COSINE-100 Collaboration

# Searching for low-mass dark matter via Migdal effect in COSINE-100

G. Adhikari  Department of Physics, University of California San Diego, La
Jolla, CA 92093, USA  N. Carlin  Physics Institute, University of São Paulo,
05508-090, São Paulo, Brazil  J. J. Choi  Department of Physics and Astronomy,
Seoul National University, Seoul 08826, Republic of Korea  S. Choi  Department
of Physics and Astronomy, Seoul National University, Seoul 08826, Republic of
Korea  A. C. Ezeribe  Department of Physics and Astronomy, University of
Sheffield, Sheffield S3 7RH, United Kingdom  L. E. França  Physics Institute,
University of São Paulo, 05508-090, São Paulo, Brazil  C. Ha  Department of
Physics, Chung-Ang University, Seoul 06973, Republic of Korea  I. S. Hahn
Department of Science Education, Ewha Womans University, Seoul 03760, Republic
of Korea  Center for Exotic Nuclear Studies, Institute for Basic Science
(IBS), Daejeon 34126, Republic of Korea  IBS School, University of Science and
Technology (UST), Daejeon 34113, Republic of Korea  S. J. Hollick  Department
of Physics and Wright Laboratory, Yale University, New Haven, CT 06520, USA
E. J. Jeon  Center for Underground Physics, Institute for Basic Science (IBS),
Daejeon 34126, Republic of Korea  J. H. Jo  Department of Physics and Wright
Laboratory, Yale University, New Haven, CT 06520, USA  H. W. Joo  Department
of Physics and Astronomy, Seoul National University, Seoul 08826, Republic of
Korea  W. G. Kang  Center for Underground Physics, Institute for Basic Science
(IBS), Daejeon 34126, Republic of Korea  M. Kauer  Department of Physics and
Wisconsin IceCube Particle Astrophysics Center, University of Wisconsin-
Madison, Madison, WI 53706, USA  H. Kim  Center for Underground Physics,
Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea  H. J. Kim
Department of Physics, Kyungpook National University, Daegu 41566, Republic of
Korea  J. Kim  Department of Physics, Chung-Ang University, Seoul 06973,
Republic of Korea  K. W. Kim  Center for Underground Physics, Institute for
Basic Science (IBS), Daejeon 34126, Republic of Korea  S. H. Kim  Center for
Underground Physics, Institute for Basic Science (IBS), Daejeon 34126,
Republic of Korea  S. K. Kim  Department of Physics and Astronomy, Seoul
National University, Seoul 08826, Republic of Korea  W. K. Kim  IBS School,
University of Science and Technology (UST), Daejeon 34113, Republic of Korea
Center for Underground Physics, Institute for Basic Science (IBS), Daejeon
34126, Republic of Korea  Y. D. Kim  Center for Underground Physics, Institute
for Basic Science (IBS), Daejeon 34126, Republic of Korea  Department of
Physics, Sejong University, Seoul 05006, Republic of Korea  IBS School,
University of Science and Technology (UST), Daejeon 34113, Republic of Korea
Y. H. Kim  Center for Underground Physics, Institute for Basic Science (IBS),
Daejeon 34126, Republic of Korea  Korea Research Institute of Standards and
Science, Daejeon 34113, Republic of Korea  IBS School, University of Science
and Technology (UST), Daejeon 34113, Republic of Korea  Y. J. Ko
<EMAIL_ADDRESS>Center for Underground Physics, Institute for Basic Science
(IBS), Daejeon 34126, Republic of Korea  H. J. Kwon  IBS School, University of
Science and Technology (UST), Daejeon 34113, Republic of Korea  Center for
Underground Physics, Institute for Basic Science (IBS), Daejeon 34126,
Republic of Korea  D. H. Lee  Department of Physics, Kyungpook National
University, Daegu 41566, Republic of Korea  E. K. Lee  Center for Underground
Physics, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea
H. Lee  IBS School, University of Science and Technology (UST), Daejeon 34113,
Republic of Korea  Center for Underground Physics, Institute for Basic Science
(IBS), Daejeon 34126, Republic of Korea  H. S. Lee<EMAIL_ADDRESS>Center
for Underground Physics, Institute for Basic Science (IBS), Daejeon 34126,
Republic of Korea  IBS School, University of Science and Technology (UST),
Daejeon 34113, Republic of Korea  H. Y. Lee  Center for Underground Physics,
Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea  I. S. Lee
Center for Underground Physics, Institute for Basic Science (IBS), Daejeon
34126, Republic of Korea  J. Lee  Center for Underground Physics, Institute
for Basic Science (IBS), Daejeon 34126, Republic of Korea  J. Y. Lee
Department of Physics, Kyungpook National University, Daegu 41566, Republic of
Korea  M. H. Lee  Center for Underground Physics, Institute for Basic Science
(IBS), Daejeon 34126, Republic of Korea  IBS School, University of Science and
Technology (UST), Daejeon 34113, Republic of Korea  S. H. Lee  IBS School,
University of Science and Technology (UST), Daejeon 34113, Republic of Korea
Center for Underground Physics, Institute for Basic Science (IBS), Daejeon
34126, Republic of Korea  S. M. Lee  Department of Physics and Astronomy,
Seoul National University, Seoul 08826, Republic of Korea  D. S. Leonard
Center for Underground Physics, Institute for Basic Science (IBS), Daejeon
34126, Republic of Korea  B. B. Manzato  Physics Institute, University of São
Paulo, 05508-090, São Paulo, Brazil  R. H. Maruyama  Department of Physics and
Wright Laboratory, Yale University, New Haven, CT 06520, USA  R. J. Neal
Department of Physics and Astronomy, University of Sheffield, Sheffield S3
7RH, United Kingdom  S. L. Olsen  Center for Underground Physics, Institute
for Basic Science (IBS), Daejeon 34126, Republic of Korea  B. J. Park  IBS
School, University of Science and Technology (UST), Daejeon 34113, Republic of
Korea  Center for Underground Physics, Institute for Basic Science (IBS),
Daejeon 34126, Republic of Korea  H. K. Park  Department of Accelerator
Science, Korea University, Sejong 30019, Republic of Korea  H. S. Park  Korea
Research Institute of Standards and Science, Daejeon 34113, Republic of Korea
K. S. Park  Center for Underground Physics, Institute for Basic Science (IBS),
Daejeon 34126, Republic of Korea  S. D. Park  Department of Physics, Kyungpook
National University, Daegu 41566, Republic of Korea  R. L. C. Pitta  Physics
Institute, University of São Paulo, 05508-090, São Paulo, Brazil  H. Prihtiadi
Center for Underground Physics, Institute for Basic Science (IBS), Daejeon
34126, Republic of Korea  S. J. Ra  Center for Underground Physics, Institute
for Basic Science (IBS), Daejeon 34126, Republic of Korea  C. Rott  Department
of Physics, Sungkyunkwan University, Suwon 16419, Republic of Korea
Department of Physics and Astronomy, University of Utah, Salt Lake City, UT
84112, USA  K. A. Shin  Center for Underground Physics, Institute for Basic
Science (IBS), Daejeon 34126, Republic of Korea  A. Scarff  Department of
Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United
Kingdom  N. J. C. Spooner  Department of Physics and Astronomy, University of
Sheffield, Sheffield S3 7RH, United Kingdom  W. G. Thompson  Department of
Physics and Wright Laboratory, Yale University, New Haven, CT 06520, USA  L.
Yang  Department of Physics, University of California San Diego, La Jolla, CA
92093, USA  G. H. Yu  Department of Physics, Sungkyunkwan University, Suwon
16419, Republic of Korea

###### Abstract

We report on the search for weakly interacting massive particle (WIMP) dark
matter candidates in the galactic halo that interact with sodium and iodine
nuclei in the COSINE-100 experiment and produce energetic electrons that
accompany recoil nuclei via the the Migdal effect. The WIMP mass sensitivity
of previous COSINE-100 searches that relied on the detection of ionization
signals produced by target nuclei recoiling from elastic WIMP-nucleus
scattering was restricted to WIMP masses above $\sim$5 GeV/$c^{2}$ by the
detectors’ 1 keVee energy-electron-equivalent threshold. The search reported
here looks for recoil signals enhanced by the Migdal electrons that are
ejected during the scattering process. This is particularly effective for the
detection of low-mass WIMP scattering from the crystals’ sodium nuclei in
which a relatively larger fraction of the WIMP’s energy is transferred to the
nucleus recoil energy and the excitation of its orbital electrons. In this
analysis, the low-mass WIMP search window of the COSINE-100 experiment is
extended to WIMP mass down to 200 MeV/$c^{2}$. The low-mass WIMP sensitivity
will be further improved by lowering the analysis threshold based on a
multivariable analysis technique. We consider the influence of these
improvements and recent developments in detector performance to re-evaluate
sensitivities for the future COSINE-200 experiment. With a 0.2 keVee analysis
threshold and high light-yield NaI(Tl) detectors (22 photoelectrons/keVee),
the COSINE-200 experiment can explore low-mass WIMPs down to 20 MeV/$c^{2}$
and probe previously unexplored regions of parameter space.

##  I Introduction

A number of astrophysical observations provide evidence that the dominant
matter component of the Universe is not ordinary matter, but rather non-
baryonic dark matter Clowe:2006eq ; Ade:2015xua . Theoretically favored dark
matter candidates are weakly interacting massive particles (WIMPs)
PhysRevLett.39.165 ; Goodman:1984dc . Many direct searches for WIMP dark
matter in deep underground laboratories have been performed and have yet to
find a signal PhysRevLett.118.021303 ; Agnese:2017njq ; Aprile:2017iyp ;
DarkSide:2018bpj ; XENON:2018voc ; CRESST:2019jnq ; Zyla:2020zbs . In light of
the absence of signal in the WIMP dark matter mass range of GeV/c2 to TeV/c2,
there is an increasing interest in low-mass dark matter particles in the sub-
GeV/c2 mass range Essig:2013lka ; XENON:2016jmt ; XENON:2019gfn ;
DAMIC:2019dcn ; EDELWEISS:2020fxc ; SENSEI:2020dpa ; SuperCDMS:2020aus ;
PandaX-II:2021nsg .

In this paper, we report on low-mass dark matter searches for WIMP-nuclei
interactions by looking for electron recoils induced from secondary radiation
via the Migdal process Migdal ; Ibe:2017yqa  in COSINE-100 data. Data used for
COSINE-100 searches has a 1 keVee analysis threshold Adhikari:2020xxj ;
COSINE-100:2021xqn , where the unit keVee is the electron recoil-equivalent
energy in kiloelectron volts. Since the total energy in the Migdal electron
and the nuclear recoil is larger than the deposited energy of typical elastic
nuclear recoil, our searches are extended to WIMP masses as low as 200 MeV/c2.

In the future, this search can be enhanced by lowering the analysis threshold
through multivariable analysis or deep machine learning techniques, as
discussed in Section V, where we evaluate sensitivities of the COSINE-200
experiment, which will have lower analysis threshold, reduced internal
background by controlled crystal growth COSINE:2020egt  and improved light
yield using a novel encapsulation method Choi:2020qcj .

##  II Experiment

The COSINE-100 experiment Adhikari:2017esn  is installed in the Yangyang
underground laboratory (Y2L) utilizing the space provided by the Yangyang
pumped storage power plant in South Korea Kims:2005dol ; Kim:2012rza . The
laboratory is located at a vertical depth of 700 m that provides a water-
equivalent overburden of 1800 m Prihtiadi:2017inr . A 2-km-long driveway
provides access to the laboratory as well as air ventilation. The laboratory
is equipped with a cleanroom and an air-conditioning system providing a low
dust level, and constant temperature and humidity of 24.21$\pm$0.06∘C and
36.7$\pm$1.0%, respectively Adhikari:2017esn ; Kim:2021rsj . The contamination
level of 222Rn in the room is measured to 36.7$\pm$5.5 Bq/m3. The readout
electronics, high voltages that are applied to photomultiplier tubes (PMTs),
and data acquisition system are also monitored and stably maintained
Kim:2021rsj .

The COSINE-100 detector, shown in Fig. 1, consists of a 106 kg array of eight
ultra-pure NaI(Tl) crystals each coupled to two PMTs. The crystal array is
immersed in an active veto detector comprised of 2,200 L of linear
alkylbenzene (LAB)-based liquid scintillator (LS) to attenuate or tag the
influence of external or internal radiations Park:2017jvs ; Adhikari:2020asl .
The LAB-LS is contained within a box made with 1 cm thick acrylic and 3 cm
thick oxygen-free copper that is surrounded by a 20 cm thick lead shield. An
outer array of plastic scintillation counters is used to tag and veto cosmic-
ray muons Prihtiadi:2017inr ; Prihtiadi:2020yhz .

Figure 1: Schematic of the COSINE-100 detector. The NaI(Tl) (106 kg) detectors
are immersed in the 2,200 L LAB-LS that is surrounded by layers of copper and
lead shielding.

An event is triggered when coincident single photoelectrons in both PMTs that
are coupled to a single crystal are observed within a 200 ns time window. If
at least one crystal satisfies the trigger condition, data from all crystals
and the LAB-LS are recorded. The signals from the crystal PMTs are processed
by 500 MHz flash analog-to-digital converters and are 8 $\mu$s long waveforms
that start 2.4 $\mu$s before the trigger. The LAB-LS and plastic scintillator
signals are processed by charge-sensitive flash analog-to-digital converters.
Muon events are triggered by coincident signals from at least two plastic
scintillators. The LAB-LS signals do not generate triggers, except in the case
of energetic muon events that are coincident with one of the muon detector
panels. A trigger and clock board read the trigger information from individual
boards and generate a global trigger and time synchronizations for all of the
modules. Details of the COSINE-100 data acquisition system are described in
Ref. Adhikari:2018fpo .

##  III Migdal effect

Direct detection of WIMP dark matter with mass below sub-GeV/c2 is limited by
an energy threshold of the detector in the range about 0.1–1 keVee. Because
the nuclear recoil energies from WIMP-nuclei interactions are quenched (the
scintillation signals from nuclear recoils are only an order of 10 % of the
signals from the same energy deposition of electrons Manzur:2009hp ;
Lee:2015xla ; Joo:2018hom ; Kimura:2019rdg ), this energy range corresponds to
1–10 keVnr, where keVnr is kiloelectron volt nuclear recoil energy. The WIMP-
nucleus interaction used in typical direct detection searches assumes that the
electron cloud is tightly bound to the nucleus and that the orbit electrons
remain in stable states. However, energy transferred to nuclei after collision
may lead to excitation or ionization of atomic electrons via the Migdal
process Migdal ; Ibe:2017yqa . This process can lead to the production of
energetic electron-induced signals that are produced in association with the
primary nuclear recoil. For a WIMP-nucleus interaction, even if the electron
equivalent energy implied by the quenching factor is below the energy
threshold of the detector, these Midgal-effect secondary electrons can produce
electron equivalent energy that are above the threshod, making detectors
sensitive to sub-GeV/c2 dark matter interactions. Several experimental groups
have already exploited this effect to search for dark matter with sub GeV/c2
masses LUX:2018akb ; EDELWEISS:2019vjv ; CDEX:2019hzn ; XENON:2019zpr ;
GrillidiCortona:2020owp .

The differential nuclear recoil rate per unit target mass for elastic
scattering between WIMPs of mass $m_{\chi}$ and target nuclei of mass $M$ is
Savage:2008er ,

$\displaystyle\frac{dR_{\mathrm{nr}}}{dE_{\mathrm{nr}}}=\frac{\rho_{\chi}}{2m_{\chi}\mu^{2}}~{}\sigma(M,~{}E_{\mathrm{nr}})\int_{v>v_{\mathrm{min}}}d^{3}v~{}f(\textbf{v},~{}t),$
(1)

where $\rho_{\chi}$ is the local dark matter density, $E_{\mathrm{nr}}$ is the
nuclear recoil energy, $\sigma(M,E_{\mathrm{nr}})$ is the WIMP-nucleus cross
section and $f(\textbf{v},t)$ is the time-dependent WIMP velocity
distribution. The reduced mass $\mu$ is defined as $m_{\chi}M/(m_{\chi}+M)$
and the minimum WIMP velocity $v_{\mathrm{min}}$ is
$\sqrt{ME_{\mathrm{nr}}/2\mu^{2}}$.

The rate of ionization due to the Migdal effect for a nuclear recoil energy
$E_{\mathrm{nr}}$ accompanied by an ionization electron with energy $E_{ee}$
is given by the nuclear recoil in Eq. 1 multiplied by the ionization rate
Ibe:2017yqa ,

$\begin{split}\frac{dR}{dE_{\mathrm{ee}}}&=\int
dE_{\mathrm{nr}}dv\frac{d^{2}R}{dE_{\mathrm{nr}}dv}\\\
&\times\frac{1}{2\pi}\sum_{n,l}\frac{d}{dE_{\mathrm{nr}}}p^{c}_{q_{e}}(n,l\rightarrow
E_{\mathrm{ee}}-E_{n,l}).\end{split}$ (2)

Here $p^{c}_{q_{e}}$ is the probability for an atomic electron with quantum
number ($n,l$) and binding energy $E_{n,l}$ to be ejected with a kinetic
energy $E_{\mathrm{ee}}-E_{n,l}$, and $q_{e}$ is the electron momentum in the
nucleus rest frame. When the shell vacancy is refilled, an X-ray or an auger
electron with energy $E_{n,l}$ is emitted. This takes into account the fact
that the emitted electron may come from an inner orbital and the remaining
excited state will release additional energy when returns to its ground state.
The differential probability rates for sodium and iodine were calculated in
Ref. Ibe:2017yqa . Figure 2 shows the differential ionization rates as a
function of the electron recoil energy $E_{\mathrm{ee}}$ for sodium and iodine
nuclei considering two different WIMP masses.

Figure 2: Expected signals without energy resolution from WIMP-nuclei spin-
independent (SI) interaction via the Migdal process are presented for WIMP
masses of 0.2 GeV/c2 and 1.0 GeV/c2 assuming WIMP-nucleon SI cross-section of
1 pb. Sodium and iodine spectra produced by the Migdal effect are separately
presented and compared with the nuclear recoil spectrum of WIMP-sodium
interaction for 1.0 GeV/c2 WIMP mass. Here the nuclear recoil energy is
quenched to the electron recoil energy using the measured quenching factor
reported in Ref. Joo:2018hom . Although the nuclear recoil deposit is below
the 1 keVee energy threshold, the electron energy from the Migdal effect can
produce above-threshold signals.

This description assumes isolated atomic targets that interact with WIMP
particles Ibe:2017yqa ; Kouvaris:2016afs , which for inner-shell electrons
provided a correct estimate of the expected signal rate. For outer electrons,
the complicated electronic band structure and crystal form factor can affect
the rate for the Migdal effect and significantly improved sensitivity in
semiconductors has been reported in Refs. Essig:2019xkx ; Knapen:2020aky . In
this analysis, we follow the atomic target approximation because at our
analysis threshold, inner shell electrons are the dominant contributors to the
Migdal process.

##  IV Data analysis

We use data obtained from October 2016 to July 2018, corresponding to 1.7
years exposure that were used for our first annual modulation search
Adhikari:2019off  and the model-dependent WIMP dark matter search using the
energy spectra COSINE-100:2021xqn . During the 1.7 years data-taking period,
no significant environmental anomalies or unstable detector performance were
observed. Six of the eight crystals have a high light yield of approximately
15 NPE/keVee, where NPE corresponds to the number of photoelectron, and
enables an analysis threshold of 1 keVee. The other two crystals had lower
light yields and required higher analysis thresholds Adhikari:2017esn ;
Adhikari:2018ljm . Since their direct impact on the low-energy signal search
is not substantial, we do not include these two crystals in this analysis.

In the offline analysis, muon-induced events are rejected when the crystal hit
events and muon candidate events in the muon detector Prihtiadi:2017inr ;
Prihtiadi:2020yhz  are coincident within 30 ms. Additionally, we require that
the leading edges of the trigger pulses start later than 2.0 $\mu$s after the
start of the recording, that the waveforms from the hit crystal contain more
than two single photoelectrons and the integral waveform area below the
baseline does not exceed a limit. These criteria reject muon-induced phosphor
events and electronic interference events. A multiple-hit event is one in
which more than one crystal has a signal with more than four photoelectrons in
an 8 $\mu$s time window or, has an LS signal above an 80 keVee threshold
within 4 $\mu$s of the hit crystal Adhikari:2020asl . A single-hit event is
classified as one where only one crystal is hit and none the other detectors
meet the above criteria.

Figure 3: The distribution of two input parameters, mean-time parameter (left)
and the likelihood parameter (center), and output BDT scores (right) are
presented separately for the WIMP-search data (top) and 60Co calibration data
(bottom). Details of all parameters are described in Adhikari:2020xxj .

In the low-energy signal region below 10 keVee, PMT-induced noise events
contribute to the single-hit WIMP-search data. Although PMT noise involves
complex phenomena that are far from being completely understood, we categorize
two distinct classes of the PMT-induced noise events. The first class has a
fast decay time of less than 50 ns, compared with typical NaI(Tl)
scintillation of about 250 ns. This class of noise events may be induced by
radioactive decays of U, Th, and K inside the PMT materials. These decays may
generate ultraviolet and/or visible photons inside the PMTs. The second class,
that occurs less often than the first, is characterized by slow rise times
(about 100 ns) and decay times (about 150 ns), as described in Refs.
Adhikari:2018ljm ; Kang:2019fvz . This class of noise may be caused by
accumulated charge somewhere in the PMT arising from the high voltage and
subsequent-discharging that produces a flash inside the PMTs. This class noise
events are intermittently produced by certain PMTs. We have developed
monitoring tools for data quality verification, including monitoring event
rates of the second class of noise. If a crystal has an increased rate due to
the second class of noise, the relevant period of data is removed. One crystal
detector has this class of noise for the whole data-taking period; for the
other five detectors the second-class noise-induced events are absent during
more than 95 % of the data taking period. The effective data exposure for the
five crystals is 97.7 kg$\cdot$year.

The first class of PMT noise-induced events is efficiently rejected by a
boosted decision tree (BDT)-based multivariable analysis techinique BDT . The
parameters used in the BDT include the balance of the deposited charge from
two PMTs, the ratio of the leading-edge (0–50 ns) to trailing-edge (100 ns–600
ns) charge, a mean-time parameter, which is a logarithm of the amplitude
weighted average time of the events, and a likelihood parameter for samples of
scintillation-signal events and the fast PMT-induced events Adhikari:2020xxj ;
COSINE-100:2021xqn . Figure 3 shows input parameters of mean-time and
likelihood, as well as output BDT scores for calibration samples and WIMP
search data. This procedure reduces the noise contamination level to less than
0.5% and maintains an 80% selection efficiency at the lowest energy bin
(1–1.25 keVee) can be achieved Adhikari:2020xxj .

Geant4 Agostinelli:2002hh -based simulations are used to understand the
contribution of each background component Adhikari:2017gbj ; cosinebg ;
cosinebg2 , as well as to verify the energy scales and resolutions. We
classify four categories of the NaI-deposited events based on their energies
and detector multiplicities. Single-hit and multiple-hit events are further
divided into low-energy events 1–70 keVee and high-energy events 70–3000
keVee. The fraction of each background component is determined from a
simultaneous fit to the four categorized distributions. For the single-hit
events, only 6–3000 keVee events are used to avoid a bias of the signal in the
region of interest (ROI). A detailed description of our modeling of the
background with the same data is described in Ref. cosinebg2 .

We consider various sources of systematic uncertainties in the background and
signal models. Errors associated with the selection efficiency, the energy
resolution, the energy scale, and the background modeling technique are
accounted for the shapes of the signal and background probability density
functions, as well as in rate changes as described in Ref. COSINE-100:2021xqn
. These quantities are allowed to vary within their uncertainties as nuisance
parameters in the data fit used to extract the signal.

To estimate the dark matter signal enhancement that is provided by the Migdal
effect, we generate signals based on Eq. 2 for various interaction models and
different masses in the specific context of the standard WIMP galactic halo
model Lewin:1995rx ; Freese:2012xd . Both a spin-independent (SI) interaction
between WIMP and nucleons and a spin-dependent (SD) interaction between WIMP
and proton are considered in this analysis. Because both sodium and iodine
have non-zero proton spin due to their odd numbers of protons Bednyakov:2006ux
; Gresham:2014vja , NaI(Tl) detectors are sensitive to the WIMP-proton SD
interactions. Responses that include form factors and proton spin values of
the nuclei are implemented from the publicly available dmdd package dmdd ;
Gluscevic:2015sqa ; Anand:2013yka ; Fitzpatrick:2012ix ; Gresham:2014vja . The
energy spectra of electron-equivalent energy for the detector are simulated
with the energy resolutions of the detectors and the nuclear recoil quenching
factors (QFs), where QF is the ratio of the scintillation light yield from
sodium or iodine recoil relative to that from electron recoil for the same
energy. We used the QF values from recent measurements with monoenergetic
neutron beam Joo:2018hom . The measurements were modeled using a modified
Lindhard formula osti_4701226  and described in Ref. Ko:2019enb . Examples of
quenched signal spectra from the Migdal effect of the WIMP-nucleon SI
interactions for the WIMP masses of 0.2 and 1.0 GeV/c2 are presented in Fig.
2. The output events are subjected to the same selection criteria that are
applied to the data.

Figure 4: An example of the fit for a WIMP mass 1.1 GeV/c2 using the Migdal
effect is presented. The summed energy spectrum for the five crystals (black
filled circles) and the best fit (blue solid line) for which no WIMP signals
are obtained, are shown together with signal spectra from WIMP masses and SI
cross-sections of 0.2 GeV/c2 and 107pb (red dashed line), 1.0 GeV/c2 and 102
pb (green dotted line). The fitted distribution is broken down into cumulative
contributions to the background from external sources, the surface of the
crystals and nearby materials, internal radionuclide contaminations, and
cosmogenic activation, as indicated. The green (yellow) bands are the 68%
(95%) CL intervals of the systematic uncertainty obtained from the likelihood
fit.

A Bayesian approach is adopted to extract the WIMP interaction signals using
the Migdal effect from the COSINE-100 data. A likelihood function based on
Poisson probability is built including constraints that reflect the known
levels of the background components. The likelihood fit is applied to the
measured single-hit energy spectra between 1 and 6 keVee for each WIMP model
with various masses. Each crystal is fitted with a crystal-specific background
model and a crystal-correlated dark matter signal. The combined fit is
constructed by multiplying likelihoods of the five crystals. The systematic
uncertainties are included as nuisance parameters with Gaussian constraints.
The same machinery was used for the WIMP dark matter searches using the same
dataset but with only the energy from the nuclear recoils without the Migdal
effect COSINE-100:2021xqn . An example of the fit for the SI interaction for a
WIMP mass of 1.1 GeV/c2 is shown in Fig. 4. The summed event spectrum for the
five crystals is shown together with the best-fit result. For comparison, the
expected signals for WIMP masses (cross-sections) of 0.2 (107) and 1.0 GeV/c2
(102 pb) are presented together. No significant signal for event excess that
could be attributed to WIMP interactions is found and 90% confidence level
(CL) limits are determined from the marginalization of the likelihood
function. Figure 5 shows the 90% CL upper limits from the COSINE-100 data for
the WIMP-nucleon SI interactions (A) and the WIMP-proton SD interactions (B)
compared with the limits from XENON1T XENON:2019zpr , EDELWEISS surface
measurement EDELWEISS:2019vjv , and CDEX CDEX:2019hzn  using the Migdal
effect, as well as CRESST-III CRESST:2019jnq , CRESST LiAlO2G CRESST:2020tlq ,
DarkSide-50 Agnes:2018ves , PICASSO Behnke:2016lsk , CDMSlite
SuperCDMS:2017nns , EDELWEISS surface EDELWEISS:2019vjv , Collar
Collar:2018ydf , and PICO-60 PICO:2019vsc  results. Here, our search extends
to the low-mass WIMP of 200 MeV/c2. Although our limits do not consider earth
shielding effects Kouvaris:2015laa ; Kavanagh:2017cru ; EDELWEISS:2019vjv , we
found no significant impact on the upper limits using the verne code verne .
Because of the relatively higher threshold energy and background rates, our
search cannot investigate the unexplored parameter space. This will be
addressed in the future with improved detectors and analysis methods.

Figure 5: Limits on WIMP-nucleon SI interaction (A) and WIMP-proton SD
interaction (B) induced by the Migdal effect from the COSINE-100 data (black
dots) at 90% CL are compared with XENON1T XENON:2019zpr , EDELWEISS surface
measurement EDELWEISS:2019vjv , and CDEX CDEX:2019hzn  with the Migdal effect,
and CRESST-III CRESST:2019jnq , CRESST LiAlO2G CRESST:2020tlq , DarkSide-50
Agnes:2018ves , PICASSO Behnke:2016lsk , CDMSlite SuperCDMS:2017nns ,
EDELWEISS surface EDELWEISS:2019vjv , Collar Collar:2018ydf , and PICO-60
PICO:2019vsc .

##  V Sensitivity for COSINE-200

An effort to upgrade the on-going COSINE-100 to the next-phase COSINE-200 has
resulted in the production of NaI(Tl) crystals with reduced internal
background from 40K and 210Pb Shin:2018ioq ; Shin:2020bdq ; COSINE:2020egt  as
well as an increased light yield of 22 NPE/keV Choi:2020qcj . The
recrystalization method has achieved chemical purification of the raw NaI
powder with sufficient reduction of K and Pb contamination Shin:2018ioq ;
Shin:2020bdq . A dedicated Kyropoulos grower for small test crystals has
produced low-background NaI(Tl) crystals with reduced 40K and 210Pb of less
than 20 ppb and 0.5 mBq/kg, respectively, corresponding to background rates of
less than 1 counts/day/kg/keVee at the 1–6 keVee ROI COSINE:2020egt . A full-
size Kyropoulos grower has been built for the 100 kg-size crystal ingot and
will provide approximately 200 kg of low-background NaI(Tl) detectors for the
COSINE-200 experiment. The expected background level of those crystals is less
than 0.5 counts/day/kg/keVee in the ROI as shown in Fig. 6. This estimate is
based on the measured background levels for small test crystals as discussed
in Ref. COSINE:2020egt .

Figure 6: Expected background spectrum (blue solid line) of the COSINE-200
crystal based on the developed low-background NaI(Tl) crystal COSINE:2020egt
is compared with expected signals using the Migdal effect for WIMP-nucleon SI
interactions of masses and cross sections of 0.2 GeV/c2, 100 pb (red dashed
line) and 1.0 GeV/c2, 1 pb (green dotted line), respectively. A dominant
background contribution is expected from the internal 40K and 210Pb remaining
after purification.

A high light yield of the NaI(Tl) crystal is crucial for enabling low-energy
thresholds below 1 keVee. With an optimized concentration of thallium doping
in the crystal, we achieved high light yield of 17.1$\pm$0.5 NPE/keVee,
slightly larger than that of the COSINE-100 crystal of approximately 15
NPE/keVee. Further increase in the light collection efficiency by $\sim$50% is
possible with an improved encapsulation scheme as described in Ref.
Choi:2020qcj  that directly connects the crystal and PMTs without an
intermediate quartz window for which a 22 NPE/keVee light yield is reported.

The typical trigger requirement of the COSINE-100 experiment is satisfied with
coincident photoelectrons in two PMTs attached to each side of the crystal at
approximately 0.13 keVee. However, the PMT-induced noise events are dominantly
triggered below energies of a few keVee. The multivariable BDT provided a 1
keVee analysis threshold with less than 0.1% noise contamination and above 80%
selection efficiency Adhikari:2020xxj . A key variable in the BDT is the
likelihood parameter using the event shapes of the scintillation-like events
and the PMT-induced noise-like events. A further improvement of the low-energy
event selection is ongoing with the COSINE-100 data by developing new
parameters for the BDT as well as employing a machine learning technique that
uses raw waveforms directly. COSINE-200 targets an analysis threshold of 5 NPE
(0.2 keVee), which is similar to the energy threshold that has already been
achieved by the COHERENT experiment with CsI(Na) crystals COHERENT:2017ipa .

The COSINE-200 experiment can be realized in a 4$\times$4 array of 12.5 kg
NaI(Tl) modules by replacing crystals inside the COSINE-100 shield
Adhikari:2017esn . The COSINE-200 experiment will run at least 3 years for an
unambiguous test of the DAMA/LIBRA annual modulation signals Adhikari:2015rba
. In addition, this detector can be used for general dark matter searches,
especially for low-mass WIMPs via the Migdal process. Assuming the background
reduction shown in Fig. 6, a high light yield of 22 NPE/keVee, and an analysis
threshold of 5 NPE corresponding to 0.2 keVee, the sensitivities of the
COSINE-200 experiment are evaluated below using the Migdal effect.

Figure 7: The expected signal counts using the Migdal effect for a one year of
data assuming 0.2 keVee analysis threshold are presented as a function of WIMP
masses for SI (blue filled points) and SD interactions (green open points) for
1 kg of sodium (circle points) and 1 kg of iodine (triangle points). The
cross-sections for the SI and SD interactions are assumed to be 1 pb and 200
pb, respectively. Figure 8: COSINE-200 expected 90% CL limits using the Migdal
effect on the WIMP-nucleon SI cross-section (A) and the WIMP-proton SD cross-
section (B) are presented assuming the background-only hypothesis indicating
the 1$\sigma$ and 2$\sigma$ standard deviation probability regions over which
the limits have fluctuated. Those limits are compared with the current best
limits from the XENON1T Migdal XENON:2019zpr , DarkSide-50 Agnes:2018ves ,
PICASSO Behnke:2016lsk , CDMSlite SuperCDMS:2017nns , Collar Collar:2018ydf ,
and PICO-60 PICO:2019vsc  together with the sensitivity limits from future
liquid Ar experiment (TEA-LAB) GrillidiCortona:2020owp , Xe Essig:2019xkx ,
and Si Knapen:2020aky  with Migdal.

We generate the WIMP interaction signals including the Migdal effects as
discussed above. Here we assume a one year data exposure with 200 kg crystals
and the aforementioned detector performances. Poisson fluctuations of the
measured NPE are considered for the detector resolution. Figure 7 presents the
expected signal rate as a function of the WIMP mass for 1 kg of sodium and 1
kg of iodine for different interactions assuming 0.2 keVee threshold. As one
can see, sodium has an advantage for the low-mass WIMP searches with the
Migdal process. In this scenario, the COSINE-200 experiment can probe the sub-
GeV/c2 WIMP with mass down to 20 MeV/c2.

We use an ensemble of simulated experiments to estimate the sensitivity of the
COSINE-200 experiment, expressed as the expected cross-section limits for the
WIMP-nucleon SI and WIMP-proton SD interactions using the Migdal effect in the
case of no signals. For each experiment, we determine a simulated spectrum for
a background-only hypothesis with assumed background from Fig. 6. A gaussian
fluctuation of each background component and a poisson fluctuation of each
energy bin are considered for each simulated experiment. We then fit the
simulated data with a signal-plus-background hypothesis with flat priors for
the signal and Gaussian constraints for the backgrounds based on understanding
of the NaI(Tl) crystals cosinebg2 ; COSINE:2020egt . Examples of signal
spectra using the Migdal effect for SI interactions with WIMP masses (cross
sections) of 0.2 GeV/c2 (100 pb) and 1.0 GeV/c2 (1 pb) are presented in Fig.
6. The same Bayesian approach is used for the single-hit energy spectra
between 5 NPE (0.2 keVee) and 130 NPE (6 keVee) for each WIMP model for
several masses. The 1$\sigma$ and 2$\sigma$ standard-deviation probability
regions of the expected 90% CL limits are calculated from 2000 simulated
experiments. Figure 8 shows those 1$\sigma$ and 2$\sigma$ regions, for the
COSINE-200 experiment using the Migdal effect. The limits on the WIMP-nucleon
SI interaction shown in Fig. 8 (A) are compared with the current best limit on
the low-mass WIMP searches of XENON1T with Migdal, DarkSide-50, and the
expected sensitivities from future liquid Ar (TEA-LAB) GrillidiCortona:2020owp
, Xe Essig:2019xkx , and Si Knapen:2020aky  with Migdal. We also verify no
significant impact on the upper limits using the verne code verne . The
COSINE-200 experiment has a potential to probe unexplored cross section values
for the WIMP mass below 200 MeV/c2. In case of the WIMP-proton SD interactions
shown in Fig. 8 (B), our projected sensitivities are compared with the current
best limits from XENON1T with Migdal, PICO-60, CDMSlite SuperCDMS:2017nns ,
Collar Collar:2018ydf , and PICASSO. Taking advantages of odd-proton numbers
in both iodine and sodium, the projected sensitivities from the COSINE-200
experiments can probe unexplored parameter spaces of WIMP masses below 2
GeV/c2.

##  VI Conclusion

We consider the Migdal effect to search for the low-mass dark matter using the
COSINE-100 data. With 1 keVee analysis threshold, our search extends down to
200 MeV/c2 WIMP mass. We have investigated the expected sensitivities of the
COSINE-200 experiment with a total mass of 200 kg, a 1-year period of stable
operation, about 0.5 counts/day/keVee/kg background rate, and 0.2 keVee energy
threshold. In this scenario, the COSINE-200 detector can explore low-mass dark
matter down to 20 MeV/c2, with a potential to probe currently unexplored
parameter spaces for both SI and SD interactions.

###### Acknowledgements.

We thank the Korea Hydro and Nuclear Power (KHNP) Company for providing
underground laboratory space at Yangyang. This work is supported by: the
Institute for Basic Science (IBS) under project code IBS-R016-A1 and
NRF-2021R1A2C3010989, Republic of Korea; NSF Grants No. PHY-1913742,
DGE1122492, WIPAC, the Wisconsin Alumni Research Foundation, United States;
STFC Grant ST/N000277/1 and ST/K001337/1, United Kingdom; Grant No.
2017/02952-0 FAPESP, CAPES Finance Code 001, CNPq 131152/2020-3, Brazil.

## References

  * (1) D. Clowe et al., A direct empirical proof of the existence of dark matter, Astrophys. J. 648, L109 (2006).
  * (2) P. A. R. Ade et al., (Planck Collaboration), Planck 2015 results. XIII. Cosmological parameters, Astron. Astrophys. 594, A13 (2016).
  * (3) B. W. Lee and S. Weinberg, Cosmological lower bound on heavy-neutrino masses, Phys. Rev. Lett. 39, 165 (1977).
  * (4) M. W. Goodman and E. Witten, Detectability of Certain Dark Matter Candidates, Phys. Rev. D 31, 3059 (1985).
  * (5) D. S. Akerib et al., (LUX Collaboration), Results from a Search for Dark Matter in the Complete LUX Exposure, Phys. Rev. Lett. 118, 021303 (2017).
  * (6) R. Agnese et al., (SuperCDMS Collaboration), Results from the Super Cryogenic Dark Matter Search Experiment at Soudan, Phys. Rev. Lett. 120, 061802 (2018).
  * (7) E. Aprile et al., (XENON Collaboration), First Dark Matter Search Results from the XENON1T Experiment, Phys. Rev. Lett. 119, 181301 (2017).
  * (8) P. Agnes et al., (DarkSide Collaboration), Low-Mass Dark Matter Search with the DarkSide-50 Experiment, Phys. Rev. Lett. 121, 081307 (2018).
  * (9) E. Aprile et al., (XENON Collaboration), Dark Matter Search Results from a One Ton-Year Exposure of XENON1T, Phys. Rev. Lett. 121, 111302 (2018).
  * (10) A. H. Abdelhameed et al., (CRESST Collaboration), First results from the CRESST-III low-mass dark matter program, Phys. Rev. D 100, 102002 (2019).
  * (11) P. Zyla et al., (Particle Data Group Collaboration), Review of Particle Physics, PTEP 2020, 083C01 (2020).
  * (12) R. Essig et al., Working Group Report: New Light Weakly Coupled Particles, in Proceedings, 2013 Community Summer Study on the Future of U.S. Particle Physics: Snowmass on the Mississippi (CSS2013): Minneapolis, MN, USA, July 29-August 6, 2013, 2013.  arXiv:1311.0029.
  * (13) E. Aprile et al., (XENON Collaboration), Low-mass dark matter search using ionization signals in XENON100, Phys. Rev. D 94, 092001 (2016). [Erratum: Phys.Rev.D 95, 059901 (2017)].
  * (14) E. Aprile et al., (XENON Collaboration), Light Dark Matter Search with Ionization Signals in XENON1T, Phys. Rev. Lett. 123, 251801 (2019).
  * (15) A. Aguilar-Arevalo et al., (DAMIC Collaboration), Constraints on Light Dark Matter Particles Interacting with Electrons from DAMIC at SNOLAB, Phys. Rev. Lett. 123, 181802 (2019).
  * (16) Q. Arnaud et al., (EDELWEISS Collaboration), First germanium-based constraints on sub-MeV Dark Matter with the EDELWEISS experiment, Phys. Rev. Lett. 125, 141301 (2020).
  * (17) L. Barak et al., (SENSEI Collaboration), SENSEI: Direct-Detection Results on sub-GeV Dark Matter from a New Skipper-CCD, Phys. Rev. Lett. 125, 171802 (2020).
  * (18) I. Alkhatib et al., (SuperCDMS Collaboration), Light Dark Matter Search with a High-Resolution Athermal Phonon Detector Operated Above Ground, Phys. Rev. Lett. 127, 061801 (2021).
  * (19) C. Cheng et al., (PandaX-II Collaboration), Search for Light Dark Matter-Electron Scatterings in the PandaX-II Experiment, Phys. Rev. Lett. 126, 211803 (2021).
  * (20) A. Migdal, Ionization of atoms accompanying $\alpha$\- and $\beta$-decay., J. Phys. USSR 4, 449 (1941).
  * (21) M. Ibe, W. Nakano, Y. Shoji, and K. Suzuki, Migdal Effect in Dark Matter Direct Detection Experiments, JHEP 03, 194 (2018).
  * (22) G. Adhikari et al., (COSINE-100 Collaboration), Lowering the energy threshold in COSINE-100 dark matter searches, Astropart. Phys. 130, 102581 (2021).
  * (23) G. Adhikari et al., (COSINE-100 Collaboration), Strong constraints from COSINE-100 on the DAMA dark matter results using the same sodium iodide target, arXiv:2104.03537.
  * (24) B. J. Park et al., (COSINE Collaboration), Development of ultra-pure NaI(Tl) detectors for the COSINE-200 experiment, Eur. Phys. J. C 80, 814 (2020).
  * (25) J. J. Choi, B. J. Park, C. Ha, K. W. Kim, S. K. Kim, Y. D. Kim, Y. J. Ko, H. S. Lee, S. H. Lee, and S. L. Olsen, Improving the light collection using a new NaI(Tl) crystal encapsulation, Nucl. Instrum. Meth. A 981, 164556 (2020).
  * (26) G. Adhikari et al., (COSINE-100 Collaboration), Initial Performance of the COSINE-100 Experiment, Eur. Phys. J. C 78, 107 (2018).
  * (27) H. S. Lee et al., (Kims Collaboration), First limit on wimp cross section with low background csi(tl) crystal detector, Phys. Lett. B 633, 201–208 (2006).
  * (28) S. C. Kim et al., New Limits on Interactions between Weakly Interacting Massive Particles and Nucleons Obtained with CsI(Tl) Crystal Detectors, Phys. Rev. Lett. 108, 181301 (2012).
  * (29) H. Prihtiadi et al., (COSINE-100 Collaboration), Muon detector for the COSINE-100 experiment, JINST 13, T02007 (2018).
  * (30) H. Kim et al., The environmental monitoring system at the COSINE-100 experiment, arXiv:2107.07655.
  * (31) J. S. Park et al., (KIMS Collaboration), Performance of a prototype active veto system using liquid scintillator for a dark matter search experiment, Nucl. Instrum. Meth. A 851, 103 (2017).
  * (32) G. Adhikari et al., The COSINE-100 liquid scintillator veto system, Nucl. Instrum. Meth. A 1006, 165431 (2021).
  * (33) H. Prihtiadi et al., (COSINE-100 Collaboration), Measurement of the cosmic muon annual and diurnal flux variation with the COSINE-100 detector, JCAP 02, 013 (2021).
  * (34) G. Adhikari et al., (COSINE-100 Collaboration), The COSINE-100 Data Acquisition System, JINST 13, P09006 (2018).
  * (35) A. Manzur, A. Curioni, L. Kastens, D. N. McKinsey, K. Ni, and T. Wongjirad, Scintillation efficiency and ionization yield of liquid xenon for mono-energetic nuclear recoils down to 4 keV, Phys. Rev. C 81, 025808 (2010).
  * (36) J. H. Lee et al., Measurement of the quenching and channeling effects in a CsI crystal used for a WIMP search, Nucl. Instrum. Meth. A782, 133–142 (2015).
  * (37) H. W. Joo, H. S. Park, J. H. Kim, S. K. Kim, Y. D. Kim, H. S. Lee, and S. H. Kim, Quenching factor measurement for NaI(Tl) scintillation crystal, Astropart. Phys. 108, 50–56 (2019).
  * (38) M. Kimura, M. Tanaka, T. Washimi, and K. Yorita, Measurement of the scintillation efficiency for nuclear recoils in liquid argon under electric fields up to 3 kV/cm, Phys. Rev. D 100, 032002 (2019).
  * (39) D. S. Akerib et al., (LUX Collaboration), Results of a Search for Sub-GeV Dark Matter Using 2013 LUX Data, Phys. Rev. Lett. 122, 131301 (2019).
  * (40) E. Armengaud et al., (EDELWEISS Collaboration), Searching for low-mass dark matter particles with a massive Ge bolometer operated above-ground, Phys. Rev. D 99, 082003 (2019).
  * (41) Z. Z. Liu et al., (CDEX Collaboration), Constraints on Spin-Independent Nucleus Scattering with sub-GeV Weakly Interacting Massive Particle Dark Matter from the CDEX-1B Experiment at the China Jinping Underground Laboratory, Phys. Rev. Lett. 123, 161301 (2019).
  * (42) E. Aprile et al., (XENON Collaboration), Search for Light Dark Matter Interactions Enhanced by the Migdal Effect or Bremsstrahlung in XENON1T, Phys. Rev. Lett. 123, 241803 (2019).
  * (43) G. Grilli di Cortona, A. Messina, and S. Piacentini, Migdal effect and photon Bremsstrahlung: improving the sensitivity to light dark matter of liquid argon experiments, JHEP 11, 034 (2020).
  * (44) C. Savage, G. Gelmini, P. Gondolo, and K. Freese, Compatibility of DAMA/LIBRA dark matter detection with other searches, JCAP 0904, 010 (2009).
  * (45) C. Kouvaris and J. Pradler, Probing sub-GeV Dark Matter with conventional detectors, Phys. Rev. Lett. 118, 031803 (2017).
  * (46) R. Essig, J. Pradler, M. Sholapurkar, and T.-T. Yu, Relation between the Migdal Effect and Dark Matter-Electron Scattering in Isolated Atoms and Semiconductors, Phys. Rev. Lett. 124, 021801 (2020).
  * (47) S. Knapen, J. Kozaczuk, and T. Lin, Migdal Effect in Semiconductors, Phys. Rev. Lett. 127, 081805 (2021).
  * (48) G. Adhikari et al., (COSINE-100 Collaboration), Search for a dark matter-induced annual modulation signal in NaI(Tl) with the COSINE-100 experiment, Phys. Rev. Lett. 123, 031302 (2019).
  * (49) G. Adhikari et al., (COSINE-100 Collaboration), An experiment to search for dark-matter interactions using sodium iodide detectors, Nature 564, 83 (2018).
  * (50) G. Adhikari et al., (COSINE-100 and Sogang Phenomenology Group Collaboration), COSINE-100 and DAMA/LIBRA-phase2 in WIMP effective models, JCAP 1906, 048 (2019).
  * (51) J. H. Friedman, Greedy function approximation: A gradient boosting machine, Ann. Stat. 29, 1189 (2001).
  * (52) S. Agostinelli et al., (GEANT4 Collaboration), GEANT4: A Simulation toolkit, Nucl. Instrum. Meth. A 506, 250 (2003).
  * (53) G. Adhikari et al., (KIMS Collaboration), Understanding NaI(Tl) crystal background for dark matter searches, Eur. Phys. J. C 77, 437 (2017).
  * (54) P. Adhikari et al., (COSINE-100 Collaboration), Background model for the NaI(Tl) crystals in COSINE-100, Eur. Phys. J. C 78, 490 (2018).
  * (55) G. Adhikari et al., (COSINE-100 Collaboration), Background modeling for dark matter search with 1.7 years of COSINE-100 data, Eur. Phys. J. C 81, 837 (2021).
  * (56) J. Lewin and P. Smith, Review of mathematics, numerical factors, and corrections for dark matter experiments based on elastic nuclear recoil, Astropart. Phys. 6, 87 (1996).
  * (57) K. Freese, M. Lisanti, and C. Savage, Colloquium: Annual modulation of dark matter, Rev. Mod. Phys. 85, 1561 (2013).
  * (58) V. A. Bednyakov and F. Simkovic, Nuclear spin structure in dark matter search: The Finite momentum transfer limit, Phys. Part. Nucl. 37, S106–S128 (2006).
  * (59) M. I. Gresham and K. M. Zurek, Effect of nuclear response functions in dark matter direct detection, Phys. Rev. D 89, 123521 (2014).
  * (60) V. Gluscevic and S. D. McDermott, dmdd: Dark matter direct detection, Astrophysics Source Code Library [ascl:1506.002], 2015.
  * (61) V. Gluscevic, M. I. Gresham, S. D. McDermott, A. H. G. Peter, and K. M. Zurek, Identifying the Theory of Dark Matter with Direct Detection, JCAP 1512, 057 (2015).
  * (62) N. Anand, A. L. Fitzpatrick, and W. C. Haxton, Weakly interacting massive particle-nucleus elastic scattering response, Phys. Rev. C 89, 065501 (2014).
  * (63) A. L. Fitzpatrick, W. Haxton, E. Katz, N. Lubbers, and Y. Xu, The Effective Field Theory of Dark Matter Direct Detection, JCAP 1302, 004 (2013).
  * (64) J. Lindhard, V. Nielsen, M. Scharff, and P. Thomsen, Integral equations governing radiation effects. (Notes on Atomic collisions, III), Mat. Fys. Medd. Dan. Vid. Selsk. 33, (1, 1963).
  * (65) Y. J. Ko et al., (COSINE-100 Collaboration), Comparison between DAMA/LIBRA and COSINE-100 in the light of Quenching Factors, JCAP 1911, 008 (2019).
  * (66) A. H. Abdelhameed et al., (CRESST Collaboration), Cryogenic characterization of a $\hbox{LiAlO}_{2}$ crystal and new results on spin-dependent dark matter interactions with ordinary matter, Eur. Phys. J. C 80, 834 (2020).
  * (67) P. Agnes et al., (DarkSide Collaboration), Low-Mass Dark Matter Search with the DarkSide-50 Experiment, Phys. Rev. Lett. 121, 081307 (2018).
  * (68) E. Behnke et al., Final Results of the PICASSO Dark Matter Search Experiment, Astropart. Phys. 90, 85–92 (2017).
  * (69) R. Agnese et al., (SuperCDMS Collaboration), Low-mass dark matter search with CDMSlite, Phys. Rev. D 97, 022002 (2018).
  * (70) J. I. Collar, Search for a nonrelativistic component in the spectrum of cosmic rays at Earth, Phys. Rev. D 98, 023005 (2018).
  * (71) C. Amole et al., (PICO Collaboration), Dark Matter Search Results from the Complete Exposure of the PICO-60 C3F8 Bubble Chamber, Phys. Rev. D 100, 022001 (2019).
  * (72) C. Kouvaris, Earth’s stopping effect in directional dark matter detectors, Phys. Rev. D 93, 035023 (2016).
  * (73) B. J. Kavanagh, Earth scattering of superheavy dark matter: Updated constraints from detectors old and new, Phys. Rev. D 97, 123013 (2018).
  * (74) B. Kavanagh, bradkav/verne:v1.2, https://github.com/bradkav/verne/tree/v1.2, 2015.
  * (75) K. Shin, O. Gileva, Y. Kim, H. S. Lee, and H. Park, Reduction of the radioactivity in sodium iodide (NaI) powder by recrystallization method, J. Radioanal. Nucl. Chem. 317, 1329 (2018).
  * (76) K. Shin, J. Choe, O. Gileva, A. Iltis, Y. Kim, C. Lee, H. S. Lee, M. H. Lee, and H. K. Park, A facility for mass production of ultra-pure NaI powder for the COSINE-200 experiment, JINST 15, C07031 (2020).
  * (77) D. Akimov et al., (COHERENT Collaboration), Observation of Coherent Elastic Neutrino-Nucleus Scattering, Science 357, 1123 (2017).
  * (78) P. Adhikari et al., Understanding internal backgrounds in NaI(Tl) crystals toward a 200 kg array for the KIMS-NaI experiment, Eur. Phys. J. C 76, 185 (2016).