Physics potential of searching for $0\nu\beta\beta$ decays in JUNO

In the past few decades, numerous searches have been made for the neutrinoless double-beta decay (0$\nu\beta\beta$) process, aiming to establish whether neutrinos are their own antiparticles (Majorana neutrinos), but no 0$\nu\beta\beta$ decay signal has yet been observed. A number of new experiments are proposed but they ultimately suffer from a common problem: the sensitivity may not increase indefinitely with the target mass. We have performed a detailed analysis of the physics potential by using the Jiangmen Underground Neutrino Observatory (JUNO) to improve the sensitivity to 0$\nu\beta\beta$ up to a few meV, a major step forward with respect to the experiments currently being planned. JUNO is a 20 kton low-background liquid scintillator (LS) detector with 3\%/$\sqrt{E \text{(MeV)}}$ energy resolution, now under construction. It is feasible to build a balloon filled with enriched xenon gas (with $^{136}$Xe up to 80\%) dissolved in LS, inserted into the central region of the JUNO LS. The energy resolution is $\sim$1.9\% at the $Q$-value of $^{136}$Xe 0$\nu\beta\beta$ decay. Ultra-low background is the key for 0$\nu\beta\beta$ decay searches. Detailed studies of background rates from intrinsic 2$\nu\beta\beta$ and $^{8}$B solar neutrinos, natural radioactivity, and cosmogenic radionuclides (including light isotopes and $^{137}$Xe) were performed and several muon veto schemes were developed. We find that JUNO has the potential to reach a sensitivity (at 90\% C. L.) to $T^{0\nu\beta\beta}_{1/2}$ of $1.8\times10^{28}$ yr ($5.6\times10^{27}$ yr) with $\sim$50 tons (5 tons) of fiducial $^{136}$Xe and 5 years exposure, while in the 50-ton case the corresponding sensitivity to the effective neutrino mass, $m_{\beta\beta}$, could reach (5--12) meV, covering completely the allowed region of inverted neutrino mass ordering.


Introduction
Currently, the neutrinoless double-beta decay (0νββ) process is the only experimentally feasible and most sensitive way to probe if massive neutrinos are their own antiparticles, namely, Majorana particles. Violation of lepton number is a direct consequence of the 0νββ process, in which a nucleus decays by emitting two electrons and nothing else, N (A, Z) → N (A, Z +2)+2e − . Furthermore, searching for 0νββ decay can shed light on the absolute scale of neutrino masses.
Under the standard three neutrino framework, the effective neutrino mass in 0νββ decay is defined as m ββ ≡ | i (m i U 2 ei )|, where U ei (for i = 1, 2, 3) denote the matrix elements in the first row of lepton flavor mixing matrix U , and m i (for i = 1, 2, 3) are neutrino masses. For Majorana neutrinos, m ββ is sensitive to the neutrino masses, neutrino mixing angles and Majorana CP phases. Using the standard parametrization of U , m ββ = |m 1 c 2 12 c 2 13 e 2iφ 1 + m 2 s 2 12 c 2 13 e 2iφ 2 + m 3 s 2 13 | [1], where c 12 = cosθ 12 , c 13 = cos θ 13 , s 13 = sin θ 13 , s 12 = sin θ 12 , {θ 12 , θ 13 } are neutrino mixing angles, and {φ 1 , φ 2 } are Majorana CP phases. In this definition of m ββ , it has been assumed that the 0νββ process is dominated only by the exchange of light Majorana neutrinos. Sterile neutrinos or other exotic physics are not considered. If neutrinos have an inverted mass ordering, m ββ will be greater than ∼0.015 eV, based on current and projected knowledge of the neutrino mixing parameters [2]. For the normal neutrino mass ordering case, no lower bound exists and m ββ could vanish due to the cancellation among the m i U 2 ei terms that are modulated by the Majorana phases. Enormous experimental efforts have been made to search for 0νββ in the last few decades, using various nuclear isotopes, such as 136 Xe, 76 Ge, 130 Te, etc, as discussed in recent reviews (see [3] and references therein). None of them observed a 0νββ decay signal. It is desirable for the next generation 0νββ experiments to have a sensitivity of m ββ ∼10 meV. With such sensitivity, if the neutrino mass ordering is determined to be inverted by future reactor and accelerator experiments, either a positive (observation of 0νββ decay) or a negative (no observation) result would be able to probe the Majorana nature or Dirac nature of neutrinos, respectively.
The half-life of 0νββ, T 0ν 1/2 , is related to the effective Majorana neutrino mass, m ββ , by a phase space factor G 0ν and a nuclear matrix element (NME) M 0ν : (1) where both G 0ν and M 0ν can be calculated theoretically. However, the NME has relatively large uncertainties from different nuclear models, see Ref. [4] and references therein.
Two-neutrino double-beta decay (2νββ) is allowed by the Standard Model and has been observed in many nuclei. 0νββ can be distinguished from 2νββ by measuring the sum energy of the two electrons and looking for a mono-energetic peak at the Q-value. The region around the Q-value is referred to as the 0νββ window, namely the region of interest (ROI). Different experiments might choose different ROIs, e.g, ±1σ, ±2σ, ± 1 2 FWHM or even an asymmetric window around the Q-value, due to different background levels and energy resolutions. Excellent energy resolution and ultra-low background in the ROI are the keys to searching for 0νββ. The Jiangmen Underground Neutrino Observatory (JUNO) is a multi-purpose experiment that primarily aims to determine the neutrino mass ordering and to measure precisely the neutrino mixing parameters [2,5]. Such precision measurement could reduce the range of T 0ν 1/2 predictions by a factor of 2 [6]. The way to distinguish the neutrino mass ordering at JUNO is via exploring the effect of interference between atmospheric-and solar-∆m 2 driven oscillations [7][8][9]. The baseline design of the JUNO detector is a 20 kton low-background liquid scintillator (LS) with an unprecedented energy resolution (σ/E) of 3%/ E(MeV). At the Q-value of 136 Xe 0νββ decay (Q 0νββ =2457.8 keV), or 130 Te (Q 0νββ =2530 keV), the energy resolution is expected to be ∼1.9%, which is suitable for a 0νββ search. In addition, online purification is another advantage of LS detectors, and the liquid can reach the adequate level for 0νββ searches. KamLAND-Zen [10] and SNO+ [11] are two examples, using 136 Xe and 130 Te isotopes, respectively. However, their detector sizes are limited so that their sensitivity to m ββ can only reach a few tens of meV. A very large LS detector can perform a better measurement [12].
In this paper, we explore the physics potential of searching for 0νββ decays of 136 Xe with the JUNO detector, aiming for a few meV sensitivity on m ββ , by dissolving enriched pure xenon gas into the liquid scintillator. The Xe-loaded LS target could be separated from the normal LS by deploying a highly transparent and clean balloon. The clean normal LS can provide sufficient passive shielding against external radioactivity, and act as an active zone to track the muons and veto the cosmogenic backgrounds.

JUNO detector
The JUNO site has an overburden of ∼ 700 m rock. The central detector (CD) is an acrylic sphere of 35.4 m in diameter, holding the 20 kton LS, supported by a spherically latticed shell made of stainless steel (SS) with a diameter of 40.1 m. About ∼18000 20-inch PMTs are mounted on the SS latticed shell, looking inward towards the LS target. In addition, up to ∼36000 3-inch PMTs will be installed in the gaps between the 20-inch PMTs, to form a complementary calorimetry system and improve the muon measurement. Outside the SS latticed shell, an ultra-pure water pool of 43.5 m diameter and 44 m depth is equipped with ∼2000 20-inch PMTs, providing an active cosmic muon veto as a water Cerenkov detector and sufficient passive shielding from the environmental radioactivity. On top of the water pool, the OPERA [13] target trackers are re-used as a complementary Top Tracker system, providing precise track measurement of cosmic muons.
The JUNO LS uses linear alkyl-benzene (LAB) as the solvent, 2,5-diphenyloxazole (PPO) as the primary fluor, and 1,4-bis [2-methylstyryl]benzene (bis-MSB) as the wavelength shifter. The current baseline recipe is adopted from the Daya Bay experiment [14,15] but without gadolinium doping. As discussed in [2], the baseline LS purity requirement for reactor antineutrino studies is less than 10 −15 g/g for 238 U and 232 Th, 10 −16 g/g for 40 K and 1.4×10 −22 g/g for 210 Pb. This is sufficient for the determination of neutrino mass ordering. A sophisticated on-line purification system can be set up, and eventually two orders of magnitude better purity is expected to be achievable. Such optimal purity (10 −17 g/g for 238 U and 232 Th, 10 −18 g/g for 40 K and 10 −24 g/g for 210 Pb) is adequate for 0νββ searches. The backgrounds caused by the internal impurities are discussed in Section 3.3.
The target element for 0νββ searches in this study, as an example, is chosen to be 136 Xe for its high purity, high Q-value, and high solubility in LS. Of course other elements are not excluded at present. 130 Te is another possible element and has a natural abundance of 34.1%. It is technically challenging to purify tellurium and reach >5% tellurium loading in LAB-based scintillator. As an example, in the Te-loaded phase of the SNO+ experiment, with 0.3% Te-loading, the projected 238 U and 232 Th concentration would be two orders of magnitude worse than the pure LAB-PPO scintillator [11]. The stability, transparency and light yield would also decrease with high tellurium loading. Unlike xenon, cosmogenic activation of the tellurium nuclei could produce a large number of long-lived radioactive isotopes. To suppress such background, the exposure time of tellurium on the surface should be controlled. A purification process and additional long cooling time underground is necessary [16]. At the depth of JUNO, the cosmogenic background could be serious for 0νββ searches. In this study, we choose 136 Xe as an example to evaluate the physics potential of the 0νββ search at JUNO. The possibility of using 130 Te will be evaluated in future.
A transparent and strong balloon can be used to separate the Xe-LS from the normal LS. Xenon gas is found to be soluble into liquid scintillator more than 3% by weight, but the light yield could be reduced depending on the xenon concentration [18]. We expect that such an effect can be compensated by tuning the concentration of the fluors. Thus we assumed 5% by weight of the enriched xenon gas ( enr Xe) that consists of 80% 136 Xe. We chose the ROI as the ± 1 2 FWHM region around the Q ββ value. The parameters that were chosen in our calculation are compared with the KamLAND-Zen detector in Table 1. The efficiency of 0νββ events in the ROI, defined as ε 0νββ , was calculated according to the energy resolution at Q ββ and the selected ROI window.

Backgrounds
The natural radioactivity in the liquid scintillator and the long-lived radioactive isotopes produced by muon spallation are the dominant background for the 0νββ search. The spallation neutrons produced by cosmic muons can induce the β-decay isotope 137 Xe, with a halflife of 3.82 minutes, via the 137 Xe(n, γ) reaction. The Q-value for 137 Xe decay is 4173±7 keV [19], so the β spectrum overlaps the Q-value of 136 Xe 0νββ decay. The background rates are evaluated below.

Intrinsic 2νββ background
With finite energy resolution, 2νββ events leaking into the 0νββ ROI are the intrinsic background. Such background decreases dramatically as energy resolution improves. Hereafter, the background index, defined as the background rate per unit 136 Xe mass per ROI, was introduced to quantify the background. We estimated the intrinsic 2νββ background rate to be 0.2/ROI/(ton 136 Xe)/yr by convoluting the theoretical 2νββ energy spectrum [20] with the detector energy resolution curve.

Solar-ν background
The ν-e scattering signal from 8 B solar neutrinos has a continuous spectrum up to >10 MeV, thus it can also contribute to the ROI background. Its signal rate was estimated to be 4.5/kton/day [2]. Using the simulated energy spectrum of the 8 B ν-e scattering signal, also described in [2], we estimated the background index to be 28/ROI/(kton Xe-LS)/yr, equivalent to 0.7/ROI/(ton 136 Xe)/yr under the assumption of 5% enr Xe.
If natural xenon gas is used instead of 136 Xe-enriched xenon gas, the background index from the solar neutrinos would be 10 times larger, since the 136 Xe abundance in natural xenon is only ∼8%.

Internal 238 U and 232 Th contamination
The projected radioactivities of the JUNO detector components such as liquid scintillator, PMT glass, acrylic and supporting structures were discussed in [2,21]. The external radioactivities could be eliminated by a sufficient fiducial volume cut, e.g, 1 m inward from the LS edge, thus only the internal LS radio-impurities need to be considered. As discussed in Section 2, an optimal radio-purity level ∼ 10 −17 g/g for U and Th is reachable. The following studies are based on this optimal radio-purity assumption.
The β+γ emissions from 214 Bi ( 238 U chain, Q = 3.272 MeV) could be a serious background for 0νββ searches, because there is a 2.448 MeV γ line, which can leak into the ROI. From the simulated energy spectra of events from the 238 U chain, the background index was calculated to be 8.3/ROI/(ton 136 Xe)/yr. The 214 Bi-214 Po β-α cascade decay (τ = 237 µs) is very effective at rejecting 214 Bi events. The α energy from 214 Po decay is 7.686 MeV, and its quenched response is well above the detector threshold, resulting in a high efficiency of tagging 214 Bi events in the ROI. We evaluated the background rejection with Monte Carlo samples by requiring the time and distance between the prompt β and delayed α decay 053001-3 events to be less than 2.0 ms and 2.0 m, respectively. The residual background is due to the Bi-Po cascade decays that have a decay time longer than 2.0 ms, or occurred within one readout window (nominally 1 µs for JUNO) and their summed energy falls into the ROI. We found ∼99.97% of the events in the ROI from 238 U chain were rejected, resulting in <0.003/ROI/(ton 136 Xe)/yr residual ROI background.
The fast 212 Bi-212 Po β-α cascade decay from the 232 Th chain (τ = 431 ns) leads to 90% of the two signals occurring in the 1µs nominal readout window. Our GEANT4 MC indicated that the summation of the visible energies of 212 Bi β + γ (Q = 2.252 MeV) and 212 Po α (Q = 8.954 MeV) had a fraction of 6.2% inside the ROI window, while neither the individual β nor α decays could contribute to the ROI. Assuming 10 −17 g/g 232 Th concentration, we estimated the background index from the summation events to be 1.25/ROI/(ton Xe-LS)/yr. Thus, special care should be taken to distinguish and reject these two decays. JUNO will adopt 1 GHz Flash ADC (FADC) to record the full waveforms from all the PMTs inside the readout window, allowing a pulse shape discrimination (PSD) approach to distinguish two decays which are close in time. The LAB-based liquid scintillator was demonstrated to have good capability of e − /α discrimination [22]. A full MC simulation including scintillation processes and PMT timing resolution was performed for the decays. We developed a PSD method by using the width and the tail fraction of the measured scintillation time profile, in which the time-of-light of photons were corrected. The discrimination efficiency was found to reach >97.5%, resulting in a residual ROI background of 0.03/ROI/(ton 136 Xe)/yr. Our GEANT4 MC indicated negligible contribution from internal 208 Tl decays (Q = 4.999 MeV) to the ROI, because the visible energy inside the LS is the summation of the β and γ energies, which has a minimum energy of 3.2 MeV. This is different from the surface contamination, where βs deposit their energy in the vessel material without scintillation, but the 2.615 MeV γs could leak into the ROI.

External radioactivity
As discussed in Section 2, a highly transparent balloon can be used to contain the Xe-LS. Although the balloon material could be very radio-pure (e.g, ppt level), the possible dust contamination during installation and the radon contamination during LS purification could yield much higher 214 Bi levels on the surface of the balloon. A fiducial volume cut is effective against 214 Bi and 208 Tl decays from the balloon. We consider that a 1 m cut from the Xe-LS target edge would be sufficient.
Extreme care should be taken to prevent radon (mainly 222 Rn , τ = 5.52 day) from penetrating into the Xe-LS during the purification process. We put a requirement of 5×10 3 atoms/(kton Xe-LS)/yr external radon leakage rate. Taking into account the 99.97% rejection efficiency via 214 Bi-214 Po tagging, it would lead to a 0.2/ROI/(ton 136 Xe)/yr background rate.

Cosmogenic backgrounds
Energetic cosmic muons can cause spallation in organic liquid scintillator, and produce long-lived radioactive isotopes via the photon-nuclear or hadronic processes. The overburden for the JUNO detector is 748 m, and the muon flux at the JUNO site is about 0.003 Hz/m 2 , which is a factor of ∼2 more than the underground lab at Kamioka. The rate of muons passing through the JUNO LS volume is about 3.0 Hz, with a mean energy of 215 GeV. Table 2. Summary of the simulated muon-induced radioactive isotopes (mostly with Z 6) in the JUNO LS. Only the isotopes that can contribute to the 0νββ window are listed. 10 C, 6 He, 8  . The latter two isotopes are β-n emitters with branching ratios of 51% and 16%, respectively. Such β-n decays can be rejected by coincidence cuts and were removed in this The production of the radioactive isotopes in JUNO LS was evaluated by GEANT4 [24] simulation. A Monte Carlo (MC) muon data set of ∼342 days' worth of statistics was produced to study the cosmogenic backgrounds in the 0νββ search. The results are summarized in Table 2, including the raw production rates, the primary production processes, the fractions for different number of accompanied neutrons and the background indexes in the ROI. The production rates from the earlier analysis [2] using FLUKA [25] were also listed for comparison. Both GEANT4 and FLUKA indicate that 10 C, 6 He, 8 Li and 12 B are the dominant contributors. Other isotopes were found to have relatively small contributions in the ROI, thus they were combined in the last row of the table. Given their long half-lives and relatively high muon rate in the JUNO detector, it was challenging to reject those backgrounds. In Table 2, our GEANT4 MC predicted a similar 10 C production yield to FLUKA, whereas it gave a lower 6 He, 8 Li and 12 B production yield than FLUKA. This is probably due to different hadronic interaction models being used. In the following analysis we used the newly produced GEANT4 MC data with large statistics, showing that the residual cosmogenic backgrounds after muon veto is evaluated to be ∼10% of the total background. Thus the differences between FLUKA and GEANT4 were considered not to affect the main conclusion of this paper. To mimic a real data set, we assigned a time stamp for each primary muon and its daughters according to the average R µ =3 Hz muon rate, then the primary muons and their subsequent events were mixed and sorted.
Cosmogenic isotopes are mainly produced by energetic showering processes in the LS. Table 2 shows that ∼98% of 10 C, ∼60% of 6 He and ∼37% of 8 Li are accompanied by 1 neutrons, allowing us to develop a special veto strategy to reject those β-decays. Although the 12 B production has weak correlation with neutrons, it has a relatively short half-life and thus can be efficiently rejected by vetoing a longer time. The veto methods to reject the cosmogenic backgrounds and the results are discussed in following subsections.
The previous measurements [26] and simulations [27], as well as our simulation show that the distance from the isotope's production position to its parent muon track approximately follows an exponential profile. Thus, vetoing a cylindrical volume along the reconstructed muon track for sufficient time can significantly reduce the muon induced backgrounds.
As described in Section 2, the JUNO central detector will be equipped with a vast number of 3-inch PMTs, providing excellent track reconstruction for both minimum ionizing muons and showering muons. However, the track reconstruction of a showering muon is nontrivial. Our simulation indicated that a muon changes little in its direction after producing a shower. Thus the entry and exit points in the pattern of hit PMTs can give a good estimation of the muon track. In addition, we found that high multiplicity neutrons were produced near the high dE/dx region, and those neutrons' vertices could be used to further constrain the muon track and reconstruct the location of the muon shower.
The muon events were first categorized into two types: the normal muons (µ norm ) and the neutronassociated muons (µ n−assoc ). Their identification and corresponding veto criteria are described below: 1) µ norm identification: if the distance from the LS center to the muon track is within (R Xe +3) meters, where R Xe is the radius of Xe-LS volume. µ norm veto: any signal within a veto time window of 1.2 s and within a 3 m cylinder along the muon track was rejected.
2) µ n−assoc identification: among the µ norm samples, if a neutron-like signal occurs within 1 ms after the muon and within (R Xe + 2) meters from the detector center. The neutron-like signal is identified as an event in the n-capture energy window, (2.0, 2.4) MeV.
µ n−assoc veto: any signal within 2 meters from each associated neutron-like signal and within a veto time window of t veto n−µ was rejected. We evaluated the efficiency of the muon veto and the residual cosmogenic background for different target radii R Xe . For each assumed R Xe , the muons were first categorized according to the above criteria. By definition, the rates of µ norm and µ n−assoc depend on the Xe-LS target size R Xe . With the MC data set, the rates were parameterized as R norm µ = 9.38 × 10 −3 · (R Xe + 3) 2 Hz and R n−assoc µ = 3.58 × 10 −5 · (R Xe + 2) 3 Hz, respectively. Then we applied the above muon veto strategies to the mixed MC data set, and particularly tested different values of the veto window t veto n−µ . Finally the live time and the rate of residual background were calculated.

Long-lived light isotopes
Among the dominant isotope backgrounds, 10 C has the longest half-life τ ( 10 C) = 27.8 s, thus the veto window t veto n−µ should be sufficiently long to reject 10 C and 6 He effectively. We tested different t veto n−µ : 2τ ( 10 C), 4τ ( 10 C) and 6τ ( 10 C), as shown in Table 3.
Increasing t veto n−µ significantly reduced the 10 C and 6 He rates, with negligible loss of live-time due to the low rate of µ n−assoc . When using the µ norm veto plus 6τ ( 10 C) window for µ n−assoc veto, the reduction factors for 10 C and 6 He were 309 and 78, respectively. Although the MC indicated that the 12 B production had a weak correlation with the neutron production, it was also strongly suppressed after applying the above muon veto, due to a much shorter half-life. Table 3 showed that with a proper muon veto the cosmogenic backgrounds could be well controlled.
To estimate the veto efficiency, tracer events that were uniformly distributed in time and within the LS volume were mixed into the sorted MC data set. After applying the selections cuts, the efficiency was estimated as M s /M , where M was the total number of tracer events and M s was the number of tracer events that survived the veto. The efficiency was precisely calculated with large statistics of the tracer events. In Table 3, the efficiency varied a little when adding the µ n−assoc veto. In addition, we found the efficiency and the background index slightly changed for different Xe-LS target sizes R Xe . The last column in the table was used for sensitivity calculation.

137 Xe background
The neutrons that are produced by the cosmic muons can thermalize via collision with the nuclei in the LS, then finally get captured on a nuclide. 136 Xe can capture the thermal neutrons and produce radionuclide 137 Xe via the 136 Xe(n, γ) process, although the probability is small. 137 Xe atoms are produced in a capture state with the excited state energy of 4025.46±0.27 keV [28], then deexcite into the ground state promptly, primarily through γ emission. The ground state of 137 Xe then purely β − decays (τ = 5.51 min, Q = 4173 ± 7 keV), resulting in contamination of the ROI.
Similar to 10 C and 6 He, the 136 Xe(n, γ) 137 Xe cascade also provides a nice triple-coincidence signature of the muon, the neutron capture on 136 Xe and the subsequent 137 Xe decay, to identify and reject such muon-induced 137 Xe background. The neutron capture on 137 Xe is easy to identify due to a much higher energy than the natural radioactivity.
The 137 Xe production was estimated from the neutron capture process in the Xe-LS, as shown in Table 4. The expected neutron capture fractions on protons, 10 C, 136 Xe and 134 Xe in the KamLAND-Zen Xe-LS were reported as 0.994, 0.006, 9.5×10 −4 and 9.4×10 −5 , respectively [29]. In Section 2, we considered doping 5% by weight of enr Xe with 80% 136 Xe into the JUNO LS, thus the neutron capture fraction on 136 Xe is expected to be ∼ 1.7×10 −3 . Since KamLAND-Zen observed a ∼13% increase in the spallation neutron flux in the Xe-LS relative to the normal LS [10], thus a factor of 1.13 was taken into account when estimating the neutron rate in JUNO Xe-LS. In addition, our ROI region is a factor of 4 narrower than KamLAND-Zen due to better energy resolution, as shown in Table 1. Finally the background index from 137 Xe was calculated to be 2.3/ROI/(ton 136 Xe)/yr. Similar to the µ n−assoc veto, we can develop 137 Xeassociated muon (µ Xe−assoc ) veto criteria: • µ Xe−assoc identification: among the µ norm samples, if a n-136 Xe capture candidate occurs within 1 ms after a muon and within (R Xe +1) meters from the detector center. µ Xe−assoc veto: any signal within 1 meter of each associated n-136 Xe signature and within a veto time window of 5τ ( 137 Xe) was rejected.
A FLUKA simulation with the EXO-200 detector showed that thermal neutron capture was the absolute dominant production process for 137 Xe [30]. Our GEANT4 simulation with Xe-LS gave consistent results. After applying the above veto scheme to the GEANT4 MC data set, the residual 137 Xe β-decay was 0.07/ROI/(ton 136 Xe)/yr. Table 4. The estimated 137 Xe production rate via 136 Xe(n, γ) process in the assumed JUNO Xe-LS detector, which was scaled from the KamLAND-Zen detector.

Background summary
The ROI backgrounds are summarized in Table 5. We evaluated the total background index for various Xe-LS target sizes, and with little difference. Other backgrounds, such as (α, n) reactions, were also evaluated and found to be much less than the components in Table 5. The reduction of the cosmogenic backgrounds in each muon veto step is shown in Fig. 1.  Fig. 1. The reduction of the total background index for different muon veto schemes. The µnorm and µn−assoc refer to the normal muon veto and the neutron-associated muon veto methods, respectively, as described in Section 3.4.

Sensitivity
In an experiment that searches for rare decays, with certain projected backgrounds and no true signal, the sensitivity S(b) can be given by S(b) = ∞ n=0 P (n|b)U (n|b) [31], where P (n|b) is a Poisson p.d.f for the background fluctuation, and U (n|b) is a function yielding the upper limit at the desired C. L. for a given observation n and a mean projected background level b. In a real 0νββ experiment with non-negligible background, the sensitivity of the 0νββ half-life can be calculated as where N A = 6.022×10 23 is Avogadro's constant, M isotope is the molar mass of the 0νββ decay isotope, M is the fiducial target mass, t is the live time (the product M · t is usually referred to as the total exposure), ǫ is the detection efficiency, and η is the abundance of the 0νββ isotope. In the calculation, the efficiency ǫ included the energy cut efficiency of the 0νββ ROI in Table 1 and the efficiency of the muon veto in Table 3, and the combined efficiency is listed in Table 6. Depending on whether 90% or 95% C. L. is quoted, α is 1.64 or 1.96, respectively. versus the JUNO Xe-LS volume size and fiducial 136 Xe mass assuming 5 years livetime. The two curves represent the case w/o and w/ muon veto, respectively, and the latter is used to calculate the m ββ sensitivity. (b) The sensitivity of effective neutrino mass m ββ . The uncertainty band is due to different NME models (EDF [32], ISM [33], IBM-2 [34], Skyrme QRPA [35], QRPA [36]). The red dashed line corresponds to 15 meV.
Given that the JUNO detector has 20 kton LS, it has the capability for a large Xe-LS volume. The sensitivities of T 0νββ 1/2 and corresponding effective neutrino mass m ββ versus different Xe-LS volume size and fiducial 136 Xe mass are shown in Fig. 2. The uncertainty band of m ββ accounts for different NME models [32][33][34][35][36]. Assuming ∼50 tons of 136 Xe and 5 years live time, the projected T 0νββ 1/2 sensitivity (90% C.L) could reach 053001-7 ∼ 1.8 × 10 28 yr with a sophisticated muon veto scheme, which is a factor of 4 better than the no veto case. This allows probing of m ββ down to (5)(6)(7)(8)(9)(10)(11)(12) meV, completely below the region allowed by the inverted neutrino mass ordering scenario. We understand that the cost of producing 50 tons enriched xenon is currently practically unacceptable, however, to demonstrate that the sensitivity could really scale with target mass, we quote a large target mass.
The sensitivity for a more realistic scenario, with 5 tons of 136 Xe and 5 years live time, is superimposed in Fig. 3. The projected T 0νββ 1/2 sensitivity (90% C.L) would be ∼ 5.6 × 10 27 yr. We also would like to point out that, since M in Eq. (2) refers to the fiducial target mass, the fiducial cut efficiency was automatically included. As discussed in Section 3.3.2, a 1-m cut from the Xe-LS target edge was considered, thus the fiducial efficiency was 45% and 67% for 5 tons and 50 tons of 136 Xe, respectively. In future work, we expect to perform a 2D fit simultaneously to the energy spectra and stand-off distance, which is defined as the distance from the event position to the Xe-LS edge, in order to enlarge the fiducial volume and improve the sensitivity. Table 6. A comparison of current and future 0νββ experiments, including: the target 0νββ isotope and its abundance in the natural isotopes; the exposure of the 0νββ isotope; the detection efficiency for 0νββ; the background index (B.I.); the 90% C.L. limit or sensitivity of 0νββ decay half-life T 0ν 1/2 ; and the 90% C.L. limit or sensitivity of the effective neutrino mass m ββ . Unless specially noted, the background index, in events/(keV ton yr) unit, is defined as the background counts normalized by the ROI width and the 0νββ isotope exposure. L.). f The quoted limit is from the combination of KamLAND-Zen Phase-I and Phase-II. g The quoted B.I. is for the inner 3-ton xenon mass.

Summary and discussion
In this work, we explored the physics potential of a 0νββ search with the JUNO detector via dissolving 136 Xe-enriched xenon gas into LS. JUNO is designed to achieve 3%/ E(MeV) energy resolution for determining neutrino mass ordering, thus the energy resolution at 136 Xe Q ββ is expected to be 1.9%, resulting in relatively small intrinsic 2νββ background in the ROI. We performed detailed analyses of other ROI backgrounds from 8 B solar ν-e scattering events, LS natural radioactivity, muon induced radionuclides, and so on. An optimal purity (10 −17 g/g for 238 U and 232 Th) is assumed with proper LS on-line purification. A sophisticated muon veto scheme using the correlation between the spallation neutrons and the isotopes was developed to reject the long-lived cosmogenic backgrounds. Eventually a low background rate of ∼1.35/ROI/(ton 136 Xe)/yr was expected to be achievable. Assuming 5 tons of fiducial 136 Xe target mass and 5 years live time, we projected the 90% C.L sensitivity of T 0νββ 1/2 (or m ββ ) to be ∼ 5.6×10 27 yr (or 8-22 meV). In the case of 50 tons of fiducial 136 Xe, the 90% C.L sensitivity of m ββ can scale up to (5-12 meV), which is well below the region allowed by the scenario of inverted neutrino mass ordering.
Ultra-low background and excellent energy resolution are the two critical factors for the next generation 0νββ experiments. Table 6 summarizes the current experimental results or the projected sensitivities of CUORE [37,41], EXO-200 [38], GERDA [39], KamLAND-Zen [17], SNO+ [11], nEXO [40,43], as well as the potential Xe-LS detector at JUNO. Different experiments use different definitions when reporting the background rate, as well as choosing different 0νββ windows. In order to compare different experiments, we rewrite the sensitivity formula Eq. 2 as T 0νββ where B I = b (M ǫη · t/M isotope ) · ROI is the redefined background index, and M norm = M ǫη · t ROI · M isotope is the normalized detector exposure.
With the new definition, Fig. 3 shows a comparison of the experiments listed in Table 6. The dashed lines represent the contours of different sensitivities of T 0νββ 1/2 using Eq. (3). The data points roughly agree but do not exactly align with the calculated contours, because different experiments have different systematics and use different fitting or statistical analysis methods. Fig. 3 also indicates that the next generation 0νββ experiments should pursue both ultra-low background and very large detector exposure. , KamLAND-Zen [17], EXO-200 [38], nEXO [40] and the potential Xe-LS detector at JUNO. The dashed lines are the contours of different sensitivities.