我们在 chiral 有效场论（χEFT）中计算了实验最相关核素（包括⁷⁶Ge、¹⁰⁰Mo和¹³⁶Xe）的无中微子双β（0νββ）衰变的所有核矩阵元（NMEs），精度达到次下次 leading 阶（N²LO）。我们使用质子-中子准粒子无规相近似（pnQRPA）和核壳模型，计算了来自极低动量（超软）中微子和0νββ研究中通常被忽略的圈图的N²LO NMEs。结果表明，壳模型的N²LO总贡献约为-（5-10）%，pnQRPA的约为+（10-15）%，超软NMEs的尺度依赖性和圈NMEs的短程性质导致了较大的不确定性。多体方法之间的符号差异在所有研究核素中普遍存在，这表明0νββ衰变中间态的行为不同。在不确定性范围内，我们的超软NME结果与通常被称为“超出闭合近似”的贡献大小相似。
英文摘要：
We evaluate all nuclear matrix elements (NMEs) up to next-to-next-to leading order (N$^2$LO) in chiral effective field theory ($χ$EFT) for the neutrinoless double-beta ($0νββ$) decay of the nuclei most relevant for experiments, including $^{76}$Ge, $^{100}$Mo, and $^{136}$Xe. We use the proton-neutron quasiparticle random-phase approximation (pnQRPA) and the nuclear shell model to calculate the N$^2$LO NMEs from very low-momentum (ultrasoft) neutrinos and from loop diagrams usually neglected in $0νββ$ studies. Our results indicate that the overall N$^2$LO contribution is centered around $-(5$-$10)\%$ for the shell model and $+(10$-$15)\%$ for the pnQRPA, with sizable uncertainties due to the scale dependence of the ultrasoft NMEs and the short-range nature of the loop NMEs. The sign discrepancy between many-body methods is common to all studied nuclei and points to the different behaviour of the intermediate states of the $0νββ$ decay. Within uncertainties, our results for the ultrasoft NME are of similar size as contributions usually referred to as ``beyond the closure approximation''.
A measurement of neutrinoless double beta decay in one isotope does not allow to determine the underlying physics mechanism. We discuss the discrimination of mechanisms for neutrinoless double beta decay by comparing ratios of half life measurements for different isotopes. Six prominent examples for specific new physics contributions to neutrinoless double beta decay are analyzed. We find that the change in corresponding ratios of half lives varies from 60% for supersymmetric models up to a factor of 5-20 for extra-dimensional and left-right-symmetric mechanisms.
The detection of neutrinoless double-beta decay will establish the Majorana nature of neutrinos. In addition, if the nuclear matrix elements of this process are reliably known, the experimental lifetime will provide precious information about the absolute neutrino masses and hierarchy. I review the status of nuclear structure calculations for neutrinoless double-beta decay matrix elements, and discuss some key issues to be addressed in order to meet the demand for accurate nuclear matrix elements.
The nuclear matrix elements that govern the rate of neutrinoless double beta decay must be accurately calculated if experiments are to reach their full potential. Theorists have been working on the problem for a long time but have recently stepped up their efforts as ton-scale experiments have begun to look feasible. Here we review past and recent work on the matrix elements in a wide variety of nuclear models and discuss work that will be done in the near future. Ab initio nuclear-structure theory, which is developing rapidly, holds out hope of more accurate matrix elements with quantifiable …
Half-life estimates for neutrinoless double beta decay depend on particle physics models for lepton flavor violation, as well as on nuclear physics models for the structure and transitions of candidate nuclei. Different models considered in the literature can be contrasted - via prospective data - with a "standard" scenario characterized by light Majorana neutrino exchange and by the quasiparticle random phase approximation, for which the theoretical covariance matrix has been recently estimated. We show that, assuming future half-life data in four promising nuclei (Ge-76, Se-82, Te-130, and X…
We show that chiral effective field theory (EFT) two-body currents provide important contributions to the quenching of low-momentum-transfer Gamow-Teller transitions, and use chiral EFT to predict the momentum-transfer dependence that is probed in neutrinoless double-beta decay. We then calculate for the first time the neutrinoless double-beta decay operator based on chiral EFT currents and study the nuclear matrix elements at successive orders. The contributions from chiral two-body currents are significant and should be included in all calculations.
We devise a framework based on the generalized contact formalism that combines the nuclear shell model and quantum Monte Carlo methods and compute the neutrinoless double-beta decay of experimentally relevant nuclei, including $^{76}$Ge, $^{130}$Te, and $^{136}$Xe. In light nuclei, we validate our nuclear matrix element calculations by comparing against accurate variational Monte Carlo results. Due to additional correlations captured by quantum Monte Carlo and introduced within the generalized contact formalism, in heavier systems, we obtain long-range nuclear matrix elements that are about 30…
We evaluate the leading-order short-range nuclear matrix element for the neutrinoless double-beta ($0νββ$) decay of the nuclei most relevant for experiments, including $^{76}$Ge, $^{100}$Mo, $^{130}$Te and $^{136}$Xe. In our calculations, performed with the nuclear shell model and proton-neutron quasiparticle random-phase approximation (pnQRPA) methods, we estimate the coupling of this term by the contact charge-independence-breaking coupling of various nuclear Hamiltonians. Our results suggest a significant impact of the short-range matrix element, which is about $15\%-50\%$ and $30\%-80\%$ o…
Experiments using nuclei to probe new physics beyond the Standard Model, such as neutrinoless $ββ$ decay searches testing whether neutrinos are their own antiparticle, and direct detection experiments aiming to identify the nature of dark matter, require accurate nuclear physics input for optimizing their discovery potential and for a correct interpretation of their results. This demands a detailed knowledge of the nuclear structure relevant for these processes. For instance, neutrinoless $ββ$ decay nuclear matrix elements are very sensitive to the nuclear correlations in the initial and final…
Neutrinoless $ββ$ decay nuclear matrix elements calculated with the shell model and energy-density functional theory typically disagree by more than a factor of two in the standard scenario of light-neutrino exchange. In contrast, for a decay mediated by sterile heavy neutrinos the deviations are reduced to about 50\%, an uncertainty similar to the one due to short-range effects. We compare matrix elements in the light- and heavy-neutrino-exchange channels, exploring the radial, momentum transfer and angular momentum-parity matrix element distributions, and considering transitions that involve…
Accurate nuclear matrix elements (NMEs) for neutrinoless double beta decays of candidate nuclei are important for the design and interpretation of future experiments. Significant progress has been made in the modeling of these NMEs from first principles. The NME for 48Ca shows a good agreement among three different ab initio calculations starting from the same nuclear interaction constructed within the chiral EFT and the same decay operator. These studies open the door to ab initio calculations of the matrix elements for the decay of heavier nuclei such as 76Ge, 130Te, and 136Xe. The ultimate …
Searches of neutrinoless double-beta decay require information on the value of the nuclear matrix elements that rule the process to plan and interpret experiments. At present, however, even the matrix elements obtained with the most reliable many-body approaches do not agree to each other better than a factor two or three. A usual test of the many-body calculations is the comparison to several nuclear observables, but so far no nuclear structure property has been found to show a good correlation to neutrinoless double-beta decay. Here we propose that double charge-exchange experiments can offe…
The calculated nuclear matrix elements for the neutrinoless double-beta ($0νββ$) decay suffer from several limitations. Predicted matrix-element values depend on the many-body method used to calculate them and, in addition, they may need to be "quenched", albeit by an unknown amount due to the relatively high momentum transferred in the decay. These uncertainties are hard to figure out from theoretical calculations alone because of the unique character of $0νββ$ decay, not clearly related to other nuclear structure observables. We present recent progress in the determination of the nuclear mat…
We study double gamma ($γγ$) decay nuclear matrix elements (NMEs) for a wide range of nuclei from titanium to xenon, and explore their relation to neutrinoless double-beta ($0νββ$) NMEs. To favor the comparison, we focus on double-magnetic dipole transitions in the final $ββ$ nuclei, in particular the $γγ$ decay of the double isobaric analog of the initial $ββ$ state into the ground state. For the decay with equal-energy photons, our large-scale nuclear shell model results show a good linear correlation between the $γγ$ and $0νββ$ NMEs. Our analysis reveals that the correlation holds for $γγ$ …
Nuclear matrix elements (NME) for the most promising candidates to detect neutrinoless double beta decay have been computed with energy density functional methods including deformation and pairing fluctuations explicitly on the same footing. The method preserves particle number and angular momentum symmetries and can be applied to any decay without additional fine tunings. The finite range density dependent Gogny force is used in the calculations. An increase of $10\%-40\%$ in the NME with respect to the ones found without the inclusion of pairing fluctuations is obtained, reducing the predict…
We investigate neutrinoless double-beta decay ($0νββ$) in the minimal extension of the standard model of particle physics, the $ν$SM, where gauge-singlet right-handed neutrinos give rise to Dirac and Majorana neutrino mass terms. We focus on the associated sterile neutrinos and argue that the usual evaluation of their contributions to $0νββ$, based on mass-dependent nuclear matrix elements, is missing important contributions from neutrinos with ultrasoft and hard momenta. We identify the hadronic and nuclear matrix elements that enter the new contributions, and calculate all relevant nuclear m…
We report ab initio benchmark calculations of nuclear matrix elements (NMEs) for neutrinoless double-beta ($0νββ$) decays in light nuclei with mass number ranging from $A=6$ to $A=22$. We use the transition operator derived from light-Majorana neutrino exchange and evaluate the NME with three different methods: two variants of in-medium similarity renormalization group (IMSRG) and importance-truncated no-core shell model (IT-NCSM). The same two-plus-three-nucleon interaction from chiral effective field theory is employed, and both isospin-conserving ($ΔT=0$) and isospin-changing ($ΔT=2$) trans…
We report a systematic study of nuclear matrix elements (NMEs) in neutrinoless double-beta decays with a state-of-the-art beyond mean-field covariant density functional theory. The dynamic effects of particle-number and angular-momentum conservations as well as quadrupole shape fluctuations are taken into account with projections and generator coordinate method for both initial and final nuclei. The full relativistic transition operator is adopted to calculate the NMEs. The present systematic studies show that in most of the cases there is a much better agreement with the previous non-relativi…
We perform a global fit of the most relevant neutrinoless double beta decay experiments within the standard model with massive Majorana neutrinos. Using Bayesian inference makes it possible to take into account the theoretical uncertainties on the nuclear matrix elements in a fully consistent way. First, we analyze the data used to claim the observation of neutrinoless double beta decay in Ge-76, and find strong evidence (according to Jeffrey's scale) for a peak in the spectrum and moderate evidence for that the peak is actually close to the energy expected for the neutrinoless decay. We also …
Neutrinoless double beta decay searches are currently among the major foci of experimental physics. The observation of such a decay will have important implications in our understanding of the intrinsic nature of neutrinos and shed light on the limitations of the Standard Model. The rate of this process depends on both the unknown neutrino effective mass and the nuclear matrix element associated with the given neutrinoless double-beta decay transition. The latter can only be provided by theoretical calculations, hence the need of accurate theoretical predictions of the nuclear matrix element f…
We present the first ab initio calculations of neutrinoless double beta decay matrix elements in $A=6$-$12$ nuclei using Variational Monte Carlo wave functions obtained from the Argonne $v_{18}$ two-nucleon potential and Illinois-7 three-nucleon interaction. We study both light Majorana neutrino exchange and potentials arising from a large class of multi-TeV mechanisms of lepton number violation. Our results provide benchmarks to be used in testing many-body methods that can be extended to the heavy nuclei of experimental interest. In light nuclei we have also studied the impact of two-body sh…
We study neutrinoless double-beta decay in an effective field theory (EFT) for heavy nuclei, which are treated as a spherical core coupled to additional neutrons and/or protons. Since the low-energy constants of the EFT cannot be fitted to data for this unobserved decay, we follow an alternative strategy to constrain these through a correlation with double Gamow-Teller transitions. This correlation was recently found to hold for shell-model calculations, energy-density functionals, and other nuclear structure models. We therefore first calculate the nuclear matrix elements for double Gamow-Tel…
Theoretical estimates for the half life of neutrinoless double beta decay in candidate nuclei are affected by both particle and nuclear physics uncertainties, which may complicate the interpretation of decay signals or limits. We study such uncertainties and their degeneracies in the following context: three nuclei of great interest for large-scale experiments (76-Ge, 130-Te, 136-Xe), two representative particle physics mechanisms (light and heavy Majorana neutrino exchange), and a large set of nuclear matrix elements (NME), computed within the quasiparticle random phase approximation (QRPA). …
The neutrinoless double beta decay is analyzed using a general Lorentz invariant effective Lagrangian for various decaying nuclei of current experimental interest: $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{130}$Te, and $^{136}$Xe. We work out the half-lives and angular correlation coefficients of the outgoing electrons in several scenarios for new physics: the left-right symmetric models, the R-parity-violating SUSY and models with leptoquarks. The theoretical uncertainty in the nuclear matrix elements is discussed.
We analyze nuclear matrix elements (NME) of neutrinoless double beta decay calculated for the Cadmium isotopes. Energy density functional methods including beyond mean field effects such as symmetry restoration and shape mixing are used. Strong shell effects are found associated to the underlying nuclear structure of the initial and final nuclei. Furthermore, we show that NME for two-neutrino double beta decay evaluated in the closure approximation, $M^{2ν}_{\mathrm{cl}}$, display a constant proportionality with respect to the Gamow-Teller part of the neutrinoless NME, $M^{0ν}_{\mathrm{GT}}$. …
We present the nuclear matrix element for the neutrinoless double-beta decay of $^{48}$Ca based on large-scale shell-model calculations including two harmonic oscillator shells ($sd$ and $pf$ shells). The excitation spectra of $^{48}$Ca and $^{48}$Ti, and the two-neutrino double-beta decay of $^{48}$Ca are reproduced in good agreement to experiment. We find that the neutrinoless double-beta decay nuclear matrix element is enhanced by about 30\% compared to $pf$-shell calculations. This reduces the decay lifetime by almost a factor of two. The matrix-element increase is mostly due to pairing co…
We explore the influence of the deformation on the nuclear matrix elements of the neutrinoless double beta decay (NME), concluding that the difference in deformation -or more generally in the amount of quadrupole correlations- between parent and grand daughter nuclei quenches strongly the decay. We correlate these differences with the seniority structure of the nuclear wave functions. In this context, we examine the present discrepancies between the NME's obtained in the framework of the Interacting Shell Model and the Quasiparticle RPA. We surmise that part of the discrepancy can be due to th…
Neutrinoless double-beta decay is a forbidden, lepton-number-violating nuclear transition whose observation would have fundamental implications for neutrino physics, theories beyond the Standard Model and cosmology. In this review, we summarize the theoretical progress to understand this process, the expectations and implications under various particle physics models, as well as the nuclear physics challenges that affect the precise predictions of the decay half-life. We will also provide a synopsis of the current and future large-scale experiments that aim at discovering this process in physi…
A derivation of the neutrinoless double beta decay rate, specially adapted for the nuclear structure calculations, is presented. It is shown that the Fourier-Bessel expansion of the hadronic currents, jointly with the angular momentum recoupling, leads to very simple final expressions for the nuclear form factors. This greatly facilitates the theoretical estimate of the half life. Our approach does not require the closure approximation, which however can be implemented if desired. The method is exemplified for the $ββ$ decay $^{48}Ca \to ^{48}Ti$, both within the QRPA and a shell-model like mo…
In a previous article [Phys. Rev. D 79, 053001 (2009)] we estimated the correlated uncertainties associated to the nuclear matrix elements (NME) of neutrinoless double beta decay (0 nu beta beta) within the quasiparticle random phase approximation (QRPA). Such estimates encompass recent independent calculations of NMEs, and can thus still provide a fair representation of the nuclear model uncertainties. In this context, we compare the claim of 0 nu beta beta decay in Ge-76 with recent negative results in Xe-136 and in other nuclei, and we infer the lifetime ranges allowed or excluded at 90% C.…
We compute nuclear matrix elements for neutrinoless double electron capture on $^{152}$Gd, $^{164}$Er and $^{180}$W nuclei. Recent precise mass measurements for these nuclei have shown a large resonance enhancement factor that makes them the most promising candidates for observing this decay mode. We use an advanced energy density functional method which includes beyond mean-field effects such as symmetry restoration and shape mixing. Our calculations reproduce experimental charge radii and $B(E2)$ values predicting a large deformation for all these nuclei. This fact reduces significantly the …
We use Lee-Suzuki mappings and related techniques to construct effective two-body p-shell interactions and neutrinoless double-beta operators that exactly reproduce the results of large no-core-shell-model calculations of double-beta decay in nuclei with mass number A=6. We then apply the effective operators to the decay of nuclei with A=7, 8, and 10, again comparing with no-core calculations in much larger spaces. The results with the effective two-body operators are generally good. In some cases, however, they differ non-negligibly from the full no-core results, suggesting that three-body co…
Nuclear weak decays provide important probes to fundamental symmetries in nature. A precise description of these processes in atomic nuclei requires comprehensive knowledge on both the strong and weak interactions in the nuclear medium and on the dynamics of quantum many-body systems. In particular, an observation of the hypothetical double beta decay without emission of neutrinos ($0νββ$) would unambiguously demonstrate the Majorana nature of neutrinos and the existence of the lepton-number-violation process. It would also provide unique information on the ordering and absolute scale of neutr…
We calculate the nuclear matrix elements (NMEs) for neutrinoless double-beta decays ($0νββ$) of $pf$-shell nuclei using the shell model (SM) and energy density functional (EDF) methods. The systematic study of non-physical decays (except for $^{48}$Ca) of Ca$\rightarrow$Ti, Ti$\rightarrow$Cr and Cr$\rightarrow$Fe allows for a detailed comparison between the two nuclear structure approaches. We observe that while the dominant Gamow-Teller part of the NME differs roughly by a factor of two between SM and EDF, when we restrict the calculations to spherical EDF states and seniority-zero SM configu…
We decompose the neutrinoless double-beta decay matrix elements into sums of products over the intermediate nucleus with two less nucleons. We find that the sum is dominated by the J^pi=0^+ ground state of this intermediate nucleus for both the light and heavy neutrino decay processes. This provides a new theoretical tool for comparing and improving nuclear structure models. It also provides the connection to two-nucleon transfer experiments.
Benchmark comparisons between many-body methods are performed to assess the ingredients necessary for an accurate calculation of neutrinoless double beta decay matrix elements. Shell model and variational Monte Carlo (VMC) calculations are carried out for $A=10$ and $12$ nuclei. Different variational wavefunctions are used to evaluate the uncertainties in the {\it ab initio} calculations, finding fairly small differences between the VMC double beta decay matrix elements. For shell model calculations, the role of model space truncation, radial wavefunction choices, and short-range correlation a…
We study in this letter the behavior of the neutrinoless double beta decay nuclear matrix elements (NME's) in the framework of the Interacting Shell Model. We analize them in terms of the total angular momentum of the decaying neutron pair and as a function of the seniority truncations in the nuclear wave functions. This point of view turns out to be very adequate to gauge the accuracy of the NME's predicted by different nuclear structure models. In addition, it gives back the due protagonism in this process to the pairing interaction, the interaction which is responsible for the very existenc…
Results for neutrino flavor oscillations and neutrino mixing mechanisms, obtained from the analysis of the Sudbury Neutrino Observatory (SNO), the SuperKamiokande (SK), CHOOZ, KamLAND and WMAP data, are used to calculate the effective neutrino mass relevant for the neutrinoless double-beta decay. The observability of the decay of 76Ge is discussed within different light-neutrino mass hierarchies and by presenting a systematics on the available nuclear matrix elements.
The physics potential of neutrinoless double beta decay is discussed. Furthermore, experimental considerations are presented as well as the current status of experiments. Finally an outlook towards the future, work on nuclear matrix elements and alternative processes is given.
We study the double Gamow-Teller (DGT) strength distribution of $^{48}$Ca with state-of-the-art large-scale nuclear shell model calculations. Our analysis shows that the centroid energy of the DGT giant resonance depends mostly on the isovector pairing interaction, while the resonance width is more sensitive to isoscalar pairing. Pairing correlations are also key in neutrinoless $ββ$ ($0νββ$) decay. We find a simple relation between the centroid energy and width of the $^{48}$Ca DGT giant resonance and %the value of the $0νββ$ decay nuclear matrix element. More generally, we observe a very goo…
It is generally accepted that double neutrinoless electron capture is a resonance process. The calculations of the probability of shaking with the ionization of the electron shell occurring during the transformation of 152Gd and 164Er nuclei are performed below. These nuclides have the lowest resonance defect among all known nuclei, being considered as main candidates for discovering the neutrinoless mode of the transformation. The results show predominant contribution of the new mechanism for most of the candidate nuclei. The value of this amendment rapidly increases with an increasing resona…
Nuclear matrix elements (NMEs) for neutrinoless double beta decays (DBDs) are required for studying neutrino physics beyond the standard model by DBD. The experimental spin-dipole (SD) giant resonance energy and the SD strength are shown for the first time to be closely related to the DBD-NME, and are used for studying the spin-isospin correlation and the quenching of the axial-vector coupling. So they are used to help the theoretical model calculation of the DBD-NME.
We study the impact of new physics contributions to neutrinoless double beta decay arising from right-handed current in comparison with the standard mechanism. If the light neutrinos obtain their masses from Type-II seesaw within left-right symmetric model, where the Type-I contribution is suppressed to negligible extent, the right-handed PMNS matrix is the same as its left-handed counterpart, making it highly predictable and can be tested at next-generation experiments. It is very attractive, especially with recent cosmological constraint favoring the normal hierarchy under which the neutrino…
The variances and covariances associated to the nuclear matrix elements (NME) of neutrinoless double beta decay are estimated within the quasiparticle random phase approximation (QRPA). It is shown that correlated NME uncertainties play an important role in the comparison of neutrinoless double beta decay rates for different nuclei, and that they are degenerate with the uncertainty in the reconstructed Majorana neutrino mass.
Background: The discovery of neutrinoless double-beta ($0νββ$) decay would demonstrate the nature of neutrinos, have profound implications for our understanding of matter-antimatter mystery, and solve the mass hierarchy problem of neutrinos. The calculations for the nuclear matrix elements $M^{0ν}$ of $0νββ$ decay are crucial for the interpretation of this process. Purpose: We study the effects of relativity and nucleon-nucleon short-range correlations on the nuclear matrix elements $M^{0ν}$ by assuming the mechanism of exchanging light or heavy neutrinos for the $0νββ$ decay. Methods: The nuc…
We investigate a novel method of accurate calculation of the neutrinoless double-$β$ decay shell-model nuclear matrix elements for the experimentally relevant case of $^{76}$Ge. We demonstrate that with the new method the nuclear matrix elements have perfect convergence properties and, using only the first 100 intermediate states of each spin, the matrix elements can be calculated with better than 1% accuracy. Based on the analysis of neutrinoless double-beta decays of $^{48}$Ca, $^{82}$Se, and $^{76}$Ge isotopes, we propose a new method to estimate the optimal values of the average closure en…
In this article, we analyze some nuclear structure aspects of the neutrinoless double beta decay nuclear matrix elements (NME), in the framework of the Interacting Shell Model. We give results for the decays of 48Ca, 76Ge, 82Se, 124Sn, 128Te, 130Te, and 136Xe, using improved effective interactions and valence spaces. We examine the dependence of the NME's on the effective interaction and the valence space, and analyze the effects of the short range correlations and the finite size of the nucleon. Finally we study the influence of the deformation on the values of the NME's.
We have developed a formalism, based on the Fourier-Bessel expansion, that facilitates the evaluation of matrix elements involving nucleon recoil operators, such as appear in serveral exotic forms of neutrinoless double beta decay ($ββ_{0ν}$). The method is illustrated by applying it to the ``charged'' majoron model, which is one of the few that can hope to produce an observable effect. From our numerical computations within the QRPA performed for $^{76}Ge$, $^{82}Se$, $^{100} Mo$, $^{128}Te$ and $^{150}Nd$ nuclei, we test the validity of approximations made in earlier work to simplify the new…
We report the results of a calculation of the nuclear matrix element of neutrinoless double-$β$ decay of $^{48}$Ca, carried out taking into account nucleon-nucleon correlations in both coordinate- and spin-space. Our numerical results, obtained using nuclear matter correlation functions, suggest that inclusion of correlations leads to a $\sim$ $20\%$ decrease of the matrix element, with respect to the shell model prediction. This conclusion is supported by the results of an independent calculation, in which correlation effects are taken into account using the spectroscopic factors of $^{48}$Ca…
The recently developed formalism for the evaluation of nuclear form factors in neutrinoless double beta decay is applied to $^{48}Ca$, $^{76}Ge$, $^{82}Se$, $^{100}Mo$, $^{128}Te$ and $^{130}Te$ nuclei. Explicit analytical expressions that follows from this theoretical development, in the single mode model for the decay of $^{48}Ca$, have been worked out. They are useful both for testing the full numerical calculations, and for analytically checking the consistency with other formalisms. Large configuration space calculations are compared with previous studies, where alternative formulations w…
In this paper a microscopic state-of-the-art approach to calculation of the nuclear matrix element $M^{0ν}$ for neutrinoless double beta decay with an account for nuclear deformation is presented in length and applied for $^{76}$Ge, $^{150}$Nd and $^{160}$Gd. The proton-neutron quasiparticle random phase approximation (QRPA) with a realistic residual interaction [the Brueckner $G$ matrix derived from the charge-depending Bonn (Bonn-CD) nucleon-nucleon potential] is used as the underlying nuclear structure model. The effects of the short range correlations and the quenching of the axial vector …
Weak interaction in nuclei represents a well-known venue for testing many of the fundamental symmetries of the Standard Model. In particular, neutrinoless double-beta decay offers the possibility to test Beyond Standard Model theories predicting that neutrinos are Majorana fermions and the lepton number conservation is violated. This paper focuses on an effective field theory approach to neutrinoless double-beta decay for extracting information regarding the properties of the Beyond Standard Model Lagrangian responsible for this process. We use shell model nuclear matrix elements and the lates…
We discuss a novel effect in neutrinoless double beta (0νββ) decay related with the fact that its underlying mechanisms take place in the nuclear matter environment. We study the neutrino exchange mechanism and demonstrate the possible impact of nuclear medium via Lepton Number Violating (LNV) 4-fermion interactions of neutrino with quarks from decaying nucleus. The net effect of these interactions is generation of an effective in-medium Majorana neutrino mass matrix. The enhanced rate of the 0νββ-decay can lead to the apparent incompatibility of observations of the 0νββ-decay with the value o…
The change in the configuration of valence protons between the initial and final states in the neutrinoless double-$β$ decay of $^{130}$Te $\rightarrow$ $^{130}$Xe and of $^{136}$Xe $\rightarrow$ $^{136}$Ba has been determined by measuring the cross sections of the ($d$,$^3$He) reaction with 101-MeV deuterons. Together with our recent determination of the relevant neutron configurations involved in the process, a quantitative comparison with the latest shell-model and interacting-boson-model calculations reveals significant discrepancies. These are the same calculations used to determine the n…
