A Search for Charged Excitation of Dark Matter with the KamLAND-Zen Detector
S. Abe, S. Asami, A. Gando, Y. Gando, T. Gima, A. Goto, T. Hachiya, K. Hata, S. Hayashida, K. Hosokawa, K. Ichimura, S. Ieki, H. Ikeda, K. Inoue, K. Ishidoshiro, Y. Kamei, N. Kawada, T. Kinoshita, M. Koga, N. Maemura, T. Mitsui, H. Miyake, K. Nakamura, K. Nakamura, R. Nakamura, A. Ono, N. Ota, S. Otsuka, H. Ozaki, T. Sakai, H. Sambonsugi, I. Shimizu, Y. Shirahata, J. Shirai, K. Shiraishi, A. Suzuki, Y. Suzuki, A. Takeuchi, K. Tamae, K. Ueshima, Y. Wada, H. Watanabe, Y. Yoshida, S. Obara, D. Chernyak, A. Kozlov, S. Yoshida, S. Umehara, Y. Takemoto, K. Fushimi, S. Hirata, A. Ichikawa, K.Z. Nakamura, M. Yoshida, B.E. Berger, B.K. Fujikawa, C. Grant, A. Li, J.G. Learned, J. Maricic, S. Axani, L. A. Winslow, Z. Fu, Y. Efremenko, H.J. Karwowski, D.M. Markoff, W. Tornow, T. ODonnell, S. DellOro, J.A. Detwiler, S. Enomoto, M.P. Decowski
aa r X i v : . [ h e p - e x ] J a n A Search for Charged Excitation of Dark Matter with the KamLAND-Zen Detector
S. Abe, S. Asami, A. Gando, Y. Gando, T. Gima, A. Goto, T. Hachiya, K. Hata, S. Hayashida,
1, 2
K. Hosokawa, ∗ K. Ichimura, S. Ieki, H. Ikeda, K. Inoue,
1, 3
K. Ishidoshiro, Y. Kamei, N. Kawada, T. Kinoshita, M. Koga,
1, 3
N. Maemura, T. Mitsui, H. Miyake, K. Nakamura, K. Nakamura, R. Nakamura, A. Ono, N. Ota, S. Otsuka, H. Ozaki,
1, 4
T. Sakai, H. Sambonsugi, I. Shimizu, Y. Shirahata, J. Shirai, K. Shiraishi, A. Suzuki, Y. Suzuki, A. Takeuchi, K. Tamae, K. Ueshima,
1, 5
Y. Wada, H. Watanabe, Y. Yoshida, S. Obara, D. Chernyak,
3, 7
A. Kozlov,
3, 8
S. Yoshida, S. Umehara, Y. Takemoto,
10, 11
K. Fushimi, S. Hirata, A. Ichikawa,
14, 15
K.Z. Nakamura, M. Yoshida, B.E. Berger,
3, 16
B.K. Fujikawa,
3, 16
C. Grant, A. Li,
17, 18
J.G. Learned, J. Maricic, S. Axani, L. A. Winslow, Z. Fu, Y. Efremenko,
3, 21
H.J. Karwowski, D.M. Markoff, W. Tornow, T. O’Donnell, S. Dell’Oro, J.A. Detwiler,
24, 3
S. Enomoto,
24, 3 and M.P. Decowski
3, 25 (KamLAND-Zen Collaboration) Research Center for Neutrino Science, Tohoku University, Sendai 980-8578, Japan Present address: Imperial College London, Department of Physics, Blackett Laboratory, London SW7 2AZ, UK Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University ofTokyo Institutes for Advanced Study, The University of Tokyo, Kashiwa, Chiba, 277-8583, Japan Graduate Program on Physics for the Universe, Tohoku University, Sendai 980-8578, Japan Present address: National Institutes for Quantum and RadiologicalScience and Technology (QST), 1-1-1 Kouto, Sayo, Hyogo 679-5148, Japan Frontier Research Institute for Interdisciplinary Sciences, Tohoku University, Sendai 980-8578, Japan Present address: Department of Physics and Astronomy,University of Alabama, Tuscaloosa, Alabama 35487,USA and Institute for Nuclear Research of NASU, 03028 Kyiv, Ukraine Present address: National Research Nuclear University “MEPhI”(Moscow Engineering Physics Institute), Moscow, 115409, Russia Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan Research Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567-0047, Japan Present address: Kamioka Observatory, Institute for Cosmic Ray Research,The University of Tokyo, Hida, Gifu 506-1205, Japan Department of physics, Tokushima University, Tokushima 770-8506, JAPAN Graduate School of Integrated Arts and Sciences, Tokushima University, Tokushima 770-8502, Japan Department of Physics, Tohoku University, Sendai 980-8578, Japan Department of Physics, Kyoto University, Kyoto 606-8502, Japan Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA Boston University, Department of Physics, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA Present address: The University of North Carolina Physics & Astronomy,120 E. Cameron Ave., Phillips Hall CB3255, Chapel Hill, North Carolina 27599, USA Department of Physics and Astronomy, University of Hawaii at Manoa, Honolulu, Hawaii 96822, USA Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA Triangle Universities Nuclear Laboratory, Durham, North Carolina 27708, USA andPhysics Departments at Duke University, North Carolina CentralUniversity, and the University of North Carolina at Chapel Hill Center for Neutrino Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, USA Center for Experimental Nuclear Physics and Astrophysics, University of Washington, Seattle, Washington 98195, USA Nikhef and the University of Amsterdam, Science Park, 1098XG Amsterdam, Netherlands (Dated: January 18, 2021)There are many theories where a dark matter particle is part of a multiplet with an electricallycharged state. If WIMP dark matter ( χ ) is accompanied by a charged excited state ( χ − ) separatedby a small mass difference, it can form a stable bound state with a nucleus. In supersymmetricmodels, the χ and the χ − could be the neutralino and a charged slepton, such as the neutralino-stau degenerate model. The formation binding process is expected to result in an energy depositionof O (1–10 MeV), making it suitable for detection in large liquid scintillator detectors. We describenew constraints on the bound state formation with a xenon nucleus using the KamLAND-Zen 400Phase-II dataset. In order to enlarge the searchable parameter space, all xenon isotopes in thedetector were used. For a benchmark parameter set of m χ = 100 GeV and ∆ m = 10 MeV,this study sets the most stringent upper limits on the recombination cross section h σv i and thedecay-width of χ − of 2 . × − cm / s and 1 . × − GeV, respectively (90% confidence level).
A. Introduction
Dark matter is one of the most pressing problems in nature. It is expected to consist of one or more new, beyondthe Standard Model particles. A well-motivated class of dark matter particles is weakly interacting massive particles(WIMPs). The neutralino in supersymmetric (SUSY) theory is a good example of a WIMP [1]. It has neutral chargeand is stable relative to the age of the Universe. Direct dark matter search experiments have searched for WIMPsinteracting with nuclei with a strength weaker than the weak interaction [2, 3]. Despite achieving great sensitivityto the WIMP-nucleus cross section, no signal has been observed so far. Here, we report on an alternative search,where the WIMP is accompanied by a charged excited state. Ref. [4] proposed to observe the bound state formationbetween the charged excited state and ordinary nuclei as a method to search for this kind of dark matter particle.The KamLAND-Zen detector has the capability to search for O(1-10) MeV energy depositions via this reaction. Inthis paper, we describe new constraints on this search.
B. The KamLAND-Zen 400 detector
The main goal of KamLAND-Zen is to search for neutrino-less double-beta decays (0 νββ ) in
Xe nuclei [5].KamLAND-Zen 400 was the first phase of the project and ran from Sep. 2011 to Oct. 2015. The KamLANDdetector, located 2,700 m.w.e underground in the Kamioka mine, was originally designed to measure anti-neutrinos,such as reactor- and geo-neutrinos [6–8]. The detector is layered with an outer and an inner detector. The outerdetector (OD) is a cylindrical water Cherenkov detector to veto events primarily from cosmic muons. The innerdetector consists of a spherical stainless steel tank with 1879 Photo Multiplier Tubes (PMT) facing the inside volume,filled with organic liquid scintillator (LS) and non-scintillating mineral oil (MO). A 6.5-m-radius spherical balloonmade of nylon and EVOH inside the tank contains 1 kton of the LS (KamLS). The remainder of the volume betweenthe balloon and the stainless steel tank is filled with MO. A second, 1.54-m-radius teardrop shaped balloon (innerballoon, IB) with 13 tons of xenon-loaded LS (Xe-LS) was located at the center of the KamLAND detector. Thevertex and energy are reconstructed using charge and hit timing information extracted from waveforms acquired withthe PMTs.The IB was constructed from 25 µ m-thick nylon film and surrounded by the KamLS. The Xe-LS was composedof 80.7% decane and 19.3% psedocumene (1,2,4-trimethylbenzene) by volume, 2.29 g/liter of the fluor PPO (2,5-diphenyloxazole) and (2.91 ± ± Xe and (8.96 ± Xe. Other xenon isotopes had negligible presence. The energyresponse of the Xe-LS and the KamLS were different. The relative light yield of the KamLS to the Xe-LS is estimatedto be 1.07 [9]. The difference is taken into account in this study. The KamLAND-Zen 400 data acquisition periodis divided into two phases, before and after a Xe-LS purification to handle different background rates in the Xe-LS.Phase-I includes a background from m Ag ( β -decay, τ = 360 day, Q = 3 .
01 MeV) creating a peak near 2.7 MeVvisible energy. The peak-shape background disappeared after xenon distillation and LS replacement. This analysisonly uses the Phase-II dataset taken between Dec. 11 th th m Agbackground [10]. The livetime is 534.5 days. The total xenon mass (all isotopes) in KamLAND-Zen 400 Phase-II was380.7 ± C. The model and the expected signal
As mentioned in Section A, there are scenarios where a WIMP is part of a multiplet with an electrically chargedexcited state [4, 11]. If such a WIMP does not have a large enough annihilation cross-section, co-annihilation onlycan determine the dark matter’s abundance. If the mass difference ∆ m between the WIMP and the excited stateis sufficiently small, the charged excitation of the WIMP can form a stable bound state with a nucleus [4]. In thisprocess, the Coulomb binding energy, whose value depends on the target nucleus, is released and the observable energyis of the order O (1–10 MeV). Detectors studying neutrinos and 0 νββ are well-suited to detect events in this energyrange. The bound state formation process and the effective Yukawa-type Lagrangian, which governs the bound stateformation are given by [4](case A in the reference): N Z + χ → ( N Z χ − ) + e + , (1) L = ¯ χ ( g eL P L + g eR P R ) eχ −† + H . c ., (2) ∗ Corresponding author. [email protected] [MeV] vis
E0 2 4 6 8 10 12 14 16 18 20 P r ob a b ilit y [ a . u . ] m = 17 MeV ∆
15 MeV13 MeV11 MeV9 MeV 7 MeV 5 MeV 3 MeV 1 MeV
FIG. 1. The expected energy spectra via the bound state formation for several ∆ m in the KamLAND-Zen 400 detector. where N Z is the target nucleus with atomic number Z , g eL,R are the general complex couplings of the chiralityprojections P L,R , and χ ( χ − ) is the WIMP ground (excited) state, respectively. In SUSY models, the latter twocould be the neutralino and a charged slepton, such as the neutralino-stau degenerate model [12, 13]. If the boundstate ( N Z χ − ) is not in its ground state, it will de-excite by emitting γ -rays. In addition to the de-excitation γ -raysand a positron, annihilation γ -rays could be observed in this process. Therefore, the observable energy is given by [4]: E tot = E e + + E γ + 2 m e , (3)where E e + = E ( n,l ) b − ∆ m − m e , (4) E γ = E (0) b − E ( n,l ) b , (5)so that E tot = E (0) b − ∆ m + m e , (6)where E e + and E γ are the kinetic energy of the positron and the de-excitation γ -rays. The Coulomb binding energy E b of ( N Z χ − ) allows to bridge the mass difference ∆ m ≡ m χ − − m χ , the value depends on the target nucleus. Assuminga step-like nuclear charge distribution, E (0) b , the binding energy corresponding to the ground state of ( N Z χ − ), iscalculated to be 18.4 MeV for a xenon target [11]. By increasing Z, E (0) b also increases and the searchable ∆ m regionis larger, so that xenon nuclei offer a good target. E ( n,l ) b is the excited-state energy with the usual principal and orbitalquantum numbers of the capture level ( n,l ); The energy distributions of the positrons and the γ -rays change with E ( n,l ) b . However, E tot is monochromatic, regardless of the capture level. The signal shape is basically determined onlyby the energy response of the detector. Figure 1 shows the expected energy spectra for several ∆ m values, where E vis is the visible energy in KamLAND-Zen and differs from the intrinsic energy deposition due to energy non-linearityand the light yield difference between the Xe-LS and the KamLS. The energy non-linearity, the light yield differenceand the energy resolution ( σ E = 7 . / p E (MeV)) are taken into account [5]. The higher and lower visible energyranges correspond to lower and higher ∆ m , respectively. Here a single nuclear de-excitation γ -ray with total energy E γ is considered; multiple γ -rays emissions give a negligible difference from the single gamma-ray analysis.The expected number of signals in an energy bin ∆ E = E max − E min is given by [4]: N expected = M T N T ρ DM h σv i m χ (cid:20) Erf (cid:18) E max − E tot √ σ E (cid:19) − Erf (cid:18) E min − E tot √ σ E (cid:19)(cid:21) , (7)where MT , N T , ρ DM and h σv i are detector exposure, number of target nuclei, the local density of dark matter andthe WIMP-nucleus recombination cross section with incoming dark matter velocity v , respectively. In general, thesignal is expected to have a Gaussian peak. However, the simulated signal shapes in the KamLAND-Zen 400 detector(Fig.1) have non-Gaussian distributions due to the light yield difference between the Xe-LS and the KamLS. The∆ E has therefore to be defined considering the non-Gaussian signal shape. Once the WIMP mass m χ and ∆ m arechosen, the induced detector signal can be translated into a constraint on h σv i or the χ − ’s decay width Γ χ − , followingEq.(7) [4]: h σv i ≃ ( | g eL | + | g eR | ) / (8 πm χ ) × X n,l B n,l , (8) B n,l ≃ ( E ( n,l ) b − ∆ m − m e ) q ( E ( n,l ) b − ∆ m ) − m e × Z d r d r φ ∗ n,l ( ~r ) φ n,l ( ~r ) e iµ~v · ( ~r − ~r ) , (9)Γ χ − = τ − χ − (10) ≃ p ∆ m − m e πm χ (∆ m + m e )( | g eL | + | g eR | ) , (11)where B n,l , φ n,l and τ χ − are the contributions from the capture into the state ( n,l ), the wave function of the relativemotion of ( N χ − ) with reduced mass µ and the lifetime of χ − , respectively. A translation into a constraint on Γ χ − allows us to combine our results with the limits on the stau’s decay width Γ ˜ τ obtained in collider experiments, suchas CMS [14]. D. Analysis
As a preliminary step to the analysis, we apply the same event selection to the dataset as for the 0 νββ analysis [5]:1. Events with energies over ∼
30 MeV and OD-triggered events are vetoed as muon events. Events within 2 msafter a muon crossing are also vetoed to reject PMT afterpulses and instability of signal baseline;2. Sequential decays of
Bi–Po and
Bi–Po are tagged by delayed-coincidence and pileup-detection methodsand rejected;3. Events from shorter-lived spallation products i.e. He, Li, C and B, are suppressed by a triple-coincidencetag of a muon, a neutron identified by capture γ rays and the product’s decay;4. Anti-neutrino events which produce a positron and a neutron from inverse β -decay are identified with thedelayed-coincidence tagging method and vetoed;5. Badly reconstructed events are identified by time-charge-hit discriminator and rejected.The total detection efficiency for the bound state formation is over 99.9%, where the deadtime due to the spallationcut and post-muon events are taken into account in the livetime calculation.Figure 2 shows the observed energy spectrum, which includes the high-energy range (above 4.8 MeV) not used inthe 0 νββ analysis for two different fiducial volumes. The two-neutrino double-beta decay (2 νββ ) events dominatethe energy region. The Q-value of Xe 2 νββ is 2.458 MeV and the spectrum has a continuous distribution. The IBis not as clean as the Xe-LS and contains radioactive sources from the
Th and
U decay series. Therefore, thebackground rate with a 2-m-radius fiducial volume is much higher than with a 1-m-radius. The peak at 4 MeV in the2-m-radius analysis is dominated by β + γ -rays (Q-value ∼ Tl decay contained in the IB. The highenergy region above 5 MeV is dominated by short-lived spallation events from cosmic muons such as B, Li and B.The high energy detector response is understood within 1% uncertainty in the KamLS by using spallation events justafter muon events [9, 15].In order to optimize the fiducial volume, the radius was selected using a figure of merit (FoM), which is a functionof the energy range: FoM( r, ∆ m ) ≡ S √ B ≡ FV( r ) × ǫ det ( r, ∆m) q N , (12)where FV( r ) is the volume of the Xe-LS, N is the 90% confidence level (C.L.) upper limit on the number ofobserved events. The reconstructed position of the expected signal is spatially diffused due to the emitted γ -rays.The spatial detection efficiency ǫ det ( r, ∆m) is estimated from a Monte-Carlo simulation. Similarly to the 0 νββ analysis, this analysis uses the volume within 2-m-radius from the center of the IB and includes both the internal [MeV] vis E2 4 6 8 10 12 14 16 18 e v e n t s / . M e V
2m radius1m radius
FIG. 2. The observed energy spectra in the KamLAND-Zen 400 Phase-II dataset for a 1 m and 2-m-radius fiducial volume. and external regions of the Xe-LS and the IB. The volume was divided into 20 equal-volume spherical shell bins. TheFoM was then calculated for each of the 20 equal-volume bins and the bin with the highest FoM was chosen at 1 MeV∆ m intervals.As shown in Figure 1, the width of the expected spectrum changes with the value of ∆ m . To improve the S/Nratio, the width of the energy region of interest was defined to be twice the standard deviation of the expected signal.This region includes over 95% of the expected signal.To improve the sensitivity, the 90% upper limit of the signal rate was calculated from the number of observed andknown-background events in the energy range of interest using the Feldman and Cousins method [16]. The best-fit2 νββ spectrum and the well-known background spectra fixed in the 0 νββ analysis were used. The fixed backgroundsare ( Th series,
Bi, Kr) in the Xe-LS, (
Th series,
Bi, Kr, K) in the KamLS and (
Th series,
Bi,
Cs,
Cs, K) contained on the IB film.
E. Result and conclusion
The results of this study for the WIMP parameter space are shown in Figure 3. No significant excess of eventswas found. The upper limit for the N Z - χ recombination cross section h σv i is drawn as a function of m χ for several∆ m values, including a lower limit for the ˜ τ mass obtained by the ATLAS experiment [17]. Figure 4 shows anotherinterpretation of the results. The black curves are the upper limits on the Γ χ − by KamLAND-Zen 400 Phase-II.The curves corresponds to m χ of 100 GeV, 200 GeV, 1 TeV and 10 TeV respectively. Theoretical constraints basedon reported spectra of several experiments [4] are also shown. As are lower limits from a search for ˜ τ by the CMSassuming the minimal gauge-mediated super-symmetry breaking (GSMB) model [4, 14].A search for the bound state formation of a nucleus and an electrically charged WIMP state was performed usingdata from the 0 νββ detector KamLAND-Zen 400. The analysis has good sensitivity in the region ∆ m < . h σv i < . × − cm / s when assuming ∆ m = 10 MeV and m χ = 100 GeV. The upper limit of the decay width of χ − assuming ∆ m = 10 MeV is Γ χ − < . × − GeV andΓ χ − < . × − GeV for m χ = 100 GeV and m χ = 10 TeV, respectively.The KamLAND-Zen 800 experiment, the next phase of KamLAND-Zen 400, has recently started acquiring datawith about twice as much xenon and a new IB with ten times lower radioactive contamination [18]. It is expectedto improve the sensitivity and decrease the Tl background at 4 MeV originating from the IB. However, spallationevents from cosmic muons in the high-energy region over 5 MeV will become a challenging background.
ACKNOWLEDGMENTS
The authors wish to acknowledge Dr. Haipeng An and Dr. Josef Pradler for providing helpful advice and thevalues related to the contribution from a capture into a state ( n,l ) in equation 9. The KamLAND-Zen experiment [GeV] χ m / s ] v > [ c m σ < − − − − − − − − m = . [ M e V ] ∆ m = . [ M e V ] ∆ m = . [ M e V ] ∆ m = . [ M e V ] ∆ A TL A S FIG. 3. The N z - χ recombination cross section h σv i as a function of the WIMP mass m χ . The black solid lines show the 90%C.L. upper limit from this study for several ∆ m values. The gray dashed line shows the lower limit for the mass of the ˜ τ fromthe ATLAS experiment [17]. is supported by JSPS KAKENHI Grants No. 21000001, No. 26104002, and No. 19H05803; the World PremierInternational Research Center Initiative (WPI Initiative), MEXT, Japan; Netherlands Organization for ScientificResearch (NWO) ; and under the U.S. Department of Energy (DOE) Contract No. DE-AC02-05CH11231, the NationalScience Foundation (NSF) No. NSF-1806440, as well as other DOE and NSF grants to individual institutions. TheKamioka Mining and Smelting Company has provided service for activities in the mine. We acknowledge the supportof NII for SINET4. [1] M. Kamionkowski G. Jungman and K. Griest. Phys. Rep. , :195–373, 1996.[2] E. Aprile et al. Phys. Rev. Lett. , :111302, 2018.[3] D. S. Akerib et al. Phys. Rev. Lett. , :021303, 2017.[4] M. Pospelov H. An and J. Pradler. Phys. Rev. Lett. , :251302, 2012.[5] (KamLAND-Zen Collaboration) A. Gando et al. Phys. Rev. Lett. , :082503, 2016.[6] (KamLAND Collaboration) K. Eguchi et al. Phys. Rev. Lett. , :021802, 2003.[7] (KamLAND Collaboration) A. Gando et al. Phys. Rev. D , :052002, 2011.[8] (KamLAND Collaboration) T. Araki et al. Nature , :499–503, 2011.[9] S. Matsuda. PhD thesis, Tohoku University RCNS, 2016. [ ].[10] (KamLAND-Zen Collaboration) A. Gando et al. Phys. Rev. C , :045504, 2012.[11] M. Pospelov and A. Ritz. Phys. Rev. D , :055003, 2008.[12] T.Falk J. Ellis and K. A. Olive. Phys. Lett. B , :367–372, 1998.[13] J. Ellis et al. Astro. Phys. , :181–213, 2000.[14] (CMS Collaboration) S. Chatrchyan et al. Phys. Lett. B , :408–433, 2012.[15] S. Obara. PhD thesis, Tohoku University RCNS, 2018. [ ].[16] G. J. Feldman and R. D. Cousins. Phys. Rev. D , (7), 1998.[17] (ATLAS Collaboration) M. Aaboud et al. Phys. Rev. D , :092007, 2019.[18] on behalf of the KamLAND-Zen collaboration A. Gando et. al. J. Phys.: Conf. Ser. , :012145, 2020. m [MeV] ∆ ) [ G e V ] - χ Γ ( l og B o r e x i no SNO DAMA/LIBRA 1TeVEXO-200 X e = 10 TeV χ m = 1 TeV χ m = 200 GeV χ m = 100 GeV χ m CMS K a m L A N D - Z e n [MeV] vis E 24681012141618 − − − − − − − − − m [MeV] ∆ FIG. 4. Excluded decay width region of ˜ τ as a function of ∆ m (bottom axis) and E vis (top axis). The black curves show 90%C.L. upper limits from the KamLAND-Zen 400 Phase-II dataset. Horizontal solid (dashed) lines show the lower limit assuminga ˜ ττ