Nuclear Shell Model Analyses and Predictions of Double-Beta Decay Observables

We present effective Majorana neutrino mass limits obtained from the joint analysis of the recently published results of 76Ge and 136Xe neutrinoless double beta decay (0νββ) experiments, which was carried out by using the Bayesian calculations. Nuclear matrix elements (NMEs) used for the analysis are taken from the works, in which NMEs of 76Ge and 136Xe were simultaneously calculated. This reduced systematic errors connected with NME calculation techniques. The new effective Majorana neutrino mass limits less than [85.4–197.0] meV are much closer to the inverse neutrino mass hierarchy region.

The modern theories of Grand Unification (GUT) and supersymmetric (SUSY) extensions of standard model (SM) suppose that the conservation laws of the SM may be violated to some small degree. The nuclei are well-suited as a laboratory to test fundamental symmetries and fundamental interactions like lepton flavor (LF) and lepton number (LN) conservation. A prominent role between experiments looking for LF and total LN violation play yet not observed processes of neutrinoless double beta decay. The GUT's and SUSY models offer a variety of mechanisms which allow this process to occur. They are based on mixing of Majorana neutrinos and/or R-parity violation hypothesis. Although the neutrinoless double beta decay has not been seen it is possible to extract from the lower limits of the lifetime upper limits for the effective electron Majorana neutrino mass, effective right handed weak interaction parameters, the effective Majoron coupling constant, R-parity violating SUSY parameters etc. In this work the limits on the LN violating parameters extracted from current neutrinoless double beta decay experiments are listed. Studies in respect to future neutrinoless double beta decay experimental projects are also presented.

The study of the neutrinoless double beta(0νββ)decay mode can provide us with important information on the neutrino properties, particularly on the electron neutrino absolute mass. In this work we revise the present constraints on the neutrino mass parameters derived from the0νββdecay analysis of the experimentally interesting nuclei. We use the latest results for the phase space factors (PSFs) and nuclear matrix elements (NMEs), as well as for the experimental lifetime limits. For the PSFs we use values computed with an improved method reported very recently. For the NMEs we use values chosen from the literature on a case-by-case basis, taking advantage of the consensus reached by the community on several nuclear ingredients used in their calculation. Thus, we try to restrict the range of spread of the NME values calculated with different methods and, hence, to reduce the uncertainty in deriving limits for the Majorana neutrino mass parameter. Our results may be useful to have an updated image on the present neutrino mass sensitivities associated with0νββmeasurements for different isotopes and to better estimate the range of values of the neutrino masses that can be explored in the future double beta decay (DBD) experiments.

We present a low-scale type-I seesaw scenario with discrete flavor and CP symmetries. This scenario not only explains the measured values of the lepton mixing angles, but also makes predictions for leptonic CP violation, and connects the low-energy CP phases relevant for neutrino oscillation and neutrinoless double beta decay experiments with the high-energy CP phases relevant for leptogenesis. We show that the three right-handed Majorana neutrinos in this scenario have (almost) degenerate masses and their decays can explain the observed baryon asymmetry of the Universe via resonant leptogenesis. We study the correlation of the predicted baryon asymmetry with lepton-number-violating signals at high-energy colliders, including both prompt and displaced vertex/long-lived signatures, as well as in low-energy neutrinoless double beta decay experiments. We find that the normal ordering of light neutrino masses leads to an enhanced collider signal, whereas the neutrinoless double beta decay provides a promising probe in the inverted ordering case.

Combined bounds on the Majorana neutrino mass for light and heavy neutrino exchange mechanisms are derived from current neutrinoless double beta decay (0{\nu}\b{eta}\b{eta}) search results for a variety of nuclear matrix element (NME) models. The approach requires self-consistency of a given model to predict NMEs across different isotopes. The derived bounds are notably stronger than those from any single experiment and show less model-to-model variation, highlighting the advantages of using multiple isotopes in such searches. Projections indicate that the combination of near-term experiments should be able to probe well into the inverted mass hierarchy region. A method to visually represent 0{\nu}\b{eta}\b{eta} experimental results is also suggested to more transparently compare across different isotopes and explicitly track model dependencies.

Double beta decay, the conversion of a nucleus changing the atomic number Z by two units while leaving the atomic mass A constant, is an extremely rare nuclear decay. It can occur via the emission of two electrons or two positrons, double electron capture or a mixed mode depending on the available Q-value. Furthermore, the neutrino-less mode is of major importance for neutrino physics. This mode violates the lepton number by two units and its observation would point towards physics beyond the Standard Model. The standard interpretation is via the exchange of a light Majorana neutrino, the mass of which could be measured via a half-life determination of double beta decay. There exist 11 isotopes for the double electron mode with a Q-value above 2 MeV, and for those considered for experimental searches, the neutrino-accompanied mode has been measured in the last decade. In recent years various new developments have occurred in almost all aspects related to double beta decay. With all the mixing angles of the PMNS leptonic mixing matrix measured, the regions of interest are well determined. Furthermore, with the launch of the LHC the existence of possible TeV particles contributing to neutrino-less double beta decays can be explored, complementing the searches in underground experiments. Nuclide pairs with the potential of degenerate nuclear states which would lead to a resonance enhancement of neutrino-less double electron capture were intensively searched for with Penning traps and caused a revival of this process. Last but not least, massive progress has been made in the involved conversion factors from the experimentally accessible half-life to the quantity of interest, the neutrino mass. New phase space factors were calculated and new approaches like the interacting boson model or energy density functional approaches joined the nuclear shell model and QRPA calculations to determine the involved nuclear transitions matrix elements. This is accompanied by a massive experimental program to improve the input parameters for these calculations using charge-exchange reactions, nucleon transfer reactions and muon capture. Furthermore, Penning traps have measured almost all relevant Q-values to sub-keV precision. All these exciting new developments over the last few years triggered the idea of a focus section in Journal of Physics G: Nuclear and Particle Physics on double beta decay during a workshop on the topic held in Dresden in July 2010. In addition to the research topics mentioned before, this focus section also covers the implication of double beta decay for current particle physics and theories beyond the Standard Model.

Neutrinoless double-beta decay searches play a major role in determining the effective Majorana neutrino mass and the Majorana nature of neutrinos. The MAJORANA experiment proposes to assemble an array of HPGe detectors to search for neutrinoless double-beta decay in 76Ge. Ultra-pure electro-formed Cu will form the cryostat and inner shielding material while Pb will comprise the remaining external shield. Neutron-induced γ-rays are a contribution to background for this and other double beta decay experiments. In some cases the excitation functions for highly excited state transitions of interest are not in the nuclear database. Measuring and understanding the high-energy neutron excitations of the shielding and detector materials for neutrinoless double beta decay experiments are crucial for interpreting results and establishing shielding requirements. Specific partial γ-ray cross sections were measured using the GEANIE spectrometer surrounding natural Pb, Cu and enriched Ge (76Ge) targets in a broad-spectrum neutron beam at LANSCE. The cross sections provide useful data for benchmarking Monte Carlo simulation of background events.

The detection of the neutrinoless double beta decay would establish that the neutrino is a Majorana particle and it would allow to measure the absolute neutrino mass in the meV region. To extract from the neutrinoless double beta decay halflife the absolute neutrino mass, the transition matrix element is as important as the experimental data. The dramatic progress in the last years is reviewed to determine these transition matrix elements for the neutrinoless double beta decay. It is shown, that the values calculated in the Quasi-particle Random Phase Approach (QRPA) and the recent results in the interacting boson model agree with each other completely within the uncertainties of the theories, while the shell model yields values which in the region of 76Ge are by a factor ½ smaller than QRPA. Possible reasons for the differences and an experimental way of measuring the Fermi part for the neutrinoless double beta decay transition matrix elements are discussed. This would allow to determine experimentally which of the two approaches is the correct one. Finally we show that the renormalization parameter gpp, which multiplies the nucleon-nucleon interaction matrix elements can be overconstraint together with the axial charge gA in three nuclei, where the ground state of the intermediate nucleus in the double beta decay system is a 1+ state and apart of the 2νββ also the β− decay for the second leg and the electron capture (EC) in the first leg is measured. It is shown, that this overconstraint determination of gpp and gA leads to the same result for the transition matrix elements as when one adjusts gpp to the 2νββ alone.

Neutrinoless double beta decay is a unique process that could reveal physics beyond the Standard Model of particle physics namely, if observed, it would prove that neutrinos are Majorana particles. In addition, it could provide information regarding the neutrino masses and their hierarchy, provided that reliable nuclear matrix elements can be obtained. The two neutrino double beta decay is an associate process that is allowed by the Standard Model, and it was observed for about ten nuclei. The present contribution gives a brief review of the theoretical challenges associated with these two process, emphasizing the reliable calculation of the associated nuclear matrix elements.

The neutrinoless double beta decay transition to the first excited 0^+ collective final state is examined for A=76, 82, 100 and 136 nuclei by assuming light and heavy Majorana neutrino exchange mechanisms as well as the trilinear R-parity violating contributions. Realistic calculations of nuclear matrix elements have been performed within the renormalized quasiparticle random phase approximation. Transitions to the first excited two-quadrupole phonon 0^+ state are described within a boson expansion formalism and alternatively by using the operator recoupling method. We present the sensitivity parameters to different lepton number violating signals, which can be used in planning the neutrinoless double beta decay experiments. The half-life of neutrinoless double beta decay to the first excited state 0^+_1 is by a factor of 10 to 100 larger than that of the transition to the ground state.

It has long been pointed out that there are seven different two-zero texture neutrino mass matrices compatible with neutrino oscillation data. We perform an updated analysis with the recently published Nu-Fit 6.0 results. We also subject the seven two-zero textures to constraints on neutrino mass from cosmology, end point of beta decay spectrum, and neutrinoless double beta decay experiments. We find that all seven textures are compatible with the new oscillation parameters. However, we find five textures, whose 1-1 entry is nonvanishing, are in severe tension with the constraints from cosmology and neutrinoless double beta decay. With the next generation experiments, these five textures could be decisively ruled out. For the remaining two textures, one of them could be ruled out, or severely constrained, if the octant of θ23 is determined. Published by the American Physical Society 2025

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.

We demonstrate how a class of non-supersymmetric SO(10) GUT with asymmetric left–right theory SU(2)L × U(1)R × U(1)B−L × SU(3)C and Pati–Salam theory SU(2)L × SU(2)R × SU(4)C as intermediate symmetry breaking steps leads to successful gauge coupling unification satisfying proton decay constraints. The motivation behind this work is two fold: firstly to study the renormalization group evolution equations for gauge couplings by keeping right-handed neutral gauge boson ZR around LHC energy range leading interesting dilepton searches at collider while fixing charge partner of the gauge boson WR at very high scale; secondly to explain neutrino masses and associated lepton number violating process like neutrinoless double beta decay in three possible cases depending on how SU(2)L × U(1)R × U(1)B−L × SU(3)C breaks down to SM. The presence of Pati–Salam symmetry and Pati–Salam symmetry with D-parity (discrete left–right symmetry leading to gL = gR) at highest scale is to allow two gauge couplings and thereby ensuring precision unification for gauge couplings. We focus on neutrino mass and neutrinoless double beta decay for one particular case where TeV scale asymmetric left–right theory is spontaneously broken down to SM with non-zero VEV of both Higgs doublets with B − L = −1 and Higgs triplets with B − L = 2. We include one extra fermion singlet per generation in order to implement gauged extended seesaw where light neutrino mass is governed by dominant type-II seesaw mechanism whereas type-I seesaw contribution is cancelled out. Since light neutrino mass formula is independent of Dirac neutrino mass matrix, the value of Dirac neutrino mass is taken to be up-type quark mass matrix which is a characteristics of Pati–Salam symmetry relating quarks with leptons. This can lead to non-unitarity effects in leptonic sector and induce lepton flavor violation. We present analytic relation for effective Majorana mass parameter and corresponding half-life arising from new physics contributions due to purely left-handed currents through exchange of heavy right-handed neutrinos and sterile neutrinos. We numerically estimate effective Majorana mass parameter and half-life versus lightest neutrino mass and derive lower bound on lightest neutrino mass by saturating with experimental bounds like GERDA Phase-II, KamLANDZen and EXO.

We study the general phenomenology of neutrinoless double beta decay in seesaw models. In particular, we focus on the dependence of the neutrinoless double beta decay rate on the mass of the extra states introduced to account for the Majorana masses of light neutrinos. For this purpose, we compute the nuclear matrix elements as functions of the mass of the mediating fermions and estimate the associated uncertainties. We then discuss what can be inferred on the seesaw model parameters in the different mass regimes and clarify how the contribution of the light neutrinos should always be taken into account when deriving bounds on the extra parameters. Conversely, the extra states can also have a significant impact, canceling the Standard Model neutrino contribution for masses lighter than the nuclear scale and leading to unobservable neutrinoless double beta decay amplitudes even if neutrinos are Majorana particles. In particular, the decay rate is reduced by at least six orders of magnitude for masses of the extra states below 1 MeV in absence of extra contributions. We also discuss how seesaw models could reconcile large rates of neutrinoless double beta decay with more stringent cosmological bounds on neutrino masses.

Grand unification, nuclear structure and the double beta-decay