Search

The current experiments searching for neutrinoless double-$\beta$ ($0\nu\beta\beta$) decay also collect large statistics of Standard Model allowed two-neutrino double-$\beta$ ($2\nu\beta\beta$) decay events. These can be used to search for Beyond Standard Model (BSM) physics via $2\nu\beta\beta$ decay spectral distortions. $^{100}$Mo has a natural advantage due to its relatively short half-life, allowing higher $2\nu\beta\beta$ decay statistics at equal exposures compared to the other isotopes. We demonstrate the potential of the dual read-out bolometric technique exploiting a $^{100}$Mo exposure of 1.47 kg $\times$ y, acquired in the CUPID-Mo experiment at the Modane underground laboratory (France). We set limits on $0\nu\beta\beta$ decays with the emission of one or more Majorons, on $2\nu\beta\beta$ decay with Lorentz violation, and $2\nu\beta\beta$ decay with a sterile neutrino emission. In this analysis, we investigate the systematic uncertainty induced by modeling the $2\nu\beta\beta$ decay spectral shape parameterized through an improved model, an effect never considered before. This work motivates searches for BSM processes in the upcoming CUPID experiment, which will collect the largest amount of $2\nu\beta\beta$ decay events among the next-generation experiments.

Current bounds on neutrino Majorana mass are affected by significant uncertainties in the nuclear calculations for neutrinoless double-beta decay. A key issue for a data-driven improvement of the nuclear theory is the actual value of the axial coupling constant $g_A$, which can be investigated through forbidden $\beta$-decays. We present the first measurement of 4$^{th}$-forbidden $\beta$-decay of $^{115}$In with a cryogenic calorimeter based on Indium Iodide. Exploiting the enhanced spectral shape method for the first time to this isotope, our study accurately determines simultaneously spectral shape, $g_A$, and half-life. The Interacting Shell Model, which best fits our data, indicates a half-life for this decay at $T_{1/2}=(5.26\pm0.06) \times 10^{14}$,yr.

The first direct determination of the ground-state-to-ground-state ${\beta^{-}}$-decay $Q$-value of $^{77}$As to $^{77}$Se was performed by measuring their atomic mass difference utilizing the double Penning trap mass spectrometer, JYFLTRAP. The resulting $Q$-value is 684.463(70) keV, representing a remarkable 24-fold improvement in precision compared to the value reported in the most recent Atomic Mass Evaluation (AME2020). With the significant reduction of the uncertainty of the ground-state-to-ground-state $Q$-value and knowledge of the excitation energies in $^{77}$Se from $\gamma$-ray spectroscopy, the ground-state-to-excited-state $Q$-value of the transition $^{77}$As (3/2$^{-}$, ground state) $\rightarrow$ $^{77}$Se$^{*}$ (5/2$^{+}$, 680.1035(17) keV) was refined to be 4.360(70) keV. We confirm that this potential low $Q$-value ${\beta^{-}}$-decay transition for neutrino mass determination is energetically allowed at a confidence level of about 60$\sigma$. Nuclear shell-model calculations with two well-established effective Hamiltonians were used to estimate the partial half-life for the low $Q$-value transition. The half-life was found to be of the order of 10$^{9}$ years for this first-forbidden non-unique transition, which rules out this candidate a potential source for rare-event experiments searching for the electron antineutrino mass., Comment: 8 pages, 4 figures

Neutrinoless double beta decay ($0\nu\beta\beta$) is a yet unobserved nuclear process which would demonstrate Lepton Number violation, a clear evidence of beyond Standard Model physics. The process two neutrino double beta decay ($2\nu\beta\beta)$ is allowed by the Standard Model and has been measured in numerous experiments. In this letter, we report a measurement of $2\nu\beta\beta$ decay half-life of $^{100}$Mo to the ground state of $^{100}$Ru of $(7.07~\pm~0.02~\text{(stat.)}~\pm~0.11~\text{(syst.)})~\times~10^{18}$~yr by the CUPID-Mo experiment. With a relative precision of $\pm~1.6$ \% this is the most precise measurement to date of a $2\nu\beta\beta$ decay rate in $^{100}$Mo. In addition, we constrain higher-order corrections to the spectral shape which provides complementary nuclear structure information. We report a novel measurement of the shape factor $\xi_{3,1}=0.45~\pm 0.03~\text{(stat.)} \ \pm 0.05 \ \text{(syst.)}$, which is compared to theoretical predictions for different nuclear models. We also extract the first value for the effective axial vector coupling constant obtained from a spectral shape study of $2\nu\beta\beta$ decay., Comment: 8 pages, 5 figures

We report on the results obtained with the global CUPID-0 background model, which combines the data collected in the two measurement campaigns for a total exposure of 16.6 kg$\times$yr. We identify with improved precision the background sources in the region of interest for neutrinoless double $\beta$-decay, making more solid the foundations for the background budget of the next-generation CUPID experiment. Relying on the excellent data reconstruction, we measure the two-neutrino double $\beta$-decay half-life of $^{82}$Se with unprecedented accuracy: $T_{1/2}^{2\nu} = [8.69 \pm 0.05 \textrm{(stat.)}~^{+0.09}_{-0.06} \textrm{(syst.)}] \times 10^{19}~\textrm{yr}$.

The $\beta^-$ decay $Q$-value of $^{136}$Cs ($J^\pi = 5^+$, $t_{1/2} \approx 13$~days) was measured with the JYFLTRAP Penning trap setup at the Ion Guide Isotope Separator On-Line (IGISOL) facility of the University of Jyv\"askyl\"a, Finland. The mono-isotopic samples required in the measurements were prepared with a new scheme utilised for the cleaning, based on the coupling of dipolar excitation with Ramsey's method of time-separated oscillatory fields and the phase-imaging ion-cyclotron-resonance (PI-ICR) technique. The $Q$ value is determined to be 2536.83(45) keV, which is $\sim$4 times more precise and 11.4(20) keV ($\sim$ 6$\sigma$) smaller than the adopted value in the most recent Atomic Mass Evaluation AME2020. The daughter, $^{136}$Ba, has a 4$^+$ state at 2544.481(24) keV and a $3^-$ state at 2532.653(23) keV, both of which can potentially be ultralow $Q$-value end-states for the $^{136}$Cs decay. With our new ground-to-ground state $Q$ value, the decay energies to these two states become -7.65(45) keV and 4.18(45) keV, respectively. The former is confirmed to be negative at the level of $\sim$ 17$\sigma$, which verifies that this transition is not a suitable candidate for neutrino mass determination. On the other hand, the slightly negative $Q$ value makes this transition an interesting candidate for the study of virtual $\beta$-$\gamma$ transitions. The decay to the 3$^{-}$ state is validated to have a positive low $Q$ value which makes it a viable candidate for neutrino mass determination. For this transition, we obtained a shell-model-based half-life estimate of $2.1_{-0.8}^{+1.6}\times10^{12}$ yr., Comment: 9 pages, 8 figures

The ACCESS (Array of Cryogenic Calorimeters to Evaluate Spectral Shapes) project aims to establish a novel technique to perform precision measurements of forbidden \b{eta}-decays, which can serve as an important benchmark for nuclear physics calculations and represent a significant background in astroparticle physics experiments. ACCESS will operate a pilot array of cryogenic calorimeters based on natural and doped crystals containing \b{eta}-emitting radionuclides. In this way, natural (e.g. 113 Cd and 115In) and synthetic isotopes (e.g. 99Tc) will be simultaneously measured with a common experimental technique. The array will also include further crystals optimised to disentangle the different background sources, thus reducing the systematic uncertainty. In this paper, we give an overview of the ACCESS research program, discussing a detector design study and promising results of 115In., Comment: 12 pages, 12 figures

CUPID-Mo, located in the Laboratoire Souterrain de Modane (France), was a demonstrator for the next generation $0\nu\beta\beta$ decay experiment, CUPID. It consisted of an array of 20 enriched Li$_{2}$$ ^{100}$MoO$_4$ bolometers and 20 Ge light detectors and has demonstrated that the technology of scintillating bolometers with particle identification capabilities is mature. Furthermore, CUPID-Mo can inform and validate the background prediction for CUPID. In this paper, we present a detailed model of the CUPID-Mo backgrounds. This model is able to describe well the features of the experimental data and enables studies of the $2\nu\beta\beta$ decay and other processes with high precision. We also measure the radio-purity of the Li$_{2}$$^{100}$MoO$_4$ crystals which are found to be sufficient for the CUPID goals. Finally, we also obtain a background index in the region of interest of 3.7$^{+0.9}_{-0.8}$(stat)$^{+1.5}_{-0.7}$(syst)$\times10^{-3}$counts/$\Delta$E$_{FWHM}$/mol$_{iso}$/yr, the lowest in a bolometric $0\nu\beta\beta$ decay experiment.

Here, we study the neutrinoless double-$\beta$ ($0\nu\beta\beta$) decay between the ground state and the first $2^+$ state of $^{76}\mbox{Ge} \rightarrow {}^{76}\mbox{Se}$, $^{82}\mbox{Se} \rightarrow{}^{82}\mbox{Kr}$, $^{130}\mbox{Te} \rightarrow {}^{130}\mbox{Xe}$ and $^{136}\mbox{Xe} \rightarrow {}^{136}\mbox{Ba}$ systems. The relevant nuclear matrix elements (NMEs) involved in the process are calculated within the formalism of the microscopic interacting boson model (IBM-2). The IBM-2 has been widely used to obtain predictions for nuclear observables, such as the spectrum, but also to explore the possible emergence of beyond-the-Standard Model effects in the weak interactions of nuclei. Our calculations are carried out by considering the exchange of a Majorana neutrino between two nucleons ($2N$-mechanism). In addition to NMEs, we calculate the associated leptonic phase-space factors (PSFs) using electron radial wave functions, which are obtained by solving numerically the Dirac equation of a screened Coulomb potential that takes into account finite nuclear size. By combining our IBM-2 results for the NMEs with those for the PSFs along with experimental half-life limits, we can set limits on the $\langle \lambda \rangle$ and $\langle \eta \rangle$ couplings of left-right (L-R) models., Comment: 9 pages, 1 figure

We present the first search for the Majoron-emitting modes of the neutrinoless double $\beta$ decay ($0\nu\beta\beta\chi_0$) using scintillating cryogenic calorimeters. We analysed the CUPID-0 Phase I data using a Bayesian approach to reconstruct the background sources activities, and evaluate the potential contribution of the $^{82}$Se $0\nu\beta\beta\chi_0$. We considered several possible theoretical models which predict the existence of a Majoron-like boson coupling to the neutrino. The energy spectra arising from the emission of such bosons in the neutrinoless double $\beta$ decay have spectral indices $n=$ 1, 2, 3 or 7. We found no evidence of any of these decay modes, setting a lower limit (90% of credibility interval) on the half-life of 1.2 $\times$ 10$^{23}$ yr in the case of $n=$ 1, 3.8 $\times$ 10$^{22}$ yr for $n=$ 2, 1.4 $\times$ 10$^{22}$ yr for $n=$ 3 and 2.2 $\times$ 10$^{21}$ yr for $n=$ 7. These are the best limits on the $0\nu\beta\beta\chi_0$ half-life of the $^{82}$Se, and demonstrate the potentiality of the CUPID-0 technology in this field.

Neutrinoless Double-Beta decay (0$\nu\beta\beta$) processes sample a wide range of intermediate forbidden nuclear transitions, which may be impacted by quenching of the axial vector coupling constant ($g_A/g_V$), the uncertainty of which plays a pivotal role in determining the sensitivity reach of 0$\nu\beta\beta$ experiments. In this Letter, we present measurements performed on a high-resolution LiInSe$_{2}$~ bolometer in a ''source=detector'' configuration to measure the spectral shape of the 4-fold forbidden $\beta$-decay of $^{115}$In. The value of $g_A/g_V$ is determined by comparing the spectral shape of theoretical predictions to the experimental $\beta$ spectrum taking into account various simulated background components as well as a variety of detector effects. We find evidence of quenching of $g_A/g_V$ at $>5\sigma$ with a model-dependent quenching factor of $0.655\pm0.002$ as compared to the free-nucleon value for the Interacting Shell Model. We also measured the $^{115}$In half-life to be [$5.18\pm0.06(\text{stat.})^{+0.005}_{-0.015}(\text{sys.})]\times{10}^{14}$ yr within the Interacting Shell Model framework. This work demonstrates the power of the bolometeric technique to perform precision nuclear physics single-$\beta$ decay measurements, which can help reduce the uncertainties in the calculation of $0\nu\beta\beta$ nuclear matrix elements., Comment: 7 Pages, 4 Figures, 2 Tables, Submitted to PRL

A precise determination of the atomic mass of $^{75}$As has been performed utilizing the double Penning trap mass spectrometer, JYFLTRAP. The mass excess is measured to be -73035.519(42) keV/c$^2$, which is a factor of 21 more precise and 1.3(9) keV/c$^2$ lower than the adopted value in the newest Atomic Mass Evaluation (AME2020). This value has been used to determine the ground-state-to-ground-state electron-capture decay $Q$ value of $^{75}$Se and $\beta^-$ decay $Q$ value of $^{75}$Ge, which are derived to be 866.041(81) keV and 1178.561(65) keV, respectively. Using the nuclear energy-level data of 860.00(40) keV, 865.40(50) keV (final states of electron capture) and 1172.00(60) keV (final state of $\beta^-$ decay) for the excited states of $^{75}$As$^*$, we have determined the ground-state-to-excited-state $Q$ values for two transitions of $^{75}$Se $\rightarrow$ $^{75}$As$^*$ and one transition of $^{75}$Ge $\rightarrow$ $^{75}$As$^*$. The ground-state-to-excited-state $Q$ values are determined to be 6.04(41) keV, 0.64(51) keV and 6.56(60) keV, respectively, thus confirming that the three low $Q$-value transitions are all energetically valid and one of them is a possible candidate channel for antineutrino mass determination. Furthermore, the ground-state-to-excited-state $Q$ value of transition $^{75}$Se $\rightarrow$ $^{75}$As$^*$ (865.40(50) keV) is revealed to be ultra-low (< 1 keV) and the first-ever confirmed EC transition possessing an ultra-low $Q$ value from direct measurements., Comment: 7 pages, 3 figures

The first direct determination of the ground-state-to-ground-state $Q$ values of the $\beta^-$ decay $^{76}$As $\rightarrow$ $^{76}$Se and the electron-capture decay $^{155}$Tb $\rightarrow$ $^{155}$Gd was performed utilizing the double Penning trap mass spectrometer JYFLTRAP. By measuring the atomic mass difference of the decay pairs via the phase-imaging ion-cyclotron-resonance (PI-ICR) technique, the $Q$ values of $^{76}$As $\rightarrow$ $^{76}$Se and $^{155}$Tb $\rightarrow$ $^{155}$Gd were determined to be 2959.265(74) keV and 814.94(18) keV, respectively. The precision was increased relative to earlier measurements by factors of 12 and 57, respectively. The new $Q$ values are 1.33 keV and 5 keV lower compared to the values adopted in the most recent Atomic Mass Evaluation 2020. With the newly determined ground-state-to-ground-state $Q$ values combined with the excitation energy from $\gamma$-ray spectroscopy, the $Q$ values for ground-state-to-excited-state transitions $^{76}$As (ground state) $\rightarrow$ $^{76}$Se$^*$ (2968.4(7) keV) and $^{155}$Tb (ground state) $\rightarrow$ $^{155}$Gd$^*$ (815.731(3) keV) were derived to be -9.13(70) keV and -0.79(18) keV. Thus we have confirmed that both of the $\beta^{-}$-decay and EC-decay candidate transitions are energetically forbidden at a level of at least 4$\sigma$, thus definitely excluding these two cases from the list of potential candidates for the search of low-$Q$-value $\beta^-$ or EC decays to determine the electron-(anti)neutrino mass., Comment: 8 pages, 4 figures, to be submitted

A precise determination of the ground state $^{111}$In ($9/2^+$) electron capture to ground state of $^{111}$Cd ($1/2^+$) $Q$ value has been performed utilizing the double Penning trap mass spectrometer, JYFLTRAP. A value of 857.63(17) keV was obtained, which is nearly a factor of 20 more precise than the value extracted from the Atomic Mass Evaluation 2020 (AME2020). The high-precision electron-capture $Q$ value measurement along with the nuclear energy level data of 866.60(6) keV, 864.8(3) keV, 855.6(10) keV, and 853.94(7) keV for $^{111}$Cd was used to determine whether the four states are energetically allowed for a potential ultra-low $Q$-value $\beta^{}$ decay or electron-capture decay. Our results confirm that the excited states of 866.60(6) keV with spin-parity ($J^\pi$) of 3/2$^{+}$ and 864.8(3) keV with $J^\pi$ = 3/2$^{+}$ are ruled out due to their deduced electron-capture $Q$ value being smaller than 0 keV at the level of around 20$\sigma$ and 50$\sigma$, respectively. Electron-capture decays to the excited states at 853.94(7) keV ($J^\pi$ = 7/2$^+$) and 855.6(10) keV ($J^\pi$ = 3/2$^+$), are energetically allowed with $Q$ values of 3.69(19) keV and 2.0(10) keV, respectively. The allowed decay transition $^{111}$In (9/2$^{+}$) $\rightarrow$ $^{111}$Cd (7/2$^{+}$), with a $Q$ value of 3.69(19) keV, is a potential a new candidate for neutrino-mass measurements by future EC experiments featuring new powerful detection technologies. The results show that the indium level $2p_{1/2}$ for this decay branch leads to a significant increase in the number of EC events in the energy region sensitive to the electron neutrino mass., Comment: 12 pages, 4 figures

In this work we study ordinary muon capture (OMC) on $^{24}$Mg from a first principles perspective. Starting from a particular two- and three-nucleon interaction derived from chiral effective field theory, we use the valence-space in-medium similarity renormalization group (VS-IMSRG) framework to construct effective Hamiltonians and muon-capture operators which nonperturbatively account for many-body physics outside the valence space. The obtained nuclear matrix elements are compared against those from the phenomenological shell model. The impact of including the correlations from the nuclear shell model (NSM) as well as including the induced two-body part is studied in detail. Furthermore, the effects of realistic bound-muon wave function on the operators is studied. Finally, predictions for capture rates to the lowest excited states in $^{24}$Na are given and compared with available data. It is found that the spectroscopic properties of $^{24}$Mg and its OMC daughter $^{24}$Na are fairly well described by both the NSM and VS-IMSRG, and that the effect of the hadronic two-body currents significantly reduces the OMC rates. Both models have some difficulties in matching the measured OMC rates, especially for the $2^+$ final states. This calls for further studies in other light nuclei with available OMC data., Comment: 18 pages, 6 figures, 14 tables, including appendix. Corresponds to the published version

The gamma-ray emissions from a radiopure cerium-bromide crystal with a mass of 4381 g were measured for a total of 497.4 d by means of high-resolution gamma-ray spectrometry in the HADES underground laboratory at a depth of 500 m.w.e. A search for 0/2nee and 0/2neb+ double beta decay transitions of Ce-136 and Ce-138 was performed using Bayesian analysis techniques. No signals were observed for a total of 35 investigated decay modes. 90% credibility limits were set in the order of 1e18-1e19 a. Existing constraints from a cerium oxide powder measurement were tested with a different cerium compound and half-life limits could be improved for most of the decay modes. The most likely accessible decay mode of the Ce-136 2nee transition into the 0+1 state of Ba-136 results in a new best 90% credibility limit of 5.0e18 a.

Neutrinoless double-beta ($0\nu\beta\beta$) decay and the standard two-neutrino double-beta ($2\nu\beta\beta$) decay of $^{98}$Mo have been studied. 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 $2\nu\beta\beta$ decay and $0\nu\beta\beta$ 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 $2\nu\beta\beta$ decay are given, suggesting a much longer half-life than for the currently observed cases., Comment: 8 pages, 3 figures

{ The ground-state to ground-state electron-capture $Q$ value of $^{159}$Dy ($3/2^-$) has been measured directly utilizing the double Penning trap mass spectrometer JYFLTRAP. A value of 364.73(19)~keV was obtained from a measurement of the cyclotron frequency ratio of the decay parent $^{159}$Dy and the decay daughter $^{159}$Tb ions using the novel phase-imaging ion-cyclotron resonance technique. The $Q$ values for allowed Gamow-Teller transition to $5/2^-$ and the third-forbidden unique transition to $11/2^+$ state with excitation energies of 363.5449(14)~keV and 362.050(40)~keV in $^{159}$Tb were determined to be 1.18(19) keV and 2.68(19) keV, respectively. The high-precision $Q$ value of transition $3/2^-\to 5/2^-$ from this work, revealing itself as the lowest electron-capture $Q$ value, is utilized to unambiguously characterise all the possible lines that are present in its electron capture spectrum. { We performed atomic many-body calculations for both transitions to determine electron-capture probabilities from various atomic orbitals, and found an order of magnitude enhancement in the event rates near the end-point of energy spectrum in the transition to the $5/2^-$ nuclear excited state, which can become very interesting once the experimental challenges of identifying decays into excited states are overcome. The transition to the $11/2^+$ state is strongly suppressed and found unsuitable for measuring the neutrino mass. These results show that the electron capture in the $^{159}$Dy atom, going to the $5/2^-$ state of the $^{159}$Tb nucleus, %\textcolor{red} {is a new candidate which may open the way to determine the electron-neutrino mass in the sub-eV region by studying EC. Further experimental feasibility studies, including coincidence measurements with realistic detectors, will be of great interest.} }, Comment: 6 pages, 2 figures

We report the first direct determination of the ground-state to ground-state electron-capture $Q$-value for the $^{72}$As to $^{72}$Ge decay by measuring their atomic mass difference utilizing the double Penning trap mass spectrometer, JYFLTRAP. The $Q$-value was measured to be 4343.596(75)~keV, which is more than a 50-fold improvement in precision compared to the value in the most recent Atomic Mass Evaluation 2020. Furthermore, the new $Q$-value was found to be 12.4(40)~keV (3.1 $\sigma$) lower. With the significant reduction of the uncertainty of the ground-state to ground-state $Q$-value value combined with the level scheme of $^{72}$Ge from $\gamma$-ray spectroscopy, we confirm that the five potential ultra-low $Q$-value ${\beta^{+}}$-decay or electron capture transitions are energetically forbidden, thus precluding all the transitions as possible candidates for the electron neutrino mass determination. However, the discovery of small negative $Q$-values opens up the possibility to use $^{72}$As for the study of virtual $\beta$-$\gamma$ transitions., Comment: 8 pages, 6 figures, nuclear experiment

The structure of odd-$A$ $^{(115,117)}$Rh and $^{(115,117)}$Pd isotopes is studied by means of the neutron-proton Interacting Boson-Fermion Model (IBFM-2). $J^P = \frac{1}{2}^+$ quantum number assignment for the $^{(115,117)}$Pd ground-states is critically discussed and the predicted energy levels are compared to the existing experimental data. The resulting nuclear wave functions are used to compute the $\beta$-decay $ft$ values of the transitions from $^{(115,117)}$Rh to $^{(115,117)}$Pd in the microscopic IBFM-2 and the results compared with the data.

Neutrinoless double beta decay (0v\b{eta}\b{eta}) is considered the best potential resource to access the absolute neutrino mass scale. Moreover, if observed, it will signal that neutrinos are their own anti-particles (Majorana particles). Presently, this physics case is one of the most important research "beyond Standard Model" and might guide the way towards a Grand Unified Theory of fundamental interactions. Since the 0v\b{eta}\b{eta} decay process involves nuclei, its analysis necessarily implies nuclear structure issues. In the NURE project, supported by a Starting Grant of the European Research Council (ERC), nuclear reactions of double charge-exchange (DCE) are used as a tool to extract information on the 0v\b{eta}\b{eta} Nuclear Matrix Elements. In DCE reactions and \b{eta}\b{eta} decay indeed the initial and final nuclear states are the same and the transition operators have similar structure. Thus the measurement of the DCE absolute cross-sections can give crucial information on \b{eta}\b{eta} matrix elements. In a wider view, the NUMEN international collaboration plans a major upgrade of the INFN-LNS facilities in the next years in order to increase the experimental production of nuclei of at least two orders of magnitude, thus making feasible a systematic study of all the cases of interest as candidates for 0v\b{eta}\b{eta}.

Neutrinoless double beta decay (0{\nu}\b{eta}\b{eta}) is considered the best potential resource to determine the absolute neutrino mass scale. Moreover, if observed, it will signal that the total lepton number is not conserved and neutrinos are their own anti-particles. Presently, this physics case is one of the most important research beyond Standard Model and might guide the way towards a Grand Unified Theory of fundamental interactions. Since the \b{eta}\b{eta} decay process involves nuclei, its analysis necessarily implies nuclear structure issues. The 0{\nu}\b{eta}\b{eta} decay rate can be expressed as a product of independent factors: the phase-space factors, the nuclear matrix elements (NME) and a function of the masses of the neutrino species. Thus the knowledge of the NME can give information on the neutrino mass scale, if the 0{\nu}\b{eta}\b{eta} decay rate is measured. In the NURE project, supported by a Starting Grant of the European Research Council, nuclear reactions of double charge-exchange (DCE) will be used as a tool to extract information on the \b{eta}\b{eta} NME. In DCE reactions and \b{eta}\b{eta} decay, the initial and final nuclear states are the same and the transition operators have similar structure. Thus the measurement of the DCE absolute crosssections can give crucial information on \b{eta}\b{eta} matrix elements., Comment: arXiv admin note: substantial text overlap with arXiv:2001.09657; text overlap with arXiv:2001.09648

We report the measurement of the two-neutrino double-beta ($2\nu\beta\beta$) decay of $^{100}$Mo to the ground state of $^{100}$Ru using lithium molybdate (\crystal) scintillating bolometers. The detectors were developed for the CUPID-Mo program and operated at the EDELWEISS-III low background facility in the Modane underground laboratory. From a total exposure of $42.235$ kg$\times$d, the half-life of $^{100}$Mo is determined to be $T_{1/2}^{2\nu}=[7.12^{+0.18}_{-0.14}\,\mathrm{(stat.)}\pm0.10\,\mathrm{(syst.)}]\times10^{18}$ years. This is the most accurate determination of the $2\nu\beta\beta$ half-life of $^{100}$Mo to date. We also confirm, with the statistical significance of $>3\sigma$, that the single-state dominance model of the $2\nu\beta\beta$ decay of $^{100}$Mo is favored over the high-state dominance model., Comment: 11 pages, 6 figures, 4 tables

We report on the measurement of the two-neutrino double-$\beta$ decay of $^{82}$Se performed for the first time with cryogenic calorimeters, in the framework of the CUPID-0~experiment. With an exposure of 9.95 kg$\times$yr of Zn$^{82}$Se, we determine the two-neutrino double-$\beta$ decay half-life of $^{82}$Se with an unprecedented precision level, $T_{1/2}^{2\nu} = [8.60 \pm 0.03 \textrm{(stat.)}~^{+0.17}_{-0.10} \textrm{(syst.)}] \times 10^{19}~\textrm{yr}$. The very high signal-to-background ratio, along with the detailed reconstruction of the background sources allowed us to identify the single state dominance as the underlying mechanism of such process, demonstrating that the higher state dominance hypothesis is disfavored at the level of 5.5 $\sigma$.

A complete calculation of phase space factors (PSF) for Majoron emitting $0\nu\beta^-\beta^-$ decay modes is presented. The calculation makes use of exact Dirac wave functions with finite nuclear size and electron screening and includes life-times, single electron spectra, summed electron spectra, and angular electron correlations. Combining these results with recent interacting boson nuclear matrix elements (NME) we make half-life predictions for the the ordinary Majoron decay (spectral index $n$=1). Furthermore, comparing theoretical predictions with the obtained experimental lower bounds for this decay mode we are able to set limits on the effective Majoron-neutrino coupling constant $\langle g_{ee}^M\rangle$.

Neutrinoless double-$\beta$ decay is of fundamental importance for determining the neutrino mass. Although double electron ($\beta^-\beta^-$) decay is the most promising mode, in very recent years interest in double positron ($\beta^+\beta^+$) decay, positron emitting electron capture ($EC\beta^+$), and double electron capture ($ECEC$) has been renewed. We present here results of a calculation of nuclear matrix elements for neutrinoless double-$\beta^+$ decay and positron emitting electron capture within the framework of the microscopic interacting boson model (IBM-2) for $^{58}$Ni, $^{64}$Zn, $^{78}$Kr, $^{96}$Ru, $^{106}$Cd, $^{124}$Xe, $^{130}$Ba, and $^{136}$Ce decay. By combining these with a calculation of phase space factors we calculate expected half-lives., Comment: arXiv admin note: text overlap with arXiv:1301.4203

Direct determination of the neutrino mass is at the present time one of the most important aims of experimental and theoretical research in nuclear and particle physics. A possible way of detection is through neutrinoless double electron capture, $0\nu ECEC$. This process can only occur when the energy of the initial state matches precisely that of the final state. We present here a calculation of prefactors (PF) and nuclear matrix elements (NME) within the framework of the microscopic interacting boson model (IBM-2) for $^{124}$Xe, $^{152}$Gd, $^{156}$Dy, $^{164}$Er, and $^{180}$W. From PF and NME we calculate the expected half-lives and obtain results that are of the same order as those of $ 0\nu \beta^+\beta^+$ decay, but considerably longer than those of $0\nu \beta^-\beta^-$ decay.

Nuclear matrix elements (NME) for exchange of arbitrary mass neutrinos are calculated in the interacting boson model (IBM-2). By combining the NME with the phase space factors (PSF), expected half-lives for neutrinos of mass $m_N$ and coupling $U_{eN}$ are estimated. Limits on sterile neutrinos with masses in the eV, keV, MeV-GeV, and TeV range are given.

Neutrinoless double-$\beta$ decay is of fundamental importance for the determining neutrino mass. By combining a calculation of nuclear matrix elements within the framework of the microscopic interacting boson model (IBM-2) with an improved calculation of phase space factors, we set limits on the average light neutrino mass and on the average inverse heavy neutrino mass (flavor violating parameter).

We introduce a method for isospin restoration in the calculation of nuclear matrix elements (NME) for $0\nu\beta\beta$ and $2\nu\beta\beta$ decay within the framework of interacting boson model (IBM-2). With this method, we calculate NME for all processes of interest in $0\nu\beta^-\beta^-$, $2\nu\beta^-\beta^-$, and in $0\nu\beta^+\beta^+$, $0\nu\beta^+ EC^+$, $R0\nu ECEC$, $2\nu\beta^+\beta^+$, $2\nu\beta^+EC$, and $2\nu ECEC$. With this method, the Fermi (F) matrix elements for $2\nu\beta\beta$ vanish, and those for $0\nu\beta\beta$ are considerably reduced., Comment: arXiv admin note: text overlap with arXiv:1301.4203

A complete and improved calculation of phase space factors (PSF) for $2\nu\beta^+\beta^+$ and $0\nu\beta^+\beta^+$ decay, as well as for the competing modes $2\nu EC\beta^+$, $0\nu EC\beta^+$, and $2\nu ECEC$, is presented. The calculation makes use of exact Dirac wave functions with finite nuclear size and electron screening and includes life-times, single and summed positron spectra, and angular positron correlations., Comment: 13 pages, 14 figures. arXiv admin note: text overlap with arXiv:1209.5722

Background: Direct determination of the neutrino mass through double-$\beta$ decay is at the present time one of the most important areas of experimental and theoretical research in nuclear and particle physics. Purpose: We calculate nuclear matrix elements for the extraction of the average neutrino mass in neutrinoless double-$\beta$ decay. Methods: The microscopic interacting boson model (IBM-2) is used. Results: Nuclear matrix elements in the closure approximation are calculated for $^{48}$Ca, $^{76}$Ge, $^{82}$Se, $^{96}$Zr, $^{100}$Mo, $^{110}$Pd, $^{116}$Cd, $^{124}$Sn, $^{128}$Te, $^{130}$Te, $^{148}$Nd, $^{150}$Nd, $^{154}$Sm, $^{160}$Gd, and $^{198}$Pt decay. Conclusions: Realistic predictions for the expected half-lives in neutrinoless double-$\beta$ decay with light and heavy neutrino exchange in terms of neutrino masses are made and limits are set from current experiments., Comment: 23 pages, 13 figures; http://link.aps.org/doi/10.1103/PhysRevC.87.014315

A complete and improved calculation of phase space factors (PSF) for $2\nu\beta\beta$ and $0\nu\beta\beta$ decay is presented. The calculation makes use of exact Dirac wave functions with finite nuclear size and electron screening and includes life-times, single and summed electron spectra, and angular electron correlations.

The 110Pd double-beta decay Q-value was measured with the Penning-trap mass spectrometer ISOLTRAP to be Q = 2017.85(64) keV. This value shifted by 14 keV compared to the literature value and is 17 times more precise, resulting in new phase-space factors for the two-neutrino and neutrinoless decay modes. In addition a new set of the relevant matrix elements has been calculated. The expected half-life of the two-neutrino mode was reevaluated as 1.5(6) E20 yr. With its high natural abundance, the new results reveal 110Pd to be an excellent candidate for double-beta decay studies.