Limits on WIMP-nucleon interactions with CsI(Tl) crystal detectors
Limits on the WIMP-nucleon interactions with CsI(Tl) crystal detectors
H.S. Lee,1 H.C. Bhang,1 J.H. Choi,1 H. Dao,7 I.S. Hahn,4 M.J. Hwang,5 S.W. Jung,2 W.G. Kang,3 D.W.
Kim,1 H.J. Kim,2 S.C. Kim,1 S.K. Kim,1, ∗ Y.D. Kim,3 J.W. Kwak,1, † Y.J. Kwon,5 J. Lee,1, ‡ J.H. Lee,1 J.I.
Lee,3 M.J. Lee,1 S.J. Lee,1 J. Li,7 X. Li,7 Y.J. Li,7 S.S. Myung,1 S. Ryu,1 J.H. So,2 Q. Yue,7 and J.J. Zhu7
(KIMS Collaboration)
DMRC and Department of Physics and Astronomy, Seoul National University, Seoul, Korea
Department of Physics, Kyungpook National University, Daegu, Korea
Department of Physics, Sejong University, Seoul, Korea
Department of Science Education, Ewha Womans University, Seoul, Korea
Department of Physics, Younsei University, Seoul, Korea
Department of Engineering Physics, Tsinghua Universuty, Beijing, China
Department of Engineering Physics, Tsinghua University, Beijing, China
(Dated: November 4, 2018)
The Korea Invisible Mass Search (KIMS) experiment presents new limits on the WIMP-nucleon
cross section using data from an exposure of 3409 kg·d taken with low-background CsI(Tl) crystals
at Yangyang Underground Laboratory. The most stringent limit on the spin-dependent interaction
for a pure proton case is obtained. The DAMA signal region for both spin-independent and spin-
dependent interactions for the WIMP masses greater than 20 GeV/c2 is excluded by the single
experiment with crystal scintillators.
PACS numbers: 95.35.+d, 14.80.Ly
The existence of dark matter has been widely sup-
ported by many astronomical observations on vari-
ous scales [1][2][3]. Weakly interacting massive parti-
cles (WIMPs) are a good candidate for dark matter well
motivated by cosmology and supersymmetric models [4].
The Korea Invisible Mass Search (KIMS) experiment has
developed low-background CsI(Tl) crystals to detect the
signals from the elastic scattering of WIMP off the nu-
cleus [5][6][7]. Both 133Cs and 127I are sensitive to the
spin-independent (SI) and spin-dependent (SD) interac-
tions of WIMPs. Recently, the role of CsI in the direct
search for SD WIMP for pure proton coupling has been
pointed out [8]. It is worth noting that 127I is the dom-
inant target for the SI interactions in the DAMA exper-
iment. The pulse shape discrimination (PSD) technique
allows us to statistically separate nuclear recoil (NR) sig-
nals of WIMP interactions from the electron recoil (ER)
signals due to the gamma ray background [9][10].
The KIMS experiment is located at the Yangyang Un-
deground Laboratory (Y2L) at a depth of 700 m under an
earth overburden. Details of the KIMS experiment and
the first limit with 237 kg·d exposure data can be found
in the previous publication [11]. Four low-background
CsI(Tl) crystals are installed in the Y2L and operated
at a temperature of T = 0◦C. Throughout the exposure
period, the temperature of the detector was kept sta-
ble to within ±0.1◦C. Green-enhanced photomultiplier
tubes (PMTs) are mounted at both ends of each crystal.
The signals from the PMTs are amplified and recorded
by a 500 MHz FADC. Each event is recorded for a pe-
riod of 32 µs. Both PMTs on each crystal must have at
least two photoelectrons within a 2 µs window to form an
event trigger. We obtained 3409 kg·d WIMP search data
TABLE I: Crystals used in this analysis and amount of data
for each crystal
Crystal mass (kg) data (kg·days)
S0501A 8.7 1147
S0501B 8.7 1030
B0510A 8.7 616
B0510B 8.7 616
Total 34.8 3409
with four crystals, as shown in Table I. The energy is cali-
brated using 59.5 keV gamma rays from an 241Am source.
For calibration of the mean time, a variable used for the
PSD, NR events are obtained with small crystals ( 3 cm ×
3 cm × 3 cm ) using an Am-Be neutron source. Compton
scattering events taken with the WIMP search crystals
using the 137Cs source are used to determine the mean
time distribution of the gamma background. Compton
scattering events are also taken with the small crystals
to verify that the mean time ditributions for both the test
crystals and the WIMP search crystals are the same. In
order to understand the nature of the PMT background,
a dominant background at low energies, acrylic boxes are
mounted on the same PMTs used for the crystals. The
data obtained using this setup is used to develop the cuts
for the rejection of PMT background.
Since the decay time of the scintillation light in the
CsI(Tl) crystal is rather long, photoelectrons are well
separated at low energies and thereby enabling recon-
struction of each photoelectron. The time distribution of
photoelectrons in an event is fitted to a double exponen-
http://arxiv.org/abs/0704.0423v2
 sec)µMean Time (
FIG. 1: (color online). MT distribution of NR events (open
squares), ER events (open circles) and WIMP search
data (filled triangles) of S0501A crystal in the 5-6 keV range.
Fitted PDF functions are overlayed. χ2/DOF =0.8 and 1.3
with DOF=38 and 35 for NR and ER events respectively.
tial function given by
f(t) =
−(t− t0)
−(t− t0)
where τf and τs are decay time constants of fast and
slow components, respectively, R is ratio between two
components, and t0 is the time of the first photoelectron
in the event. The mean time (MT ) of each event is then
calculated using these quantities as
t · f(t)dt/
f(t)dt.
With this method, an improvement in PSD is achieved
over the previous analysis where we used a simple math-
ematical mean [11]. In order to reject the PMT back-
ground, we applied cuts to the fit variable, τf . The ratio
between the maximum log likelihood value of the dou-
ble exponential fit and that of the single exponential fit
is also used to reject the PMT background, since PMT
background events tend to be shaped as single exponen-
tial decay. To reject the background that originates from
the radioactivity of the PMT, the asymmetry between
the signals from two PMTs is applied. Finally events in
which signals are recorded in more than one crystal are
rejected. The event selection efficiency was estimated
by applying the same analysis cuts to the neutron and
gamma calibration samples. The efficiency depends on
the measured energy and ranges from 30% at 3 keV to
60% above 5 keV.
The estimation of the NR event rate is performed in
each 1 keV bin from 3 to 11 keV for each crystal. TheMT
distributions of NR events and ER events are compared
with the WIMP search data in Fig. 1 for the 5-6 keV
energy range. The probability density functions (PDF)
for the ER and NR events are obtained by fitting these
distributions. An unbinned maximum likelihood fit is
Electron Equivalent Energy (keV)
3 4 5 6 7 8 9 10 11
FIG. 2: (color online). Extracted NR event rates of the
S0501A (open circles), S0501B (filled circles), B0510A (filled
squares), and B05010B (filled triangles) crystals and only sta-
tistical errors (1σ) are shown. The points are shifted with
respect to each other on the x-axis to avoid overlapping.
performed with the log(MT ) distribution of the WIMP
search data using the likelihood function,
× exp{−(NNR,i +NER,i)}
[NNR,iPDFNR,i(xk) +NER,iPDFER,i(xk)],
where the index i denotes the i-th energy bin; n =
NNR,i +NER,i is the total number of events; NNR,i and
NER,i are the numbers of NR and ER events, respec-
tively; PDFNR,i and PDFER,i are PDFs of NR and ER
events, respectively; and xk = log(MT ) for each event.
The NR event rates obtained for each bin and for each
crystal after efficiency correction are shown in Fig. 2.
The extracted NR event rates are consistent with a null
observation of the WIMP signal.
In order to obtain the expected measured energy spec-
trum of a WIMP signal including instrumental effects,
a Monte Carlo (MC) simulation with GEANT4 [12] is
used. A recoil energy spectrum is generated for each
WIMP mass with the differential cross section, form fac-
tor, and quenching factor, as described in Ref. [13]. The
spin-dependent form factor for 133Cs calculated by Toiva-
nen [14] is used, while for 127I, Ressell and Dean’s cal-
culation [15] is used. The photons generated with the
fitted decay function described above are propagated to
the PMT and digitized in the same manner as in the ex-
periment. Subsequently, the photoelectrons within given
time windows are counted to check the trigger condition
and to calculate energy. In this manner, the trigger ef-
ficieny and energy resolution is accounted for in the ex-
pected energy spectrum. The trigger efficiency is found
to be higher than 99% above 3 keV. The simulation is
verified with the energy spectrum obtained using 59.5
keV gamma rays from 241Am. The peak position and
TABLE II: Spin expectation values for 133Cs and 127I
Isotope J < Sp > < Sn > Reference
133Cs 7/2 -0.370 0.003 [16]
127I 5/2 0.309 0.075 [15]
width of the distribution are very well reproduced for
each crystal as described in Ref [11].
The total WIMP rate, R, for each WIMP mass is ob-
tained by fitting the measured energy spectrum to the
simulated one. The 90% confidence level (CL) limit on
R is calculated by the Feldman-Cousins’s approach in
the case of Gaussian with a boundary at the origin [17]
and then converted to the WIMP-nucleus cross section,
σW−A. Subsequently, the limits on WIMP-nucleon cross
section is obtained from Ref. [13][18] as follows:
σW−n = σW−A
where µn,A are the reduced masses of the WIMP-nucleon
and WIMP-target nucleus of mass number A. CA/Cn =
A2 for SI interactions and CA/Cn = 4/3{ap < Sp >
+an < Sn >}2(J + 1)/J for SD interactions. Here ap,
an are WIMP-proton and WIMP-neutron SD couplings
respectively. The spin expectation values used for this
analysis are shown in Table II. Following the “model-
independent” framework [18], we report the allowed re-
gion in two cases for SD interaction: one for an = 0,
and the other for ap = 0. We express the WIMP-nucleon
cross section as follows:
σSIW−n = σW−A
σSDW−n,p = σW−A
µ2n,p
(J + 1)
< Sn,p >2
where we indicate pure proton (p, an = 0) and pure
neutron (n, ap = 0) coupling for SD interaction. We also
present the allowed region in the ap − an plane with the
following relation [18]:
where GF is the Fermi coupling constant.
The uncertainty in the MT distribution results in the
uncertainty of the NR event rate. The limited statistics
of the calibration data and different crystals used for the
neutron calibration and WIMP search data are the ma-
jor sources of this uncertainty. The former is investigated
by varying the fitted parameters in PDF function within
errors. The lattter is estimated by changing the mean of
MT by the difference between the crystals. The system-
atic uncertainties from these two souces are combined in
quadrature resulting in 20-30% of statistical uncertain-
ties depending on the energy bins. In addition, there
WIMP Mass (GeV)
210 310 410
DAMA region
FIG. 3: (color online). Exclusion plot for the SD interaction
in the case of pure proton coupling (an = 0) at the 90%
confidence level
WIMP Mass (GeV)
210 310 410
DAMA region
FIG. 4: (color online). Exclusion plot for for the SD interac-
tion in the case of pure neutron coupling (ap = 0) at the 90%
confidence level
are uncertainties in the MC estimation of the expected
event rates due to the uncertainties in the quenching fac-
tors and the difference of energy resolution between the
MC simulation and the data. The systematic error from
the MC simulation is estimated to be 13.3% of the limits.
These systematic errors are combined with the statistical
error in quadrature in the presented results.
The limits on the SD interactions are shown in Fig. 3
and 4 in the cases of pure proton coupling and pure neu-
tron coupling, respectively. We also show the results ob-
tained from CDMS [19], NAIAD [20], SIMPLE [21], and
-6 -4 -2 0 2 4 6
FIG. 5: (color online). Allowed region (90% confidence level)
in ap − an plane by KIMS data (inside the solid line contour)
for 50 GeV WIMP mass. Results of CDMS [19](dotted line)
and NAIAD [20](dot-dashed line) are also shown.
WIMP Mass (GeV)
210 310 410
FIG. 6: (color online). Exclusion plot for the SI interactions
at the 90% confidence level.
PICASSO [22]. The DAMA signal region is taken from
Ref [23]. Our limit provides the lowest bound on the
SD interactions in the case of pure proton coupling for a
WIMP mass greater than 30 GeV/c2. The allowed region
in the ap − an plane for the WIMP mass of 50 GeV/c2 is
also shown in Fig. 5 together with the limits from CDMS
and NAIAD. The limit for the SI interactions is shown
in Fig. 6 together with the results of CDMS [24], EDEL-
WEISS [25], CRESST [26], ZEPLIN I [27], and the 3σ
signal region of DAMA (1-4) [28]. Although there are
several experiments that reject the DAMA signal region,
this is the first time that it is ruled out by a crystal de-
tector containing 127I, which is the dominant nucleus for
the SI interactions in the NaI(Tl) crystal.
In summary, we report new limits on the WIMP-
nucleon cross section with CsI(Tl) crystal detectors using
3409 kg·d exposure data. The DAMA signal regions for
both SI and SD interactions are excluded for the WIMP
masses higher than 20 GeV/c2 by the single experiment.
The most stringent limit on the SD interaction in the
case of purely WIMP-proton coupling is obtained.
The authors thank Dr. J. Toivanen and M. Korte-
lainen for the calculation of the SD form factor as well
as for the useful discussions. This work is supported by
the Creative Research Initiative Program of the Korea
Science and Engineering Foundation. We are grateful to
the Korea Middland Power Co. Ltd. and the staff mem-
bers of the YangYang Pumped Storage Power Plant for
providing us the underground laboratory space.
∗ skkim@hep1.snu.ac.kr
† Current address: National Cancer Center, Ilsan, Korea
‡ Current address: Department of Physics, Ewha Womans
University, Seoul, Korea
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mailto:skkim@hep1.snu.ac.kr
