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 for the success of the experimental programs. This need drives the theoretical nuclear physics community to provide the most reliable calculations of the nuclear matrix elements. Among the various computational models adopted to solve the many-body nuclear problem, the shell model is widely considered as the basic framework of the microscopic description of the nucleus. Here, we review the most recent and advanced shell-model calculations of the nuclear matrix elements considering the light-neutrino-exchange channel for nuclei of experimental interest. We report the sensitivity of the theoretical calculations with respect to variations in the model spaces and the shell-model nuclear Hamiltonians.
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.
We point out that lepton number violation is possible even if neutrinos are Dirac particles. We illustrate this by constructing a simple model that allows for lepton number violation by four units only. As a consequence, neutrinoless double beta decay is forbidden, but neutrinoless quadruple beta decay is possible: $(A,Z) \to (A,Z+4) + 4 e^-$. We identify three candidate isotopes for this decay, the most promising one being Nd-150 due to its high $Q_{0ν4β}$-value of 2 MeV. Analogous processes, such as neutrinoless quadruple electron capture, are also possible. The expected lifetimes are extrem…
We review the potential to probe new physics with neutrinoless double beta decay $(A,Z) \to (A,Z+2) + 2 e^-$. Both the standard long-range light neutrino mechanism as well as short-range mechanisms mediated by heavy particles are discussed. We also stress aspects of the connection to lepton number violation at colliders and the implications for baryogenesis.
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.
The study of neutrinoless double beta decay is of outmost importance for neutrino physics. It is considered to be the gold plated channel to probe the fundamental character of neutrinos and to determine the neutrino mass. From the experimental point about nine different isotopes are explored for the search. After a general introduction follows a short discussion on nuclear matrix element calculations and supportive measurements. The current experimental status of double beta searches is presented followed by a short discussion of the ideas and proposals for large scale experiments.
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.
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.…
The connection of neutrino physics with neutrinoless double beta decay is reviewed. After presenting the current status of the PMNS matrix and the theoretical background of neutrino mass and lepton mixing, we will summarize the various implications of neutrino physics for double beta decay. The influence of light sterile neutrinos and other exotic modifications of the three neutrino picture is also discussed.
We consider perturbative one loop QCD corrections to the light neutrino contribution to neutrinoless double beta decay and find large enhancement to the rate. QCD corrections also generate structures which mimic new physics contributions usually considered. Within some approximations, the net effect seem to almost saturate the experimental limits, and therefore seems to implt that this is all there is to neutrinoless double beta decay.
We assess how well next generation neutrinoless double beta decay and normal neutrino beta decay experiments can answer four fundamental questions. 1) If neutrinoless double beta decay searches do not detect a signal, and if the spectrum is known to be inverted hierarchy, can we conclude that neutrinos are Dirac particles? 2) If neutrinoless double beta decay searches are negative and a next generation ordinary beta decay experiment detects the neutrino mass scale, can we conclude that neutrinos are Dirac particles? 3) If neutrinoless double beta decay is observed with a large neutrino mass el…
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…
We present a necessary condition on the solar oscillation amplitude for CP violation to be detectable through neutrinoless double beta (0νββ) decay. It depends only on the fractional uncertainty in the ν_e-ν_e element of the neutrino mass matrix. We demonstrate that even under very optimistic assumptions about the sensitivity of future experiments to the absolute neutrino mass scale, and on the precision with which nuclear matrix elements that contribute to 0νββdecay are calculable, it will be impossible to detect neutrino CP violation arising from Majorana phases.
We quantify the extent to which future experiments will test the existence of neutrinoless double-beta decay mediated by light neutrinos with inverted-ordered masses. While it remains difficult to compare measurements performed with different isotopes, we find that future searches will fully test the inverted ordering scenario, as a global, multi-isotope endeavor. They will also test other possible mechanisms driving the decay, including a large uncharted region of the allowed parameter space assuming that neutrino masses follow the normal ordering.
In the event of an observation of neutrinoless double beta decay, a relevant question would be: what lepton number violating physics is responsible for the decay? The exchange of Majorana neutrinos and/or supersymmetric particles may contribute. We point out that measurements of supersymmetric signals at the LHC, including single slepton production, could be used to help bound some supersymmetric processes contributing to neutrinoless double beta decay. LHC information about the supersymmetric spectrum could be combined with Bd-Bd bar mixing data in order to bound a competing neutrinoless doub…
We present a generator-coordinate calculation, based on a relativistic energy-density functional, of the low-lying spectra in the isotopes $^{150}$Nd and $^{150}$Sm and of the nuclear matrix element that governs the neutrinoless double-beta decay of the first isotope to the second. We carefully examine the impact of octupole correlations on both nuclear structure and the double-beta decay matrix element. Octupole correlations turn out to reduce quadrupole collectivity in both nuclei. Shape fluctuations, however, dilute the effects of octupole deformation on the double-beta decay matrix element…
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.
The modern theory of neutrinoless double beta decay includes a scaling factor that has often been treated inconsistently in the literature. The nuclear contribution to the decay half life can be suppressed by 15-20% when scaling factors are mismatched. Correspondingly, $<m_ν>$ is overestimated.
Neutrinoless double-beta decay is a unique process that could reveal physics beyond the Standard Model. Essential ingredients in the analysis of neutrinoless double-beta rates are the associated nuclear matrix elements. Most of the approaches used to calculate these matrix elements rely on the closure approximation. Here we analyze the light neutrino-exchange matrix elements of 48Ca neutrinoless double-beta decay and test the closure approximation in a shell-model approach. We calculate the neutrinoless double-beta nuclear matrix elements for 48Ca using both the closure approximation and a non…
Neutrinoless double beta decay is a hypothetical radioactive process which, if observed, would prove the neutrino to be a Majorana fermion: a particle that is its own antiparticle. In this lecture mini-series I discuss the physics of Majorana fermions and the connection between the nature of neutrino mass and neutrinoless double beta decay. We review Dirac and Majorana spinors, discuss methods of distinguishing between Majorana and Dirac fermions, and derive in outline the connection between neutrino mass and double beta decay rates. We conclude by briefly summarizing the experimental landscap…
Neutrinoless double beta decay has been the subject of intensive theoretical work as it represents the only practical approach to discovering whether neutrinos are Majorana particles or not, and whether lepton number is a conserved quantum number. Available calculations of matrix elements and phase-space factors are reviewed from the perspective of a future large-scale experimental search for neutrinoless double beta decay. Somewhat unexpectedly, a uniform inverse correlation between phase space and the square of the nuclear matrix element emerges. As a consequence, no isotope is either favore…
We have investigated the role of proton-neutron pairing in the context of the Quasiparticle Random Phase approximation formalism. This way the neutrinoless double beta decay matrix elements of the experimentally interesting A= 48, 76, 82, 96, 100, 116, 128, 130 and 136 systems have been calculated. We have found that the inclusion of proton-neutron pairing influences the neutrinoless double beta decay rates significantly, in all cases allowing for larger values of the expectation value of light neutrino masses. Using the best presently available experimental limits on the half life-time of neu…
Neutrinoless double beta decay experiments constrain one combination of neutrino parameters, while cosmic surveys constrain another. This complementarity opens up an exciting range of possibilities. If neutrinos are Majorana particles, and the neutrino masses follow an inverted hierarchy, then the upcoming sets of both experiments will detect signals. The combined constraints will pin down not only the neutrino masses but also constrain one of the Majorana phases. If the hierarchy is normal, then a beta decay detection with the upcoming generation of experiments is unlikely, but cosmic surveys…
Heavy neutrino potential for neutrinoless double beta decay is studied with focusing on its statistical property. The existence condition for heavy neutrinos is also presented. In particular sterile neutrinos are possible candidate for heavy nuetrinos. The statistics provide a gross view of understanding amplitude of constitutional components of the nuclear matrix element.
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.
In this work we use the recently measured neutron occupancies in the 76Ge and 76Se nuclei as a guideline to define the neutron quasiparticle states in the 1p0f0g shell. We define the proton quasiparticles by inspecting the odd-mass nuclei adjacent to 76Ge and 76Se. We insert the resulting quasiparticles in a proton-neutron quasiparticle random-phase approximation (pnQRPA) calculation of the nuclear matrix element of the neutrinoless double beta (0-nu-beta-beta) decay of 76Ge. A realistic model space and effective microscopic two-nucleon interactions are used. We include the nucleon-nucleon sho…
In this work we report on the effects of short-range correlations upon the matrix elements of neutrinoless double beta decay. We focus on the calculation of the matrix elements of the neutrino-mass mode of neutrinoless double beta decays of 48Ca and 76Ge. The nuclear-structure components of the calculation, that is the participant nuclear wave functions, have been calculated in the shell-model scheme for 48Ca and in the proton-neutron quasiparticle random-phase approximation (pnQRPA) scheme for 76Ge. We compare the traditional approach of using the Jastrow correlation function with the more co…
Statistical spectral distribution method based on shell model and random matrix theory is developed for calculating neutrinoless double beta decay nuclear transition matrix elements. First results obtained for $^{82}$Se and $^{76}$Ge using the spectral method are close to the available shell model results.
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.
Neutrinoless double beta decay can significantly help to shed light on the issue of non-zero neutrino mass, as observation of this lepton number violating process would imply neutrinos are Majorana particles. However, the underlying interaction does not have to be as simple as the standard neutrino mass mechanism. The entire variety of neutrinoless double beta decay mechanisms can be approached effectively. In this work we focus on a theoretical description of short-range effective contributions to neutrinoless double beta decay, which are equivalent to 9-dimensional effective operators incorp…
Neutrino potential for neutrinoless double beta decay is studied with focusing on its statistical property. The statistics provide a gross view of understanding amplitude of constitutional components of the nuclear matrix element.
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.
Using the renormalized quasiparticle random phase approximation (RQRPA), we calculate the light neutrino mass mediated mode of neutrinoless double beta decay of Ge76, Mo100, Te128 and Te130. Our results indicate that the simple quasiboson approximation is not good enough to study the neutrinoless double beta decay, because its solutions collapse for physical values of g_pp. We find that extension of the Hilbert space and inclusion of the Pauli Principle in the QRPA with proton-neutron pairing, allows us to extend our calculations beyond the point of collapse, for physical values of the nuclear…
A comprehensive analysis of the structure of the nuclear matrix elements (NMEs) of neutrinoless double beta-minus decays to the 0^+ ground and first excited states is performed in terms of the contributing multipole states in the intermediate nuclei of neutrinoless double beta-minus transitions. We concentrate on the transitions mediated by the light (l-NMEs) Majorana neutrinos. As nuclear model we use the proton-neutron quasiparticle random-phase approximation (pnQRPA) with a realistic two-nucleon interaction based on the Bonn one-boson-exchange G matrix. In the computations we include the ap…
We study neutrinoless double beta decay of several isotopes with state-of-the-art beyond self-consistent mean field methods to compute the nuclear matrix elements (NME). Generating coordinate method with particle number and angular momentum projection (GCM+PNAMP) is used for finding mother and granddaughter states and evaluating transition operators between different nuclei. We analyze explicitly the role of the deformation, pairing and configuration mixing in the evaluation of the NME.
We report on the calculation of the neutrinoless double-beta decay nuclear matrix element for 76Ge within the framework of the realistic shell model. The effective shell-model Hamiltonian and the two-body transition operator describing the decay are derived by way of many-body perturbation theory. Particular attention is focused on the role played by the so-called Pauli blocking effect in the derivation of the effective operator.
We test the effects of an approximate treatment of two-body contributions to the axial-vector current on the QRPA matrix elements for neutrinoless double-beta decay in a range of isotopes. The form and strength of the two-body terms come from chiral effective-field theory. The two-body currents typically reduce the matrix elements by about 20%, not as much as in shell-model calculations. One reason for the difference is that standard practice in the QRPA is to adjust the strength of the isoscalar pairing interaction to reproduce two-neutrino double-beta decay lifetimes. Another may be the larg…
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 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 in…
We demonstrate that in the process of deducing the constraint on the electroweak mixing angle $θ_{W}$ in our paper, we have indeed been working with three mass scales while implementing (331) model.
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…
While the discovery of non-zero neutrino masses is one of the most important accomplishments by physicists in the past century, it is still unknown how and in what form these masses arise. Lepton number-violating neutrinoless double beta decay is a natural consequence of Majorana neutrinos and many BSM theories, and many experimental efforts are involved in the search for these processes. Understanding how neutrinoless double beta decay would manifest in nuclear environments is key for understanding any observed signals. In these proceedings we present an overview of a set of one- and two-body…
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 …
We present a new contribution of the R-parity violating supersymmetry (SUSY) to neutrinoless double beta decay via the pion exchange between decaying neutrons. The pion coupling to the final state electrons is induced by the R-parity violating SUSY interactions. We have found this pion-exchange mechanism to dominate over the conventional two-nucleon one. The latter corresponds to direct interaction between quarks from two decaying neutrons without any light hadronic mediator like pion. The constraints on the certain R-parity violating SUSY parameters are extracted from the current experimental…
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.
