrico Fermi Institute, The University of
Chicago, Chicago, IL, United States  X. Bertou  Centro Atómico Bariloche and
Instituto Balseiro, Comisión Nacional de Energía Atómica (CNEA), Consejo
Nacional de Investigaciones Científicas y Técnicas (CONICET), Universidad
Nacional de Cuyo (UNCUYO), San Carlos de Bariloche, Argentina  N. Castelló-Mor
Instituto de Física de Cantabria (IFCA), CSIC - Universidad de Cantabria,
Santander, Spain  A.E. Chavarria  Center for Experimental Nuclear Physics and
Astrophysics, University of Washington, Seattle, WA, United States  J. Cuevas-
Zepeda  Kavli Institute for Cosmological Physics and The Enrico Fermi
Institute, The University of Chicago, Chicago, IL, United States  J.
Cortabitarte Gutiérrez  Instituto de Física de Cantabria (IFCA), CSIC -
Universidad de Cantabria, Santander, Spain  J. Duarte-Campderros  Instituto de
Física de Cantabria (IFCA), CSIC - Universidad de Cantabria, Santander, Spain
A. Dastgheibi-Fard  LPSC LSM, CNRS/IN2P3, Université Grenoble-Alpes, Grenoble,
France  O. Deligny  CNRS/IN2P3, IJCLab, Université Paris-Saclay, Orsay, France
C. De Dominicis  Laboratoire de physique nucléaire et des hautes énergies
(LPNHE), Sorbonne Université, Université Paris Cité, CNRS/IN2P3, Paris, France
SUBATECH, Nantes Université, IMT Atlantique, CNRS-IN2P3, Nantes, France  E.
Estrada  Centro Atómico Bariloche and Instituto Balseiro, Comisión Nacional de
Energía Atómica (CNEA), Consejo Nacional de Investigaciones Científicas y
Técnicas (CONICET), Universidad Nacional de Cuyo (UNCUYO), San Carlos de
Bariloche, Argentina  N. Gadola  Universität Zürich Physik Institut, Zürich,
Switzerland  R. Gaïor  Laboratoire de physique nucléaire et des hautes
énergies (LPNHE), Sorbonne Université, Université Paris Cité, CNRS/IN2P3,
Paris, France  T. Hossbach  Pacific Northwest National Laboratory (PNNL),
Richland, WA, United States  L. Iddir  Laboratoire de physique nucléaire et
des hautes énergies (LPNHE), Sorbonne Université, Université Paris Cité,
CNRS/IN2P3, Paris, France  L. Khalil  Laboratoire de physique nucléaire et des
hautes énergies (LPNHE), Sorbonne Université, Université Paris Cité,
CNRS/IN2P3, Paris, France  B. Kilminster  Universität Zürich Physik Institut,
Zürich, Switzerland  A. Lantero-Barreda  Instituto de Física de Cantabria
(IFCA), CSIC - Universidad de Cantabria, Santander, Spain  I. Lawson  SNOLAB,
Lively, ON, Canada  S. Lee  Universität Zürich Physik Institut, Zürich,
Switzerland  A. Letessier-Selvon  Laboratoire de physique nucléaire et des
hautes énergies (LPNHE), Sorbonne Université, Université Paris Cité,
CNRS/IN2P3, Paris, France  P. Loaiza  CNRS/IN2P3, IJCLab, Université Paris-
Saclay, Orsay, France  A. Lopez-Virto  Instituto de Física de Cantabria
(IFCA), CSIC - Universidad de Cantabria, Santander, Spain  A. Matalon  Kavli
Institute for Cosmological Physics and The Enrico Fermi Institute, The
University of Chicago, Chicago, IL, United States  Laboratoire de physique
nucléaire et des hautes énergies (LPNHE), Sorbonne Université, Université
Paris Cité, CNRS/IN2P3, Paris, France  S. Munagavalasa  Kavli Institute for
Cosmological Physics and The Enrico Fermi Institute, The University of
Chicago, Chicago, IL, United States  K. McGuire  Center for Experimental
Nuclear Physics and Astrophysics, University of Washington, Seattle, WA,
United States  P. Mitra  Center for Experimental Nuclear Physics and
Astrophysics, University of Washington, Seattle, WA, United States  D. Norcini
Kavli Institute for Cosmological Physics and The Enrico Fermi Institute, The
University of Chicago, Chicago, IL, United States  G. Papadopoulos
Laboratoire de physique nucléaire et des hautes énergies (LPNHE), Sorbonne
Université, Université Paris Cité, CNRS/IN2P3, Paris, France  S. Paul  Kavli
Institute for Cosmological Physics and The Enrico Fermi Institute, The
University of Chicago, Chicago, IL, United States  A. Piers  Center for
Experimental Nuclear Physics and Astrophysics, University of Washington,
Seattle, WA, United States  P. Privitera  Kavli Institute for Cosmological
Physics and The Enrico Fermi Institute, The University of Chicago, Chicago,
IL, United States  Laboratoire de physique nucléaire et des hautes énergies
(LPNHE), Sorbonne Université, Université Paris Cité, CNRS/IN2P3, Paris, France
K. Ramanathan  Kavli Institute for Cosmological Physics and The Enrico Fermi
Institute, The University of Chicago, Chicago, IL, United States  P. Robmann
Universität Zürich Physik Institut, Zürich, Switzerland  M. Settimo  SUBATECH,
Nantes Université, IMT Atlantique, CNRS-IN2P3, Nantes, France  R. Smida  Kavli
Institute for Cosmological Physics and The Enrico Fermi Institute, The
University of Chicago, Chicago, IL, United States  R. Thomas  Kavli Institute
for Cosmological Physics and The Enrico Fermi Institute, The University of
Chicago, Chicago, IL, United States  M. Traina  Center for Experimental
Nuclear Physics and Astrophysics, University of Washington, Seattle, WA,
United States  Laboratoire de physique nucléaire et des hautes énergies
(LPNHE), Sorbonne Université, Université Paris Cité, CNRS/IN2P3, Paris, France
I. Vila  Instituto de Física de Cantabria (IFCA), CSIC - Universidad de
Cantabria, Santander, Spain  R. Vilar  Instituto de Física de Cantabria
(IFCA), CSIC - Universidad de Cantabria, Santander, Spain  G. Warot  LPSC LSM,
CNRS/IN2P3, Université Grenoble-Alpes, Grenoble, France  R. Yajur  Kavli
Institute for Cosmological Physics and The Enrico Fermi Institute, The
University of Chicago, Chicago, IL, United States  J-P. Zopounidis
Laboratoire de physique nucléaire et des hautes énergies (LPNHE), Sorbonne
Université, Université Paris Cité, CNRS/IN2P3, Paris, France

###### Abstract

We report constraints on sub-GeV dark matter particles interacting with
electrons from the first underground operation of DAMIC-M detectors. The
search is performed with an integrated exposure of 85.23 g days, and exploits
the sub-electron charge resolution and low level of dark current of DAMIC-M
Charge-Coupled Devices (CCDs). Dark-matter-induced ionization signals above
the detector dark current are searched for in CCD pixels with charge up to 7
e-. With this data set we place limits on dark matter particles of mass
between 0.53 and 1000 MeV$/c^{2}$, excluding unexplored regions of parameter
space in the mass ranges [1.6,1000] MeV$/c^{2}$ and [1.5,15.1] MeV$/c^{2}$ for
ultra-light and heavy mediator interactions, respectively.

There is overwhelming evidence indicating that our universe is dominated by
non-luminous, non-baryonic dark matter (DM) [1, 2, 3]. The contemporary
Standard Model of Cosmology, $\Lambda$CDM, is consistent with the observed
cosmic background radiation features [4] and large-scale distribution of
galaxies [5, 6] when parameterized with a cold-DM particle density. Many
hypothetical particle candidates with the required properties [7] have been
proposed, however DM has yet to be directly detected. Motivated by a weak-
scale annihilation cross section to explain today’s measured abundance,
searches for Weakly Interacting Massive Particles (WIMPs) with masses larger
than the proton’s ($\approx 1$ GeV$/c^{2}$) have been leading the experimental
landscape. However, with null results from these multi-tonne detectors [8, 9,
10], low-threshold experiments have been developed to search for light (sub-
GeV) DM, including light WIMPs and hidden-sector particles [11]. Such
detectors are designed to be sensitive to both sub-keV nuclear recoils and eV-
scale electronic recoils induced by DM scattering. The latter scenario gives
access to possible hidden-sector DM candidates that interact via a new gauge
boson which is feebly mixed with the photon [12, 13]. Such a mixing provides a
mechanism for DM-e- scattering to occur.

The DAMIC-M (Dark Matter in CCDs at Modane) experiment [14] searches for sub-
GeV DM using skipper Charge-Coupled Devices (CCDs) under the French Alps at
the Laboratoire Souterrain de Modane (LSM). DM-induced ionization events in
the thick silicon bulk can be detected with sub-electron resolution through
non-destructive, repeated pixel readout [15, 16, 17, 18]. Combined with an
extremely low dark current [19, 20], sensitivity to single-electron
measurements allows DAMIC-M to achieve an energy threshold of a few eV. The
completed experiment will feature $\approx$700 g of target mass with an
expected total background of a fraction of a dru 1111 dru = 1
event/kg/keV/day.. A prototype detector, the Low Background Chamber (LBC), is
currently operating at LSM. The LBC aims to demonstrate the performance of the
CCDs, background control strategy, and the sensitivity to light dark matter.

In this letter, we present the first search for sub-GeV DM with the DAMIC-M
LBC. With an integrated exposure of 85.23 g days, we set world-leading limits
on dark matter-electron scattering interactions via heavy and ultralight
mediators. The DM interaction model, data-taking conditions, and analysis
strategy are detailed in the following.

Theoretical expectations for hidden-sector DM interactions in crystalline
silicon are derived in Refs. [21, 22, 23, 24]. The differential event rate
from DM-e- interactions in the detector for a DM mass $m_{\chi}$ with recoil
energy $E_{e}$ is parameterized as [21]

$\frac{dR}{dE_{e}}\propto\bar{\sigma}_{e}\int\frac{dq}{q^{2}}\eta(m_{\chi},q,E_{e})|F_{\text{DM}}(q)|^{2}|f_{c}(q,E_{e})|^{2},$
(1)

where $\bar{\sigma}_{e}$ is a model-independent reference cross section for
DM-e- elastic scattering, $q$ is the transferred momentum, $\eta$ includes
properties of the incident flux of galactic DM particles, $F_{DM}$ is the DM
form factor, and $f_{\textnormal{c}}(q,E_{e})$ quantifies the atomic
transitions of bound-state electrons [21]. The DM form factor $F_{DM}=(\alpha
m_{e}/q)^{n}$, where $\alpha$ is the fine-structure constant and $m_{e}$ the
electron mass, describes the momentum-transfer dependence of the interaction,
with $n=0$ for a point-like interaction with heavy mediators (mass $\gg\alpha
m_{e}$) or a magnetic dipole coupling, $n=1$ for an electric dipole coupling,
and $n=2$ for massless or ultra-light mediators (mass $\ll\alpha m_{e}$). The
crystal form factor $f_{c}$, which includes the material properties of the
silicon target, is calculated numerically with a DFT (density functional
theory) approach (see Refs. [21, 25]).

Figure 1: The DAMIC-M Low Background Chamber installed underground at LSM: the
two skipper CCDs are monted in a high-purity copper box (right); the box is
placed inside the copper cryostat, visible here (left) during assembly of the
external lead and polyethylene shielding.

Data are collected with two large-area, thick CCDs featuring 6144 $\times$
4128 pixels, as shown in Fig. 1(right). Each pixel is a 15$\times$15
$\mathrm{\mu m^{2}}$ square with a thickness of 670 $\mathrm{\mu m}$, such
that the total target mass per CCD is $\approx$9 g. The CCD has a three-phase
polysilicon gate structure with a buried p-channel, where charge carriers
collected from fully depleted high-resistivity ($>$10 k$\Omega$ cm) n-type
silicon bulk are clocked toward a readout amplifier [26, 27, 28]. Flex cables
wire-bonded to the CCD provide the required voltage biases and clocks.

The two CCDs are mounted in a high-purity, oxygen-free, high-conductivity
copper box, which also acts as a shield to infrared radiation. To minimize
leakage current, the CCDs are operated at low temperature ($\approx 130$ K)
under vacuum (pressure $\sim$5$\times$10-6 mbar) inside the LBC cryostat, as
in Fig. 1(left). The CCD box is surrounded by at least 7.5 cm of very low-
background lead ($\leq$ 7 mBq/kg 210Pb), with the innermost 2 cm of ancient
origin, to mitigate gamma radiation from components located in the cryostat:
cables, electronics, fasteners, and cryocooler. In addition, 15 cm of low-
background lead (54 Bq/kg 210Pb) and 20 cm of high-density polyethylene
surround the cryostat to attenuate high-energy $\gamma$-rays and neutrons, as
shown in Fig. 1(left). All parts of the detector are appropriately cleaned to
remove any surface contamination [29, 30]. A full simulation of the apparatus
with Geant4 [31] gives an expected total background of $\sim$10 dru for this
initial LBC installation. The simulation includes realistic amounts of
radioactive contaminants as determined by radioassay measurements and
bookkeeping of cosmogenic activation time of materials (see Ref. [32] for
similar methods). This level of background, similar to that achieved by DAMIC
at SNOLAB [32], was confirmed during the LBC commissioning and has negligible
impact on the analysis presented in this letter. Voltage biases and clocks to
operate the devices are provided by a commercial CCD controller from
Astronomical Research Cameras, Inc. placed outside the external shielding.

A DM-e- interaction in the bulk silicon of the CCD will generate charge
carriers in numbers proportional to the energy deposited. The voltage bias
applied for full depletion of the substrate (70 V) drifts the charge along the
z-direction toward the x-y plane of the CCD pixel array. Thermal diffusion in
the transverse direction results in a spatial variance of the charge collected
at the pixel array, $\mathrm{\sigma^{2}_{xy}}$, proportional to the transit
time [33]. To read out the pixel, charge is moved by voltage clocks, first
vertically row-by-row toward the serial register of the CCD, and then
horizontally, to the two charge-to-voltage amplifiers (referred to as U and L)
at each end of the serial register. DAMIC-M CCDs feature skipper amplifiers
[15, 16, 17], which can be configured to make multiple, non-destructive charge
measurements (NDCMs). The charge resolution improves as
$1/\sqrt{\rm{N_{skip}}}$, where $\rm{N_{skip}}$ is the number of NDCMs, when
averaging all the measurements, reaching a sub-electron level for sufficiently
large $\rm{N_{skip}}$. Details on the performance of DAMIC-M skipper CCDs can
be found in Ref. [18].

After commissioning of the CCDs – which includes optimizing the operating
parameters for charge transfer efficiency, resolution, and dark current – two
data sets with similar exposures are collected. An optimal value of
$\rm{N_{skip}}=650$ is adopted, as a good compromise between charge resolution
and pixel exposure to dark current. A 10$\times$10 pixel binning 222Pixel
binning is an operating mode of the CCD where the charge of several pixels is
summed before being read out. An n$\times$m binning corresponds to summing the
charge of n pixels in the horizontal direction and m pixels in the vertical
direction. is used for the readout. By binning, charge from a point-like
energy deposit distributed by diffusion over several physical pixels is summed
before measurement, improving the signal-to-noise ratio. The binning size is
optimized using the measured value of $\mathrm{\sigma_{xy}}$ (see [32] for the
measurement method) so that DM interactions are most likely contained in a
single binned pixel. For the remainder of this text, the term pixel is used to
describe a 10$\times$10 bin of pixels (i.e., 150$\times$150 $\mu\rm{m^{2}}$).
A continuous readout mode, where images of 640$\times$840 ($\rm{N_{col}\times
N_{row}}$) pixels are taken subsequently, each beginning immediately after the
end of the previous one, is implemented for Science Run 1 (SR1), resulting in
the same exposure time for each pixel. In Science Run 2 (SR2), only a fraction
of the CCD is read out (640$\times$110 pixels), and the charge in the CCD is
cleared between consecutive images. In this mode the pixel’s exposure time
increases linearly as a function of row, and a lower average charge
accumulates during the pixel exposure ($\approx$0.0033 e-/pixel/image in SR2
vs $\approx$0.012 e-/pixel/image in SR1) resulting in a lower rate of pixels
with charge $>$ 1 e-. As the LBC is still in its commissioning phase, this
level of dark current ($\approx$20 e-/mm2/day) is several times higher than
the lowest reached in CCDs [19, 20], but sufficiently low to perform a
sensitive search for DM.

The following procedure is used to reduce and calibrate the raw CCD images.
First, the pixel charge is obtained by averaging the NDCMs. Then, a DC offset,
or pedestal, introduced by the electronics chain is subtracted. The pedestal
value is determined row-by-row from a Gaussian fit of the charge
distribution’s most prominent peak, comprised of pixels with zero charge.

Figure 2: Example of a pixel charge distribution with peaks corresponding to
individual charges. This distribution, with pixels from the U amplifier of the
SR2 data set, constitutes about 40% of the full data set used for the DM
search. The red line is the fit result for the background-only hypothesis (no
DM-e-). The dashed violet line is the expectation for background plus a DM-e-
heavy-mediator model with $m_{\chi}$=12 MeV$/c^{2}$ and $\bar{\sigma}_{e}$ =
$2\times 10^{-37}~{}\rm{cm^{2}}$, which is equal to the 90% CL limit value
obtained at this mass.

The calibration constant, which converts the measured analog-to-digital units
(ADU) into the number of electrons 333For the sake of simplicity, we use the
term electrons to indicate charge carriers detected in the CCD. However, holes
are held in the pixels of the p-channel CCD used for this measurement., is
obtained by fitting a Gaussian function convolved with a Poisson distribution
[18]. The charge resolution, $\sigma_{\text{res}}\approx$ 0.2 $e^{-}$, is
estimated from the standard deviation of the Gaussian fit. The U and L
amplifiers in each CCD are calibrated independently. An example of a
calibrated pixel charge distribution is shown in Fig. 2 where the peaks
correspond to 0, 1 and 2 e-, from left to right. We then identify energy
deposits, which may extend over more than one pixel. Adjacent pixels with
charge $\geq 3\,\sigma_{\text{res}}$ are grouped together as a cluster if at
least one pixel has $\geq 2$ e-. Clusters or single isolated pixels with
charge $>7$ e- are excluded from further analysis since the probability that
they originate from a DM interaction is negligible for the DM mass range of
interest. We also exclude the 10 trailing pixels in the horizontal and
vertical directions to account for charge transfer inefficiencies. Defects in
the CCD may release charge during the readout process, appearing as “hot”
pixels and columns [34]. To identify these defects, we parametrize the 1e-
rate as a function of column number $i_{\rm{col}}$ with a second-order
polynomial $P_{pol}(i_{\rm{col}})$ and then tag columns with a rate exceeding
the parametrization by more than 2 $\sigma$. We also use a dedicated data set
of 13 images with 3-hour exposures to identify high-charge pixels recurring in
multiple images. Columns corresponding to the identified defects are then
excluded from the analysis. Finally, we identify the location of artifacts in
the serial register as columns with a sizable reduction in dark current, i.e.
with 1e- rate $>2~{}\sigma$ below the parametrization $P_{pol}(i_{\rm{col}})$.
While moving through a serial register, charge transfer may be delayed by the
presence of a trap or a local anomaly in the electric fields, effectively
changing the expected pixel charge distribution from a DM interaction. Thus,
we select only portions of the CCD active area not affected by serial register
artifacts. Several such artifacts are identified in one of the two prototype
CCDs, which is therefore excluded from further analysis. For the remaining
CCD, pixels in the L side with $i_{\rm{col}}~{}>$ 74 are rejected. After
applying the selection criteria, the final integrated exposure for the DM
search is 85.23 g-days (45.26 g-days for SR1 and 39.97 g-days for SR2). No
pixel with charge $\geq 4$ e- and $\leq 7$ e- is present in this data set444In
a preliminary analysis of the SR1 dataset [14] one $4$ e- event was found.
This event is removed from the present analysis by the rejection criterion for
serial register artifacts., improving by one order of magnitude previous
limits in silicon at these charge multiplicities [20].

To place an upper limit on the DM signal a joint binned-likelihood fit is
performed on four pixel distributions (one for each amplifier in each of the
two science runs). An entry in these distributions corresponds to the value of
one unmasked pixel (out of $\rm{N_{pix}}$) in one image (out of
$\rm{N_{im}}$). The charge of a pixel may come from different background
sources [34], including thermally-generated or stress-induced dark counts,
spurious clock-induced charge, and photoabsorption of light from the readout
amplifiers. These are all Poisson processes that act as a source of
uncorrelated, single electrons with mean value of $\lambda_{i}$ for the $i$th
pixel in the CCD. Since different pixels can have different exposures, and
most background sources depend on the location of the pixel in the CCD (e.g.,
local stress, physical distance from the readout amplifiers, number of charge
transfers to the readout amplifier, etc.), $\lambda_{i}$ varies for each
pixel. To estimate $\lambda_{i}$ for a given pixel $i$, we perform a fit to
the 0 and 1 electron peaks in the distribution of the $\rm{N_{im}}$ charge
values of pixel $i$. We then build the background-only hypothesis $B$ by
adding the contribution from every pixel in the data set:

$B(p|\lambda_{i},\sigma_{\text{res}})=\sum_{i=0}^{\mathrm{N_{pix}}}\mathrm{N_{im}}\sum_{n_{q}=0}^{\infty}\text{Pois}(n_{q}|\lambda_{i})\text{Gaus}(p|n_{q},\sigma_{\text{res}}),$
(2)

where $p$ is the observed charge value given $n_{q}$ electrons collected by
the pixel in an image. $\text{Pois}(n_{q}|\lambda_{i})$, the Poisson
probability of obtaining $n_{q}$ given $\lambda_{i}$, is the amplitude of
Gaussian functions $\text{Gaus}(p|n_{q},\sigma_{\rm res})$ with mean $n_{q}$
and standard deviation $\sigma_{\rm res}$ to model the readout noise.

A DM flux of particles with $m_{\chi}$ and $\bar{\sigma}_{e}$ may contribute
$j$ charges in a pixel with exposure $\epsilon_{i}$ with probability
distribution $S(j|m_{\chi},\bar{\sigma}_{e},\epsilon_{i})$. The fit function
$F$ which includes both the signal and background model is then given by:

$F(p|m_{\chi},\bar{\sigma}_{e},\epsilon_{i},\lambda_{i},\sigma_{\text{res}})=\sum_{i=0}^{\mathrm{N_{pix}}}\mathrm{N_{\mathrm{im}}}\sum_{n_{q}=0}^{\infty}\left[\sum_{j=0}^{n_{q}}S(j|m_{\chi},\bar{\sigma}_{e},\epsilon_{i})\text{Pois}(n_{q}-j|\lambda_{i}-\lambda_{S,i})\right]\text{Gaus}(p|n_{q},\sigma_{\text{res}}).$
(3)

A DM signal that contributes to the one-electron counts would make our
empirical procedure for the background model overestimate $\lambda_{i}$. We
correct for this effect by subtracting from $\lambda_{i}$ in Eq. 3 the number
of one-electron counts contributed by a given signal $S$ in the ith pixel,
$\lambda_{S,i}$. Note that for $m_{\chi}<$1 MeV$/c^{2}$, where interactions
produce at most one electron, the signal is indistinguishable from the
background model and only an upper limit on the interaction rate can be
placed.

Figure 3: DAMIC-M 90% C.L. upper limits (solid black) on DM-electron
interactions through a ultra-light mediator (left) and heavy mediator (right).
Also shown are current best direct-detection limits from other experiments,
DAMIC-SNOLAB [35] (dashed black), SENSEI [20] (solid gray), EDELWEISS [36]
(dashed gray), SuperCDMS [37, *PhysRevLett.122.069901] (dotted gray),
DarkSide-50 [39] (solid violet), XENON1T combined result from [40, 41] (dashed
violet), PandaX-II [42] (dotted violet), and a limit obtained from XENON10
data in Ref. [43] (dash-dotted violet). Theoretical expectations assuming a DM
relic abundance from freeze-in and freeze-out mechanisms are also shown in
light blue [11].

The DM signal $S$ is computed with Eq. 1 using QEDark [21] for $f_{c}$ and a
standard Maxwell-Boltzmann velocity distribution for the $\eta$ factor with
parameters of the DM density profile in the galactic halo as recommended in
Ref. [44]555Local dark matter density $\rho_{\chi}=0.3~{}$GeV/c2/cm3, mean
$v_{0}=238.0$ km/s, escape velocity $v_{\text{esc}}=544$ km/s, and mean
periodic Earth velocity $v_{\text{E}}=250.2$ km/s. We obtain the DM
interaction rate as a function of discrete ionization charges starting with
the semi-empirical electron-hole pair creation probabilities
$P_{pair}(n_{q}|E_{e})$ from the charge yield model of Ref. [45]. A Monte
Carlo (MC) simulation is then used to include the detector response. Charge is
injected uniformly across the sensitive volume of the CCD and diffused on the
pixel array with a Gaussian transverse variance
$\mathrm{\sigma^{2}_{xy}(z)}=-a\ln|1-b\mathrm{z}|\cdot(\alpha+\beta
E_{e})^{2}$, with parameters $a=2108~{}\mu\rm{m}^{2}$, $b=1.98\times
10^{-4}~{}\mu\rm{m^{-1}}$, $\alpha=0.859$, and $\beta=0.0067~{}\rm{keV^{-1}}$
calibrated with cosmic rays in a surface lab (see e.g. Ref. [32]). A 10x10
binning of the simulated CCD array is then performed to match the data-taking
conditions. This procedure, repeated for different DM masses, yields the
signal $S$ in Eq. 3.

We then fit the model of Eq. 3 to data by maximizing a binned log-likelihood
$\mathcal{L}$, which assumes Poisson bin content. Since the charge resolution
is set by the individual amplifier’s readout noise, $\sigma_{\text{res}}$ is
an independent free parameter for each of the four pixel distributions. An
example of a fit result for the background-only hypothesis ($\bar{\sigma}_{e}$
=0) is shown in Fig. 2 for the U amplifier of the SR2 data set. Also shown for
illustration is the expected distribution for the background model plus a DM
heavy-mediator signal with $m_{\chi}$=12 MeV$/c^{2}$ and $\bar{\sigma}_{e}$ =
$2\times 10^{-37}~{}\rm{cm^{2}}$ equal to the 90% CL limit value obtained at
this mass.

No preference is found for a DM signal and exclusion limits are derived
accordingly. We use the approach of Ref. [46] and the profile likelihood ratio
test statistic, $t_{\sigma}=-2\log\lambda(\sigma)$ where $\lambda(\sigma)$ is
the profile likelihood ratio, at each DM mass. The DAMIC-M $90\%~{}$C.L.
exclusion limits for heavy (right) and ultra-light (left) mediator sub-GeV DM
are shown in Fig. 3. We find these limits to be within the expected 68%
sensitivity band as estimated by MC simulations. Results from other direct
detection experiments are also shown in Fig. 3, where the limit from SENSEI
[20], which also uses skipper CCDs, was recasted for proper comparison by
using the same halo parameters [44] and charge yield model [45] adopted in
this analysis. Theoretical expectations for models which reproduce the correct
DM relic abundance by thermal “freeze-out” of DM annihilation into standard
model particles (heavy mediator) during the early universe or “freeze-in” of
standard model particles annihilation into DM (ultra-light mediator) [21] are
also shown in Fig. 3.

Several cross-checks of the analysis procedures have been performed. We verify
with dedicated data sets that pixel charge multiplicities relevant to this
analysis are not altered by charge transfer inefficiency. A more elaborate 2-D
analysis of the pixel charge distribution, which slightly improves charge
resolution by exploiting noise correlation between symmetric pixels on the U
and L side, is employed. Independent cross-checks have been performed at every
step in the analysis, starting from the low-level image processing to the
generation of the data pixel distribution, the identification of defects, the
modeling of the DM signal, and the extraction of the DM signal upper limit.
Consistent results are obtained in all of these checks, indicating no major
systematic effect in our procedure. We evaluate theoretical uncertainties
associated with the calculation of the DM-e- interaction rate by using DarkELF
[24] and EXCEED-DM [23, 47] predictions for the signal $S$. The corresponding
limits are between 2 and 60 times worse than the QEDark-based results of Fig.
3, with the largest difference at low DM masses. Thus approximations in the
theoretical models (e.g. no in-medium screening effects in QEDark) have
significant impact.

This DAMIC-M search for DM particles of mass between 0.53 and 1000 MeV$/c^{2}$
excludes unexplored regions of parameter space in mass ranges [1.6,1000]
MeV$/c^{2}$ for an ultra-light mediator and [1.5,15.1] MeV$/c^{2}$ for a heavy
mediator.

Efforts are ongoing to significantly decrease the dark current in upcoming
upgrades to the LBC, including the deployment of the final DAMIC-M CCD modules
with lower mechanical stress, better shielding from infrared radiation, and
readout electronics with lower noise.

###### Acknowledgements.

We thank the LSM for their support in the installation and operation of the
detector underground. The DAMIC-M project has received funding from the
European Research Council (ERC) under the European Union’s Horizon 2020
research and innovation programme Grant Agreement No. 788137, and from NSF
through Grant No. NSF PHY-1812654. The work at University of Chicago and
University of Washington was supported through Grant No. NSF PHY-2110585. This
work was supported by the Kavli Institute for Cosmological Physics at the
University of Chicago through an endowment from the Kavli Foundation. We thank
the College of Arts and Sciences at UW for contributing the first CCDs to the
DAMIC-M project. IFCA was supported by project PID2019-109829GB-I00 funded by
MCIN/ AEI /10.13039/501100011033. The Centro Atómico Bariloche group is
supported by ANPCyT grant PICT-2018-03069. The University of Zürich was
supported by the Swiss National Science Foundation. The CCD development work
at Lawrence Berkeley National Laboratory MicroSystems Lab was supported in
part by the Director, Office of Science, of the U.S. Department of Energy
under Contract No. DE-AC02-05CH11231. We thank Teledyne DALSA Semiconductor
for CCD fabrication.

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