Two-neutrino Double Beta Decay Research Articles

Theoretical Advances in Beta and Double-Beta Decay

Weak interaction processes continue to be hot topics in fundamental physics research. In this paper, we briefly review some recent advances in the theoretical study of beta and double-beta decays that include both the nuclear and atomic part of these processes. On the nuclear side, we present a statistical approach for the computation of the nuclear matrix elements (NME) for neutrinoless double-beta (0νββ). A range of NME values, the most probable value for NME, and the associated theoretical uncertainty are given. Correlations with other related observables are shown as well. On the atomic side, we first briefly review the methods used to obtain the electrons’ wave functions. Further, we use them for the computation of some relevant kinematic quantities such as Fermi functions, electron spectra, and angular correlation between the emitted electrons. Then, we present applications of these calculations to the experimental data analysis related to the search of the Lorentz invariance violation in two-neutrino double-beta (2νββ) decay and description of the decay rates and decay rate ratios for allowed and unique forbidden electron capture (EC) processes.

Induced Isotensor Interactions in Heavy-Ion Double-Charge-Exchange Reactions and the Role of Initial and Final State Interactions

The role of initial state (ISI) and final state (FSI) ion–ion interactions in heavy-ion double-charge-exchange (DCE) reactions A(Z,N)→A(Z±2,N∓2) are studied for double single-charge-exchange (DSCE) reactions given by sequential actions of the isovector nucleon–nucleon (NN) T-matrix. In momentum representation, the second-order DSCE reaction amplitude is shown to be given in factorized form by projectile and target nuclear matrix elements and a reaction kernel containing ISI and FSI. Expanding the intermediate propagator in a Taylor series with respect to auxiliary energy allows us to perform the summation in the leading-order term over intermediate nuclear states in closure approximation. The nuclear matrix element attains a form given by the products of two-body interactions directly exciting the n2p−2 and p2n−2 DCE transitions in the projectile and the target nucleus, respectively. A surprising result is that the intermediate propagation induces correlations between the transition vertices, showing that DSCE reactions are a two-nucleon process that resembles a system of interacting spin–isospin dipoles. Transformation of the DSCE NN T-matrix interactions from the reaction theoretical t-channel form to the s-channel operator structure required for spectroscopic purposes is elaborated in detail, showing that, in general, a rich spectrum of spin scalar, spin vector and higher-rank spin tensor multipole transitions will contribute to a DSCE reaction. Similarities (and differences) to two-neutrino double-beta decay (DBD) are discussed. ISI/FSI distortion and absorption effects are illustrated in black sphere approximation and in an illustrative application to data.

Large-scale shell-model study of two-neutrino double beta decay of 82Se, 94Zr, 108Cd, 124Sn, 128Te, 130Te, 136Xe, and 150Nd

Large-scale shell-model calculations have been performed for the study of two-neutrino double-beta (2νββ) decay in 82Se, 94Zr, 108Cd, 124Sn, 128Te, 130Te, 136Xe, and 150Nd. We have employed JUN45 interaction to calculate the nuclear matrix element (NME) for 2νββ decay in 82Se. In the case of 94Zr, the glekpn effective interaction is used. For 108Cd, we have used a realistic effective interaction derived through the G-matrix approach. In the case of 124Sn, 128,130Te and 136Xe, the sn100pn effective interaction is employed. For 150Nd, we have used KHHE effective interaction based on holes in a 208Pb core. We have extracted the half-lives of these nuclei for the 2νββ decay with the help of calculated NME. Our results are consistent with the available experimental half-lives. The variation of cumulative 2νββ NME with respect to the excitation energy of the intermediate 1+ states is also shown, and in all cases, it is ensured that their values are almost saturated. In the present work we have calculated more intermediate 1+ states as much as possible in comparison to results available in the literature.

Search for two-neutrino double-beta decay of 136Xe to the excited state of 136Ba with the complete EXO-200 dataset* *EXO-200 is supported by DOE and NSF in the United States, NSERC in Canada, SNF in Switzerland, IBS in Korea, DFG in Germany, and CAS in China. EXO-200 data analysis and simulation uses resources of the National Energy Research Scientific Computing Center

A new search for two-neutrino double-beta (2νββ) decay of 136Xe to the excited state of 136Ba is performed with the full EXO-200 dataset. A deep learning-based convolutional neural network is used to discriminate signal from background events. Signal detection efficiency is increased relative to previous searches by EXO-200 by more than a factor of two. With the addition of the Phase II dataset taken with an upgraded detector, the median 90% confidence level half-life sensitivity of 2νββ decay to the state of 136Ba is yr using a total 136Xe exposure of 234.1 kg yr. No statistically significant evidence for 2νββ decay to the state is observed, leading to a lower limit of yr at 90% confidence level, improved by 70% relative to the current world's best constraint.

Double Beta Decay Experiments: Recent Achievements and Future Prospects

The results of experiments on the search for and study of double beta decay processes obtained over the past 5 years (from 2018 to April 2023) are discussed. The results of the search for neutrinoless double beta decay are presented, in which a sensitivity of T1/2∼2×1024–2×1026 years (90% C.L.) has been achieved. The present conservative upper limit on effective Majorana neutrino mass ⟨mν⟩ was established from these experiments as 0.16 eV (90% C.L.). The results of experiments on recording and studying the processes of two-neutrino double beta decay in various nuclei (transitions to both the ground and excited states of daughter nuclei) are discussed too. The results of experiments on the search for majoron are also given. Possible progress in this field in the future is discussed.

Enhanced light signal for the suppression of pile-up events in Mo-based bolometers for the 0nu beta beta decay search.

Random coincidences of events could be one of the main sources of background in the search for neutrino-less double-beta decay of ^{100}Mo with macro-bolometers, due to their modest time resolution. Scintillating bolometers as those based on Li_2MoO_4 crystals and employed in the CROSS and CUPID experiments can eventually exploit the coincident fast signal detected in a light detector to reduce this background. However, the scintillation provides a modest signal-to-noise ratio, making difficult a pile-up pulse-shape recognition and rejection at timescales shorter than a few ms. Neganov–Trofimov–Luke assisted light detectors (NTL-LDs) offer the possibility to effectively increase the signal-to-noise ratio, preserving a fast time-response, and enhance the capability of pile-up rejection via pulse shape analysis. In this article we present: (a) an experimental work performed with a Li_2MoO_4 scintillating bolometer, studied in the framework of the CROSS experiment, and utilizing a NTL-LD; (b) a simulation method to reproduce, synthetically, randomly coincident two-neutrino double-beta decay events; (c) a new analysis method based on a pulse-shape discrimination algorithm capable of providing high pile-up rejection efficiencies. We finally show how the NTL-LDs offer a balanced solution between performance and complexity to reach background index sim 10^{-4} counts/keV/kg/year with 280 g Li_2MoO_4 (^{100}Mo enriched) bolometers at 3034 keV, the Q_{beta beta } of the double-beta decay, and target the goal of a next generation experiment like CUPID.

Shake-up and shake-off effects in neutrinoless double- β decay

We revisit the role of shake-up and shake-off effects in neutrinoless double-beta decay, following earlier work by Drukarev et al. We find in agreement with Drukarev et al. that the Q value of the decay is reduced by any atomic excitation in the final-state but not by the difference in atomic binding energy of the initial and final state atoms, as was recently suggested by Mei and Wei. We discuss how the absorption of subsequent atomic de-excitation ejecta shifts the neutrinoless double-beta decay peak back to its nominal value. We propose an in situ experimental verification of these ideas, and discuss the impact of shake-up and shake-off on two-neutrino double-beta decay spectral shapes.

Shell-model Study of Two-neutrino Double-Beta Decay for Z = 40–50 Nuclei and their SSD Properties

In this paper, large-scheme shell-model calculations are carried out for two-neutrino double-beta decay of Z = 40–50 nuclei (94Zr, 96Zr, 98Mo, 104Ru, 108Cd, and 116Cd). Within this region, only the half-lives of nuclei 96Zr and 116Cd are experimentally known. The calculated results agree well with experimental data and we predict the half-lives for the remaining four nuclei. Among them, 94Zr and 104Ru have relatively short half-lives of 4.57 × 1023 and 9.83 × 1023 years, respectively, together with large abundance, and are expected to be detected in the near future. By analyzing the convergence of nuclear matrix elements, special attention is paid to their single-state dominance (SSD) property. Here, a new SSD nucleus, i.e., 94Zr, is found, which is a supplement to the previous SSD nuclei list.

Concept of KamLAND2 DAQ system

The KamLAND-Zen experiment is searching for neutrinoless double-beta decay of 136Xe. We are preparing for the upgrade of the KamLAND detector, KamLAND2. It is designed to improve the discrimination power of two-neutrino double-beta decay and cosmic-ray muon spallation backgrounds. Data acquisition of all neutrino events from nearby supernova is also an important issue of the KamLAND2 experiment and the data rate is a key factor to design a new DAQ system. High speed sampling will be realized with RFSoC on the front-end electronics. Data is read out from FEE to DAQ computers via 10 GbE, and FairMQ is one of the candidates for KamLAND2 DAQ software. In the KamLAND DAQ, the whole trigger system is implemented in hardware, while the KamLAND2 DAQ adopts hardware trigger for photon detection and software trigger to extract physics events. A simulation study of the software trigger is proceeding in order to detect low energy events using timing and charge information.

Double Beta Decay: A Shell Model Approach

Studies of weak interaction in nuclei are important tools for testing different aspects of the fundamental symmetries of the Standard Model. Neutrinoless double beta decay offers an unique venue of investigating the possibility that neutrinos are Majorana fermions and that the lepton number conservation law is violated. Here, I use a shell model approach to calculate the nuclear matrix elements needed to extract the lepton-number-violating parameters of a few nuclei of experimental interest from the latest experimental lower limits of neutrinoless double beta decay half-lives. The analysis presented here could reveal valuable information regarding the dominant neutrinoless double beta decay mechanism if experimental half-life data become available for different isotopes. A complementary shell model analysis of the two-neutrino double beta decay nuclear matrix elements and half-lives is also presented.

Two-neutrino double- β decay matrix elements based on a relativistic nuclear energy density functional

Nuclear matrix elements (NMEs) for two-neutrino double-beta decay ($2\nu\beta\beta$) are studied in the framework of relativistic nuclear energy density functional (REDF). The properties of nuclei involved in the decay are obtained using the relativistic Hartree-Bardeen-Cooper-Schrieffer theory and relevant nuclear transitions are described using the relativistic proton-neutron quasiparticle random phase approximation based on relativistic energy density functional (REDF-QRPA). Three effective interactions have been employed, including density-dependent meson-exchange (DD-ME2) and point coupling interactions (DD-PC1 and DD-PCX), and pairing correlations are described consistently both in $T=1$ and $T=0$ channels using a separable pairing interaction. The optimal values of $T=0$ pairing strength parameter $V_{0pp}$ are constrained by the experimental data on $\beta$-decay half lives. The $2\nu\beta\beta$ matrix elements and half-lives are calculated for several nuclides experimentally known to undergo this kind of decay: $^{48}$Ca, $^{76}$Ge, $^{82}$Se, $^{96}$Zr, $^{100}$Mo, $^{116}$Cd, $^{124}$Xe, $^{128}$Te, $^{130}$Te, $^{136}$Xe and $^{150}$Nd. The model dependence of the NMEs and their sensitivity on $V_{0pp}$ is investigated, and the NMEs obtained using optimal values of $V_{0pp}$ are discussed in comparison to previous studies. The results of the present work represent an important benchmark for the future applications of the relativistic framework in studies of neutrinoless double-beta decay.

Expected sensitivity to 128Te neutrinoless double beta decay with the CUORE TeO2 cryogenic bolometers

The CUORE experiment is a ton-scale array of hbox {TeO}_2 cryogenic bolometers located at the underground Laboratori Nazionali del Gran Sasso of Istituto Nazionale di Fisica Nucleare (INFN), in Italy. The CUORE detector consists of 988 crystals operated as source and detector at a base temperature of sim 10 mK. Such cryogenic temperature is reached and maintained by means of a custom built cryogen-free dilution cryostat, designed with the aim of minimizing the vibrational noise and the environmental radioactivity. The primary goal of CUORE is the search for neutrinoless double beta decay of ^{130}hbox {Te}, but thanks to its large target mass and ultra-low background it is suitable for the study of other rare processes as well, such as the neutrinoless double beta decay of ^{128}hbox {Te}. This tellurium isotope is an attractive candidate for the search of this process, due to its high natural isotopic abundance of 31.75%. The transition energy at (866.7 ± 0.7) keV lies in a highly populated region of the energy spectrum, dominated by the contribution of the two-neutrino double beta decay of ^{130}hbox {Te}. As the first ton-scale infrastructure operating cryogenic hbox {TeO}_2 bolometers in stable conditions, CUORE is able to achieve a factor >10 higher sensitivity to the neutrinoless double beta decay of this isotope with respect to past direct experiments.

The first large-scale shell-model calculation of the two-neutrino double beta decay of 76Ge to the excited states in 76Se

Large-scale shell-model calculations were carried out for the half-lives and branching ratios of the 2νββ decay of 76Ge to the ground state and the lowest three excited states 21+, 02+ and 22+ in 76Se. In total, the wave functions of more than 10,000 intermediate 1+ states in 76As were calculated in a three-step procedure allowing an efficient use of the available computer resources. In the first step, 250 lowest states, below some 5 MeV of excitation energy, were calculated without truncations within a full major shell 0f5/2−1p−0g9/2 for both protons and neutrons. The wave functions of the rest of the states, up to some 30 MeV, were computed in two more steps by introducing two consecutive stages of truncation. The computed magnitudes of the 2νββ nuclear matrix elements (including the value of the axial-vector coupling gA), |M2ν|gA2, converged to the values 0.168gA2, 1.2×10−3gA2, 0.121gA2, and 3.1×10−3gA2 for the 0g.s.+, 21+, 02+, and 22+ states, respectively. Using up-to-date phase-space integrals, the corresponding branching ratios were derived to be 99.926%, 4.4×10−5%, 0.074% and 2.5×10−7%. The experimental half-life (1.926±0.094)×1021 yr of the ground-state transition was used to derive the value gA=0.80±0.01 for the axial-vector coupling, which is consistent with other shell-model calculations suggesting a quenched value of gA. Using this value of gA, predictions for the transition half-lives were derived.

Global calculation of two-neutrino double- β decay within the finite amplitude method in nuclear density functional theory

Two-neutrino double-beta ($2\nu\beta\beta$) decay has been used to constrain the neutron-proton part of effective interactions, which in turn is used to compute the nuclear matrix elements for neutrinoless double-beta decay, the observation of which would have important consequences for fundamental physics. We carefully examine $2\nu\beta\beta$ matrix elements within the proton-neutron quasiparticle random-phase approximation with nuclear energy density functionals. We work with functionals that are fit globally to single-beta-decay half-lives and charge-exchange giant-resonance energies, but not to $2\nu\beta\beta$ half-lives themselves, to evaluate the $2\nu\beta\beta$ nuclear matrix elements for all important nuclei, including those whose half-lives have not yet been measured. Such a comprehensive evaluation in large model spaces without configuration truncation requires an efficient computational scheme; we employ a double contour integration within the finite amplitude method. The results generally reproduce the nuclear matrix element extracted from half-lives well, without the use of any of those half-lives in the fitting procedure. We present predictions of the matrix elements in a total of 27 nuclei with half-lives that are still unmeasured.

Investigation of the Lorentz invariance violation in two-neutrino double-beta decay

We make a comprehensive investigation of the Lorentz invariance violation (LIV) effects that may occur in two-neutrino double-beta ($2\nu\beta\beta$) decay for all the experimentally interesting nuclei. We deduce the formulas for the LIV deviations and provide single and summed energy electron spectra and angular correlation between electrons with and without LIV contributions, to be used for constraining the LIV coefficient $\mathring{a}_{\text{of}}^{(3)}$. First, we confirm the shifting of the electron spectra to higher electron energies due to LIV for all nuclei. Next, we analyze other LIV signatures that can be used in LIV investigations. Thus, from the comparison of the electron and angular correlation spectra calculated with the inclusion of the LIV contributions, with their standard forms, information can be obtained about the strength versus observability of the LIV effects in the current experimental statistics. Then, we present the alternative method of constraining $\mathring{a}_{\text{of}}^{(3)}$ from the measurement of the angular correlation coefficient and estimate the statistics that different double-beta decay experiments should reach to constrain the LIV coefficient at the level of the current beta decay experiments. We hope that our work will improve the theoretical support and further stimulate the search for LIV in double-beta decay.

High-precision Q-value measurement and nuclear matrix element calculations for the double-beta decay of ^{98}Mo

The ^{98}Mo double-beta decay Q-value has been measured, and the corresponding nuclear matrix elements of neutrinoless double-beta (0nu beta beta ) decay and the standard two-neutrino double-beta (2nu beta beta ) decay have been provided by nuclear theory. The double-beta decay Q-value has been determined as Q_{beta beta }=113.668(68) keV using the JYFLTRAP Penning trap mass spectrometer. It is in agreement with the literature value, Q_{beta beta }=109(6) keV, but almost 90 times more precise. Based on the measured Q-value, precise phase-space factors for 2nu beta beta decay and 0nu beta beta decay, needed in the half-life predictions, have been calculated. Furthermore, the involved nuclear matrix elements have been computed in the proton–neutron quasiparticle random-phase approximation (pnQRPA) and the microscopic interacting boson model (IBM-2) frameworks. Finally, predictions for the 2nu beta beta decay are given, suggesting a much longer half-life than for the currently observed cases.

Determination of Double Beta Decay Half-Life of 136Xe with the PandaX-4T Natural Xenon Detector.

Precise measurement of two-neutrino double beta decay (DBD) half-life is an important step for the searches of Majorana neutrinos with neutrinoless double beta decay. We report the measurement of DBD half-life of 136Xe using the PandaX-4T dual-phase Time Projection Chamber (TPC) with 3.7-tonne natural xenon and the first 94.9-day physics data release. The background model in the fiducial volume is well constrained in situ by events in the outer active region. With a 136Xe exposure of 15.5 kg-year, we establish the half-life as 2.27 ± 0.03(stat.) ± 0.10(syst.) × 1021 years. This is the first DBD half-life measurement with natural xenon and demonstrates the physics capability of a large-scale liquid xenon TPC in the field of rare event searches.

Searching for New Physics in two-neutrino double beta decay with CUPID

In the past few years, attention has been drawn to the fact that a precision analysis of two-neutrino double beta decay (2υββ) allows the study of interesting physics cases like the emission of Majoron bosons and possible Lorentz symmetry violation. These processes modify the summed-energy distribution of the two electrons emitted in 2υββ. CUPID is a next-generation experiment aiming to exploit 100Mo-enriched scintillating Li2MoO4 crystals, operating as cryogenic calorimeters. Given the relatively fast half-life of 100Mo 2υββ and the large exposure that can be reached by CUPID, we expect to measure with very high precision the 100Mo 2υββ spectrum shape, reaching great sensitivities in the search for distortions induced by the physics beyond the Standard Model. In this contribution, we present the CUPID exclusion sensitivity for such New Physics processes, as well as the preliminary projected background of CUPID.

Prospects for searching new Double Beta Decay physics with KamLAND-Zen 800

Two-neutrino double beta decay (2υββ) is a rare second-order weak radioactive decay process. It has been observed in neutrinoless double beta decay (0υββ) search experiments. Precise observation of 2υββ is essential to reduce the theoretical uncertainty in the calculation of nuclear matrix elements required to obtain the effective Majorana mass from a lifetime of 0υββ. Also, 2υββ itself is interesting because new physics could be hiding in the energy spectrum, such as for example, Majoron emission mode 0υββ and 2υββ with neutrino self-interaction. KamLAND-Zen 800 is an experiment to search for 0υββ of 136Xe with a large ultra-pure liquid scintillator detector, KamLAND. KamLAND-Zen 800 has been observing 745 kg of xenon gas at 91% enriched in 136Xe since 2019, providing a high statistics 2υββ decay sample. We describe the potential for new physics searches in 2υββ with KamLAND-Zen 800.

Estimation of nuclear matrix elements of double-varvec{beta } decay from shell model and quasiparticle random-phase approximation

The nuclear matrix element (NME) of neutrinoless double-beta (0nu beta beta ) decay is an essential input for determining the neutrino effective mass, if the half-life of this decay is measured. Reliable calculation of this NME has been a long-standing problem because of the diversity of the predicted values of the NME, which depends on the calculation method. In this study, we focus on the shell model and the QRPA. The shell model has a rich amount of the many-particle many-hole correlations, and the quasiparticle random-phase approximation (QRPA) can obtain the convergence of the calculation results with respect to the extension of the single-particle space. It is difficult for the shell model to obtain the convergence of the 0nu beta beta NME with respect to the valence single-particle space. The many-body correlations of the QRPA may be insufficient, depending on the nuclei. We propose a new method to phenomenologically modify the results of the shell model and the QRPA compensating for the insufficiencies of each method using the information of other methods in a complementary manner. Extrapolations of the components of the 0nu beta beta NME of the shell model are made toward a very large valence single-particle space. We introduce a modification factor to the components of the 0nu beta beta NME of the QRPA. Our modification method yields similar values of the 0nu beta beta NME for the two methods with respect to ^{48}Ca. The NME of the two-neutrino double-beta decay is also modified in a similar but simpler manner, and the consistency of the two methods is improved.