Low background measurement in CANDLES-III for studying the neutrino-less double beta decay of 48 Ca

We developed a CANDLES-III system using 96 CaF2 scintillation crystals with a total mass of 305 kg to study the neutrino-less double beta (0νββ) decay of 48Ca. The system was equipped with a 4π active shield using a liquid scintillator to reject external backgrounds. The internal backgrounds caused by the radioactive impurities within the CaF2 crystals can be effectively reduced by observing the signal pulse shape. We analyzed the data observed in the Kamioka underground for the live-time of 130.4 days to evaluate the feasibility of the low background measurement with the CANDLES-III detector. Moreover, we estimated the number of background events from the simulation based on the radioactive impurities in the CaF2 crystals and the rate of high energy γ-rays caused by the (n, γ) reaction induced by environmental neutrons. The expected background rate was in a good agreement with the measured rate. In conclusion, the background candidates were properly estimated by comparing the measured energy spectrum with the background simulations. Consequently, no events were observed in the Qββ-value region when 21 high purity CaF2 crystals were selected. This gave a lower limit on the half-life of T 1/2 > 5.6 × 10 22 yr (90% confidence level) for the 0νββ decay of 48Ca. With this measurement, we achieved the first 0νββ decay search in a low background condition with a detector using a Ca isotope, which was not enriched but natural, in a scale of hundreds of kg. The 48Ca isotope has a high potential for the 0νββ decay search, and expected to be useful for the development of the next detector for a highly sensitive measurement. ∗ Present address: Research Center for Neutrino Science, Tohoku University † Present address: Sector of Fukushima Research and Development, Japan Atomic Energy Agency ‡ Present address: Institute for Cosmic-ray Research, the University of Tokyo § Present address: Graduate School of Medicine, Nagoya University ¶ Present address: Department of Physics, Kobe University


I. INTRODUCTION
The remaining questions on the neutrino property are the absolute mass and its origin.
These property can be potentially investigated by observing the neutrino-less double beta decay (0νββ decay) [1]. A double beta (ββ) decay has two modes. One is the two-neutrino ββ decay (2νββ decay) accompanied with two electrons and two anti-neutrinos [2]. This decay mode is allowed within the standard model of particle physics and has been observed in several isotopes [3] [4]. The other is the 0νββ decay, which can only occur if the neutrino is a Majorana particle [5]. This process is forbidden in the standard model because it violates the lepton number conservation law. The half-life of this decay is inversely proportional to the square of the effective Majorana neutrino mass; hence, the observation of the 0νββ decay establishes the Majorana nature of the neutrinos and gives the absolute scale of the effective neutrino mass [6] [7] [8].
The 0νββ decay has been searched using several isotopes [9], but has not yet been ob- They published results of the lower limit on the half-life of T 0ν 1/2 ≥ 1.07×10 26 yr for the KamLAND-Zen Collaboration [10], and 3.5×10 25 yr for the EXO-200 Collaboration [11].
The GERDA and MAJORANA experiments have searched for the 0νββ decay of 76 Ge and set limits on the half-lives of T 0ν 1/2 ≥ 0.9×10 26 yr [12] and 1.9×10 25 yr [13], respectively. The CUORE experiment has searched for the 0νββ decay of 130 Te and published the result on the half-life of T 0ν 1/2 ≥ 3.2×10 25 yr [14].
The T 0ν 1/2 sensitivity scales linearly with the source mass (M ) and the measurement time (t) in a background-free case, as opposed to √ M t in the case of background dominance.
Thus, a background-free experiment is the key to scaling up the source volume and the measurement time. In this respect, the search for the 0νββ decay using the 48 Ca isotope is particularly promising because it has the highest Q-value (Q ββ =4267.98±0.32 keV [15]) among any ββ decaying isotopes. This Q ββ -value is above the bulk of natural radioactive backgrounds and ensures a favorable phase space that enhances the 0νββ decay rate. Searches for the 0νββ decay of 48 Ca were firstly demonstrated approximately 60 years ago [16]. Since then, various measurements have been performed [17][18][19][20][21][22][23], no signals for the 0νββ decay were found in either measurements, with the best limit on 48 Ca currently set by the ELEGANT VI experiment using 6.6 kg of CaF 2 (Eu) scintillators (7.6 g of 48 Ca) at T 0ν 1/2 ≥ 5.8×10 22 yr [22]. The measurement was not limited by the backgrounds. The characteristic of the ELEGANT VI detector was the usage of a 4π active shield by its scintillator complex, and the success of which was the key to achieving a background-free measurement.
Our strategy for achieving better sensitivity is to increase a number of target nuclei and keep the background at a lower level, for which the initial concept of the CANDLES system is proposed. The Eu-doped CaF 2 used in ELEGANT VI has a large light output and gives a good energy resolution. However it has a short attenuation length because of the selfabsorption of its scintillation light and is not suitable for the next step. A scale up with a good energy resolution without degrading the light collection can be achieved by utilizing the combination of undoped CaF 2 with a long attenuation length (more than 10 m) and the layer of the adjacent wavelength shifter (WLS). We realize a 4π active shield by surrounding the CaF 2 crystals in all directions with a luminous liquid scintillator (LS) to accomplish a background-free measurement. The highest Q ββ -value combined with the 4π active shield achieved a substantial reduction of the backgrounds, which will be described in this paper.
The natural abundance of 48 Ca is denoted by the least amount of approximately 0.2% among the ββ decaying nuclei. On the contrary, this shows a big advantage of approximately 500 enhancement in case enrichment could be achieved, because CANDLES-III already reached a large volume of 300 kg. Several approaches for the 48 Ca enrichment are under development, including electromagnetic/optical separators [24], laser isotope separation [25], chemical separation [26] [27], and electrophoresis [28].
This article presents a method of achieving a low background condition. We will also show herein our first result of CANDLES-III in the Kamioka underground, which is comparable to the best result among the 0νββ measurements with 48 Ca. CANDLES has the potential to be the most competitive experiment, provided that an effective method for enriching 48 Ca and a detector with high energy resolution are available.

CANDLES (CAlcium fluoride for the study of Neutrinos and Dark matters by Low Energy
Spectrometer) is an experiment peformed to search for the 0νββ decay of 48 Ca with undoped CaF 2 (CaF 2 ) scintillation crystals. The conceptual design of the CANDLES detector is described in Ref. [29]. The current setup of the detector system, which is called CANDLES-III, is installed at lab-D in the Kamioka Underground Laboratory (2700 m.w.e.) in the Institute of Cosmic Ray Research of the University of Tokyo. Fig. 1 shows CANDLES-III system comprising 96 CaF 2 modules, a LS, a water buffer, 62 photomultiplier tubes (PMTs), and external shields.
The CaF 2 module consisted of a 10 cm cube (3.18 kg) undoped CaF 2 crystal, a 5 mm-thick layer of the WLS phase, and a 3 mm-thick acrylic container. In the WLS phase, the emission light of CaF 2 with a peak in the ultraviolet (UV) region was immediately converted to visible light, where the quantum efficiency of the PMTs was sufficient (maximum; ∼ 400 nm), and the materials in the optical path had good transparencies [29]. The structure of the WLS phase surrounding the CaF 2 crystals was essential because the LS was not transparent to The LS vessel was filled with the LS consisted of 80% mineral oil, 20% pseudo-cumene, and WLSs (PPO; 1.0 g/ and Bis-MSB; 0.1 g/ ). The LS was used as an active shield, as will be described later. Prior to the commissioning run, we performed the LS purification process consisting of liquid-liquid extraction and nitrogen purge.
The scintillation lights from the CaF 2 modules and the LS were viewed by 62 PMTs (20-inch × 14, 13-inch × 36, and 10-inch × 12). Fig.1 illustrates the configuration of three types of PMTs. Twenty-inch PMTs were installed on the top and bottom, and 13-inch and 10-inch PMTs were installed on the side in 4 rows and 12 columns. The 10-inch PMTs were used on the top row and the 13-inch PMTs were used on the other rows. A light collection system was installed between the PMTs and the LS vessel to improve the scintillation light collection [30]. The LS vessel and the PMTs were installed in a stainless-steel water tank of 3 m in diameter and 4 m in height. We employed cancellation coils outside the external shield to reduce the Earth's magnetic field, which affects the charge collection efficiency of large-diameter PMTs. The coils were covered with a flame-retardant material. We also adjusted the coil current to reduce the Earth's magnetic field of ∼ 400 mG to below 60 mG in average at every PMT position based on a magnetic field simulation. A high-voltage power supply for the PMTs and the current supplies for the cancellation coils with the interlock were installed in the DAQ hut.
The whole detector was covered with external passive shields to reduce the high energy γ-rays produced by the environmental neutron capture reactions ((n,γ) reaction) in the detector materials and rocks [35].
We employed the Pb shield (gray bricks, Fig. 1) outside of the water tank for the γ-ray produced by (n,γ) reaction on rocks. The typical Pb thickness was 10 cm to reduce γ-rays with several MeVs by 1/100. Considering a more effective reduction of the external background, Pb thickness was 12 cm in the center of the detector side, where the passive water shield was relatively thin.
The stainless-steel water tank was another source of high energy γ-ray. Accordingly, Si rubber sheets containing 40 wt.% of B 4 C (B sheet, purple sheets shown in Fig. 1) were attached both inside and outside of the tank to prevent (n,γ) reaction inside the Pb shield.
The B sheet thickness of 4 mm was enough to reduce the thermal neutrons by approximately 1/1000. A detector cooling system was installed to increase the scintillation light output emitted by CaF 2 . The light output from the undoped CaF 2 increased by 2% with the temperature decrease of 1 • C around room temperature [36]. The lab-D temperature was cooled down to a temperature slightly higher than the freezing point of water used as the passive shield (2 • C for setting temperature). Consequently, the center of the detector was cooled down to 4.5 • C and stabilized within ±0.05 • C. The light output of CaF 2 was increased by approximately 30% compared in the case of operating at room temperature. The stabilized temperature led to no detectable change of gain caused by the temperature [33].
For a long-term stable measurement, a monitoring system for the laboratory environment (e.g., temperature, humidity, atmospheric pressure in the lab-D, water temperatures inside the water tank, temperature and humidity in the DAQ hut, etc.) was installed, and the data were continuously recorded. The liquid levels of water and LS were constantly monitored.
We also installed leak detectors for water and LS and connected their alarm signals to the interlock of the power supplies for a safe operation of the detector containing a flammable substance (i.e., LS).
The DAQ system consisted of hardware including Flash ADCs (FADCs), and a trigger logic on the µTCA system, and a network DAQ software. The signal waveform for each PMT was recorded for approximately 9 µsec by an 8-bit 500 MHz FADC [37]. The waveform was recorded in a 2 nsec time-bin for the first 768 nsec and in a 64 nsec time-bin, which was the sum of 32 samples of 2 nsec time-bin data, for 8.2 µsec with a time stamp. It was read through a SpaceWire datalink [38] on the µTCA backplane. The pulse shape digitized from the analog waveform was used in an offline analysis of the background reduction through pulse shape discrimination.
We developed a dual-gate trigger system to efficiently collect the long decay-time signals by rejecting the LS signals with short decay-times [39]. The signals were integrated into two different time windows ("dual gate") in the FPGA, and triggered only when both integrated values exceed each threshold.
A random trigger event using a pulser was acquired at 3 Hz. A single photoelectron event, which accidentally entered in a random trigger event, was collected. The chargephotoelectron conversion coefficient was calculated for each PMT every 24 hours by taking the average value of the FADC counts of single photoelectron events.
The energy threshold was set to tag the α decay of 212 Bi → 208 Tl. This α-ray of 6.05 MeV caused a scintillation that was of the same amount as the β-ray of 1.63 MeV due to the In the analysis of the CANDLES-III experiment, pulse shape discrimination (PSD) parameters were used to discriminate the following β-rays and γ-rays events that deposited energy only in the CaF 2 crystals (β-events); events involving LS emission (β+LS-events) to realize a 4π active shield; and α-ray events in CaF 2 (α-events) for the background rejection analysis.
The LS acted as an active shield for the immersed CaF 2 modules to reduce the background events accompanied by the γ-rays. The active shield was achieved by observing the pulse shapes. The decay-time of CaF 2 scintillation was 1 µsec, whereas that of the LS was typically a few tens of nanoseconds. The events from the 0νββ decay led to an energy deposit only in CaF 2 , while the background events accompanied by the γ-rays can yield energy deposits in the LS as well as in CaF 2 (β+LS-events). The pulse shape of the β+LS-events had a large prompt component, whereas that of the 0νββ candidate signals did not, as shown in The other major backgrounds in CANDLES-III were the 208 Tl decay and the 212 Bi→ 212 Po→ 208 Pb sequential decay within the CaF 2 crystal. Alpha-rays were involved in these background reduction because 212 Po emitted an α-ray, and the 208 Tl decays were proceeded through the α-ray by the 212 Bi decay, as described detail in Section IV A. Thus, identifying α-events is important for the background reduction. CaF 2 can discriminate between α-and β-events based on the characteristics of the prompt part of the signal pulse shape [30]. the 215 Po decay accompanied almost no γ-rays. The pure α-event reference pulse shape can be obtained.

PSD parameters
Two types of PSD analysis were performed using each signal pulse shape within 500 nsec from the starting time of the pulse shape, where the reference pulse shapes were particularly different among the α-, β-, and β+LS-events. The first analysis aimed to remove the β+LSevents. Meanwhile, the second analysis used a shape indicator (SI) [42] to discriminate between the α-and β-events in CaF 2 .
We removed the β+LS-event by performing a chi-square test of each event pulse shape.
The 500 nsec to 4000 nsec interval from the starting time of pulse shape was fitted using the reference pulse shape of a β-event (i.e., normalizing the reference pulse shape to the pulse height of each event). The chi-square of each event pulse shape to the reference pulse shape was calculated in the 2 nsec time-bin region up to 500 nsec. In obtaining the chi-square, an error was given by the number of the photoelectrons converted from the pulse height. The chi-square calculated using only the reference pulse shape of the β-events was presented as PSD β , while that calculated using both the reference pulse shapes of the β-and LS-events was denoted by PSD β+LS . At this time, the pulse height of the reference pulse shape of the LS-events was also fitted such that the PSD β+LS was minimized to evaluate the energy deposit in the LS. The β-events peaked at 1 in the PSD β distribution, and the β+LS-events were distributed at large values, and vice versa, taking PSD β+LS . Fig. 3(b) shows the discrimination ability between the β-and β+LS-events for each energy deposit in the LS at around 2.6 MeV, where the γ-rays from the 208 Tl decay were observed. When the energy deposit of the LS was 140 keV (approximately 5% of the total observed energy), the β+LS-events can be discriminated with a separation level of more than 3 σ, where σ is defined as σ 2 β + σ 2 β+LS . We adopted the SI for the PSD analysis to discriminate between α-and β-events in CaF 2 .
The SI obtained by weighting to emphasize the difference had a better discrimination ability.
The α-events can be discriminated from the β-events at the 4 σ level in the 2.6 MeV region, which corresponds with the energy of 7.7 MeV for the α-ray (Fig. 3 of Ref. [30]). The position was determined by the following formula using the light yield centroid method: Here, N pe (i) is the number of photoelectrons observed in each PMT, and − −− → PMT(i) depicts the position coordinates of each PMT. Fig. 4 shows a two-dimensional plot of the reconstructed position for the β-events caused by the γ-rays from the 40 K decays mostly contained in the PMTs. Each cluster corresponded to a crystal. The hit-crystal was unambiguously determined. Subsequently Gaussian fitting was performed for each crystal on three axes.
Its mean and sigma values were then evaluated. Consequently, the peak-to-peak distance between the crystals was found to be 7-8 sigma. The mean and sigma values obtained here were used in the analysis for the hit-crystal determination.

C. Energy reconstruction and energy calibration
The amount of light yield for each CaF 2 module was slightly different from each other, and the light collection efficiency differed depending on the position. The hit-crystal was determined by the reconstructed position, and then the energy for each event was determined based on the number of photoelectrons using the following formula: Here, C relative is a photoelectron-energy conversion coefficient determined for each CaF 2 module, and C f ine is a fine correction coefficient for the energy scale linearity in the high energy region determined for each layer. N m and N l represent the module and layer numbers, respectively.
We performed a relative energy calibration for each CaF 2 module with 1.836 MeV γ-ray of an 88 Y source to determine C relative (N m ). Coefficient C f ine was estimated for the whole data period with the background events of the 208 Tl γ-ray (2.615 MeV). The energy scale and the resolution near the Q ββ -value were evaluated using 3 to 9 MeV γ-rays emitted by the neutron captures on the Si, Fe, and Ni nuclei using a 252 Cf neutron source.
A calibration run was performed with the 88 Y source inserted into the LS vessel and placed between the CaF 2 modules. The data were collected at 18 locations in the detector to sufficiently irradiate all the 96 modules with γ-rays. Fig. 5 plots the average number of photoelectrons for each crystal at 1.836 MeV γ-ray. Accordingly, C relative was calculated to correct this variation.
The energy scale was then corrected using the background peak caused by 2.615 MeV γ-rays from 208 Tl decays. Despite the relative correction between the CaF 2 modules, a few % of the energy scale dependence existed on the Z direction of the detector. The cause of the layer dependence was unknown, but it was considered herein to be the asymmetry in the Z direction of the detector (PMT sizes, etc.). After this fine correction, the energy scale uniformity of all the crystals was confirmed using 1.461 MeV γ-rays of 40 K in the physics run data.
Finally, the calibration was performed in the energy region above 3 MeV using the γ-rays emitted by the neutron capture reaction of 28 Si and 58 Ni. This calibration was performed once per whole data taking term. Polyethylene bricks mixed with Si or Ni powder were made and assembled inside the Pb shield on top of the water tank. A 252 Cf source was placed in the center of the bricks to generate neutron capture γ-rays. The calibration results showed that the systematic error of the energy scale at the Q-value was less than 0.3%. Furthermore, the energy resolution at the Q ββ -value was σ = 2.4%. The details of the system and the analysis results were discussed in Ref. [43].
After all the calibrations, the energy scale stability was confirmed every 24 hours using the 208 Tl peak. Its stability was found to be better than 0.3% for the live-time.

A. Background candidates
The backgrounds around the Q ββ -value were identified by event information, such as energy, position (i.e., hit-crystal), timing, and signal pulse shape. The background origins were limited to the following three sources since the Q ββ -value was sufficiently high.

(n,γ) reaction
The environmental neutron produced many γ-rays, whose energies exceeded the Q ββvalue of 48 Ca. Many events above the Q ββ -value were observed. Prominent peaks were particularly observed around 7 -8 MeV in the initial run of CANDLES-III before the Pb shield construction. The background origin was identified to be the high energy γ-rays produced by the neutron capture in the surrounding materials. A rock containing Si and Fe isotopes was largely abundant. A high energy γ-ray was occasionally absorbed by a single CaF 2 crystal because of its large size (10 cm cube). The environmental neutrons were induced by an (α,n) interaction in the surrounding rocks. The α-rays were produced by the decays of the progenies of the 238 U and 232 Th contents in the rocks. The neutron-induced background was reduced by installing the Pb shield outside of the water tank, as described in Section II.
The high energy γ-ray events were almost rejected by the PSD β analysis. The remaining events caused by the high energy γ-rays were estimated by the experimental data obtained by irradiating an artificial neutron source. The details of the (n,γ) background estimation were described in Ref. [35]. The background rate by the neutron captured in the surrounding rocks was estimated as 0.9±0.6 events for the live-time. The 208 Tl decay in the CaF 2 crystal was another background candidate for the 0νββ decay search, because the Q-value (5.001 MeV) was above the Q ββ -value of 48 Ca. 208 Tl did not directly decay to the ground state, but to the excited states of 208 Pb, thereby always emitting 2.615 MeV γ-rays (Fig. 6). Most of the events induced by the 208 Tl decay were removed by the PSD β analysis because the γ-ray of 2.615 MeV caused multiple scattering in both CaF 2 and the LS. However, it became a background when the β-ray and γ-ray (2.615 MeV) from 208 Tl decay were fully absorbed in the same CaF 2 crystal. Such event can be effectively identified by tagging the preceding α decay of 212 Bi → 208 Tl. The α-ray of 212 Bi was followed by the β decay of 208 Tl (T 1/2 = 3.05 min). The α-ray with 6.05 MeV energy was observed at 1.63 MeV in the energy scale determined by the energy calibration (Section III C) because of the CaF 2 scintillation quenching. When the β-ray and γ-ray made the background for the 0νββ decay search.

B. Background rejection and 0νββ decay analysis
The criteria for selecting the candidate events for the 0νββ decay are given as follows: (1) CaF 2 signal without energy deposit in the LS; (2) not a sequential signal caused by the 212 BiPo event; (3) not a candidate of the 208 Tl decay; and (4) reconstructed event at the CaF 2 crystal position.
As mentioned in section III A, criterion (1) was applied using the PSD analysis to remove β+LS events.
Criterion (2) was applied by analyzing the pulse shape [30]. The 212 BiPo event was easily recognized as a sequential event when the time-lag was longer than 20 nsec since the typical rise-time of the CaF 2 signal was 20 nsec. The events with time-lags shorter than 20 nsec were rejected using SI to discriminate between the β-and α-events. This was because a large portion of the pulse shape was caused by the 212 Po α-events. The total rejection efficiency of the 212 BiPo events was more than 99%.
Criterion (3) was applied by a time correlation analysis between the 212 Bi α decay and 208 Tl β decay. The 212 Bi α-ray was identified by the SI and its energy (1.63 MeV). The timing and the hit-crystal of the α-events were recorded. The event observed in the identical crystal and within 18 minutes after the α-event was tagged as the 212 Bi→ 208 Tl→ 208 Pb event [34].
The rejection efficiency of the 208 Tl decays by this α-tagging analysis was 89%.
The event, in which the 2.615 MeV γ-ray was absorbed in the other CaF 2 crystal as a 208 Tl β-ray, can be rejected through criterion (4). This multi-crystal event might be reconstructed in the position of the LS area. To apply criterion (4), we selected the events within the ±2 σ region from the center of each CaF 2 crystal, as presented in Section III B.  (1) and (2), which were required for rejecting the β+LS-events. The event rates of the blue lines were less than those of the black lines by more than two orders of magnitude  The red-colored spectrum represents the sum of the simulated background spectra, comprising 212 BiPo events, 208 Tl decays, γ-rays by neutron capture reactions, and 2νββ decays with the half-life of T 2νββ 1/2 = 5.3 × 10 19 year [4]. We considered the following parameters for the background rate estimation: (1) concentration of the radioactive impurities of the 232 Th series in each CaF 2 crystal determined by the time-correlation analysis of the decays 220 Rn → 216 Po (T 1/2 = 145 msec) → 212 Pb; (2) detection efficiency of the event selection criteria; and (3) detector energy resolution [43]. We obtained the estimated background rate of 27.1 counts/130.4 days/(93 CaF 2 crystals) within the 4-5 MeV region (Fig. 8). The estimated background rate was consistent with the measured rate of 24 events. This fact strongly supported our hypothesis that the considered three background candidates were the major candidates in the CANDLES-III detector.
We can set a lower limit and an experimental sensitivity on the half-life of the 0νββ decay by using the expected background rate of 1.0 counts in the 0νββ window of 4.17 -4.48 MeV for the 21 CaF 2 crystals. The half-life limit with 90% C.L. obtained by selecting 21 CaF 2 crystals was 5.6 × 10 22 year. This limit was comparable to the result obtained for more than 2 years using our previous detector, ELEGANT VI [22]. We also obtained an experimental sensitivity of 2.7 × 10 22 year (90% C.L.) because the observed event rate was lower than expected. The obtained half-life limit derived an upper limit on the effective Majorana neutrino mass m ν ≤ 2.9 -16 eV (90% C.L.) using the nuclear matrix elements given in Ref. [44] and the reference therein.
The present limits on the half-life and the effective Majorana mass were obtained using natural Ca instead of enriched 48 Ca crystals. The limit on m ν did not reach sufficient sensitivity compared with the experiments using other enriched ββ isotopes, such as 76 Ge and 136 Xe, because of the lack of 48 Ca isotope amount overcome by realizing 48 Ca enrichment.
The results obtained herein demonstrated that 48 Ca is a promising isotope that is sufficiently competitive in other sensitive experiments.

V. CONCLUSION
This study evaluated the feasibility of low background measurements with the CANDLES-III detector using the live-time of 130.4 day data. We confirmed that the structure of the 4π active shield and the passive shields can effectively reduce the external backgrounds. The backgrounds caused by the radioactive impurities of the 232 Th series contained in the CaF 2 crystals can be effectively removed by analyzing the signal pulse shape and tagging the time correlated α decay. After the background rejection analyses, no events in the Q ββ -value region were found when we selected high purity 21 CaF 2 crystals. This gave a lower limit on the half-life of the 0νββ decay of 48 Ca as T 0νββ 1/2 > 5.6 × 10 22 yr (90% C.L.), which was almost comparable with the limit obtained by ELEGANT VI over two years of long-term data [22]. We also presented the experimental sensitivity of 2.7 × 10 22 yr (90% C.L.) by the predicted background rate. The observed energy spectrum around the Q ββ -value region was well reproduced by the simulated one, which estimated by the three background candidates considered. In other words, there were likely no additional high-impact backgrounds. The present result is useful for the development of the next detector and shows that 48 Ca is a promising target nucleus for the 0νββ decay search using CaF 2 crystals.