Measurement of cosmic-ray muon spallation products in a xenon-loaded liquid scintillator with KamLAND

Cosmic-ray muons produce various radioisotopes when passing through material. These spallation products can be backgrounds for rare event searches such as in solar neutrino, double-$\beta$ decay, and dark matter search experiments. The KamLAND-Zen experiment searches for neutrinoless double-$\beta$ decay in 745 kg of xenon dissolved in liquid scintillator. The experiment includes dead-time-free electronics with a high efficiency for detecting muon-induced neutrons. The production yields of different radioisotopes are measured with a combination of delayed coincidence techniques, newly developed muon reconstruction, and xenon spallation identification methods. The observed xenon spallation products are consistent with results from the fluka and geant4 simulation codes.

Figure 1

Schematic view of the KamLAND-Zen detector. The black dotted rectangle, corresponding to a 1.5 m-radius cylinder in the upper hemisphere, illustrates a tube cut that is applied to exclude the droplet-like region of Xe-LS. The 0.7 m-diameter sphere centered at $(x,y,z)=(0,0,-1.9\mathrm{m}$) is vetoed due to contamination (hot spot veto).

Figure 2

Schematic of KamFEE, BLR and MoGURA. After a high charge event, the PMT baseline overshoot is subtracted and the baseline stabilized.

Figure 3

Illustration of the adaptive trigger in MoGURA. (a) Number of PMT hits in a 120 ns window following a muon crossing. The red dashed line shows the average of $N_{\mathrm{Hit}}$ for 240 ns. (b) The adaptive trigger uses the difference of $N_{\mathrm{Hit}}$ and its 240-ns average to efficiently extract the sharp peaks from neutron capture events.

Figure 4

Schematic of the main muon track reconstruction algorithm. The entrance point is determined by the earliest hit PMT, while the muon exit point is determined by the PMT with the largest signal. The earliest scintillation light and Cherenkov light propagate with Cherenkov angle $\theta$.

Figure 5

Schematic of the scintillation light path of a muon event. $t_{\mathrm{Hit}}$ is the expected hit timing calculated by adding the arrival time and the time of flight.

Figure 6

An example of the reconstructed shower charge along the track of a measured muon. The red line ($L_{\mathrm{long}}=995$ cm) is the position of the interaction. As detailed in Sec. 5b, the shower charge, $dQ/d{L}_{\mathrm{long}}=3.96\times {10}^5$ p.e./cm, is calculated by integrating the deposition in the orange band.

Figure 7

$N_S$ and $\mathrm{\Delta }T$ distribution of neutron capture candidates in a radius less than 5.5 m. ${}^1\mathrm{H}{(n,\gamma )}^2\mathrm{H}$ events concentrate around $N_S\approx 180$. Noise events are localized around $\mathrm{\Delta }T<30\mu \mathrm{s}$. The selection criteria for neutron capture events are indicated by the red lines.

Figure 8

$N_S$ of the neutron capture candidates in the Xe-LS with a radius less than 1.9 m. The 2.223 (4.945) MeV $\gamma$ ray from neutron capture on ${}^1\mathrm{H}$ (${}^{12}\mathrm{C}$) gives a peak around $N_S\approx 180$ (350). The 4.025 MeV $\gamma$ ray from neutron capture on ${}^{136}\mathrm{Xe}$ is expected at $N_S\approx 290$ but is not visible due to background.

Figure 9

The cross section ratio of the measurements to the fluka simulations, for a 500 MeV/nucleon ${}^{136}\mathrm{Xe}$ beam (top) and a 1 GeV/nucleon ${}^{136}\mathrm{Xe}$ beam (bottom). Only $Z>40$ was reported in [26].

Figure 10

Deviation of the visible spallation isotope decay energy spectrum compared to fluka. The data spectrum is constructed from the measured cross sections of the 500 MeV/nucleon ${}^{136}\mathrm{Xe}$ beam experiment (red solid) [26] and the 1 GeV/nucleon ${}^{136}\mathrm{Xe}$ beam experiment (blue dashed) [27]. The ROI is indicated by the band.

Figure 11

Muon-induced spallation production yields in the Xe-LS from fluka simulation.

Figure 12

Muon-induced spallation production yields in the liquid xenon from fluka simulations. The initial muon energy is 273 GeV and 283 GeV for XENON [32] (top) and LZ [33] (bottom), respectively. $A\le 4$ is omitted.

Figure 13

Simulated visible energy spectra of spallation isotopes in Xe-LS. The colored histograms show the contribution from a part of the spallation daughters which have large impacts in the ROI. The black histogram is the total of all spallation isotopes. The $0\nu \beta \beta$ decay search ROI is indicated by black dashed lines.

Figure 14

Time difference between the cosmic-ray muon and neutron capture in the KamLAND-LS ($2.5<r<4.5\mathrm{m}$ with the tube cut). The red line shows the exponential fit constrained to $207.5\pm 2.8\mu \mathrm{s}$. Fit range is illustrated by the shaded region. The detection efficiency is lower at small $\mathrm{\Delta }T$ due to PMT baseline overshoot.

Figure 15

Spatial distribution of neutron capture events. $r$ is the distance from the detector center. The boundary of Xe-LS and KamLAND-LS is indicated by the red line. The vertex resolution and droplet-like shape of the inner balloon cause the deviation from a step function.

Figure 16

Time difference between the cosmic-ray muon and the spallation isotope's $\beta$ decay selected by $n$-tag. The energy bin is $2<E<3\mathrm{MeV}$ and the $\beta$ decay candidates in $2.5<r<4.0$ m with the tube cut are shown.

Figure 17

PDFs of neutron capture events and accidental coincidences in Eq. (10) are given as red solid line and blue dashed line, respectively.

Figure 18

Neutron multiplicity of ${}^{10}\mathrm{C}$ from simulation (red line) and data (black points) in $r<$ 4 m with the tube cut and the hot spot veto.

Figure 19

$\mathrm{\Delta }{\chi }^2$ of the xenon spallation rate fitted to the energy spectrum. The results of KamLAND-Zen 400 phase2 and KamLAND-Zen 800 are shown as blue and red dashed lines, and the combined result is shown in black. The fluka prediction is indicated with an orange band.

Figure 20

Time difference between the cosmic-ray muon and xenon spallation candidates. The data was plotted after correcting the muon detection efficiency.

Figure 21

Upper figure shows the PDFs of neutron multiplicity of ${}^{137}\mathrm{Xe}$ events (red solid line) and other xenon spallation events (blue dashed line). Bottom figure shows the PDFs of $N_S$ for neutron captures on ${}^{136}\mathrm{Xe}$ (red solid line) and ${}^1\mathrm{H}$ and ${}^{12}\mathrm{C}$ (blue dashed line).

Figure 22

Time difference between a cosmic-ray muon and the ${}^{137}\mathrm{Xe}{\beta }^{-}$ decay candidate in $2.4\le E<3.2$ MeV. ${}^{208}\mathrm{Tl}{\beta }^{-}$ decay is derived from the ${}^{232}\mathrm{Th}$ series.

Figure 23

Visible energy of the ${}^{137}\mathrm{Xe}{\beta }^{-}$ decay candidates in $80\le \mathrm{\Delta }T<1980$ s.