Search for charged excitations of dark matter by KamLAND-Zen experiment

There are many scenarios in which dark matter is a part of a multiplet with an electrically charged state. If WIMP dark matter is accompanied by a charged state separated by a small mass difference, it can form stable bound states with nuclei. The region of observable energy deposition via this process of bound state formation is O(1˜10 MeV). KamLAND-Zen is a large scintillator detector designed for neutrino-less double-beta decay search. This detector is also useful to detect dark matter bound state formations with nuclei. The result from the KamLAND-Zen 400 dataset is reported.


Introduction
Dark matter is one of the most important problems in particle physics [1]. It is expected to be a new particle(s) beyond the Standard Model. One strong candidate for dark matter is the weakly interacting massive particle (WIMP). The neutralino in SUSY is a good example of a WIMP. It has neutral charge and is stable relative to the age of the Universe. WIMPs are expected to interact with ordinary matter with a strength weaker than the weak nuclear force.
There are a lot of scenarios in which the WIMP is a part of a multiplet with an electrically charged excited state. It enables us to naturally control the dark matter's abundance through coannihilation. If the mass difference is sufficiently small, the WIMP can form a stable bound state with a nucleus. In this process, the observable energy is O(1∼10 MeV). Detectors for neutrino-less double-beta decay (0νββ), for example, are suitable to detect events in this energy region.

Observables
The bound state formation process is written as [2] N Z , X 0 and X − represent a target nucleus with an atomic number Z, the WIMP like the neutralino and the excited state of the WIMP like the stau (τ ), respectively. If the bound state (N Z X − ) is not in its ground state, it will de-excite by emitting γ-rays. Besides the de-excitation γ-rays and the positron (e + ), the annihilation γ-rays would be observed in this process. The observable energy is written as The Coulomb binding energy E b of (N Z X − ) enables to bridge the mass difference ∆m ≡ m X − − m X 0 . E is the excited-state energy with the usual initial principal and the orbital quantum numbers of the capture (n,l). The energy distributions of the positrons and the γ-rays change with its value. However, the total energy deposition E vis would be monochromatic, regardless of the capture level. The signal shape is basically determined only by the energy response of the detector.
Once ∆m and the WIMP mass m X 0 are chosen, the induced signal in a detector can be translated into a constraint on the recombination cross section with the incoming dark matter velocity ⟨σv⟩ or the combination of the Yukawa couplings (|g eL | 2 + |g eR | 2 ). They are traded off against a constraint on the stau's decay width Γτ = τ −1 τ . This enables us to compare our result with the limit obtained in collider experiments [4].

Search for the WIMPs using KamLAND-Zen
KamLAND-Zen 400 is a 0νββ search experiment in the Kamioka mine [3]. It is a 1 kton liquid scintillator (LS) detector with Xe-loaded LS located in a 3.08-m-diameter spherical nylon balloon located at the center of the detector. The bound state formation search was performed by using the KamLAND-Zen 400 phase-II dataset. The total Xe amount (all isotopes) is 378.4 ± 2.2 kg. The livetime of the KamLAND-Zen 400 phase-II is 534.5 days. The exposure is 139.3 or 554.7 [kg·yr], when a 1 or 2 m-radius fiducial volume is used for analysis, respectively. Figure 1 shows the expected energy spectra for several ∆m values. The energy non-linearity and the energy resolution (σ E = 7.3%/ √ E (MeV)) are taken into account. Only single atomic de-excitation γ-ray emission with the total energy E γ is assumed. Figure 2 shows the observed energy spectra including the higher energy region not used in the 0νββ analysis. The radius DM. As we have argued, the total energy in Eq. (5) is monochromatic with all its energy injected almost instantaneously. The signal shape is hence determined by the energy resolution e of the experiment. Given an exposure MT, the total number of events in an energy bin ÁE ¼ E max À E min then reads spectrum from which we only su from the 2 decay of 136 Xe. Th excellent so that we only need t which E tot lies including the neighb priate statistical penalty) in de Unfortunately,  was selected using a figure of merit (FoM) in order to enlarge the fiducial volume as much as possible. The FoM was defined as where FV(r) is the volume of the Xe-loaded LS, N 90% obs is 90% C.L. upper limit on the number of the observed events and ϵ det (r, ∆m) is the spatial detection efficiency estimated by a Monte-Carlo simulation. The radius with highest FoM was chosen at 1 MeV ∆m intervals. The results of this study are shown in Figure 3. The black solid curve corresponds to a fiducial volume selected by the FoM. The results from analyses in which the 1 or 2 m-radius fiducial volume is chosen, are shown by the blue and red dotted curves. Zero the background and m X 0 = 100 GeV is assumed. For ∆m ≳ 12 MeV, the present analysis provides a better limits than the CMS experiment [4].

Summary
A search for a WIMP dark matter was performed by using the dataset from the 0νββ detector KamLAND-Zen 400. It provides a better limit than the CMS experiment for the low ∆m region. The sensitivity of this search will be improved by a background subtraction obtained from the best-fit of the energy spectrum in the 0νββ search [3].