Non-collapsing QRPA for neutrinoless double beta decay

The standard quasiparticle random phase approximation(QRPA) is widely used to describe the neutrinoless double beta decay process. Although it has been quite successful in many cases of interest, it has some shortcomings. The most important one is that its solutions collapse for physical values of the particle-particle strength. We shall show that modifications can be done which can extend the validity of this standard QRPA beyond the point of collapse. Such modifications are: The introduction of proton-neutron pairing, the inclusion of the Pauli principle and the extension of the Hilbert space. If all these modifications are introduced into the standard QRPA then the collapse does not occur for physical values of the particle-particle strengths. Thus, one might be able to extract more accurate values on the effective neutrino mass by using the best available experimental limits on the half life of neutrinoless double beta decay. Presented by G. Pantis at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997.     

Calculation of double beta decay rates and the neutrino mass

Predictions for 2v and 0v double beta decay rates are given for all nuclei with A ⩾ 70, for which double beta decay is energetically allowed. These predictions are based on detailed nuclear structure studies of the beta strength distribution and replace earlier estimates basing mostly on phase space considerations. New and more stringent limits on the Majorana neutrino mass are deduced from existing double beta decay experiments. Since the collective effects arising from spin-isospin as well as quadrupole-quadrupole forces are found to lead to a strong reduction of the nuclear matrix elements for two-neutrino double beta decay, but to have only minor influence on the matrix elements M^0v for the neutrinoless decay mode, the smaller limits for m_v result mainly from the fact that the widely used scaling procedure underestimates the 0_v matrix elements. It is further discussed to what extent interference between different neutrinos affects the obtained mass limits.     

The neutrinoless double-beta decay: A test for new physics

The neutrinoless double-beta decay is not allowed in the Standard Model (SM) but it is allowed in most Grand Unified Theories (GUTs). The neutrino must be a Majorana particle (identical with its antiparticle) and must have a mass to allow the neutrinoless double-beta decay. Apart of one claim that the neutrinoless double-beta decay in ⁷⁶Ge is measured, one has only upper limits for this transition probability. But even the upper limits allow to give upper limits for the electron Majorana neutrino mass and upper limits for parameters of GUTs and the minimal R-parity violating supersymmetric model. One further can give lower limits for the vector boson mediating mainly the right-handed weak interaction and the heavy mainly right-handed Majorana neutrino in left-right symmetric GUTs. For that, one has to assume that the specific mechanism is the leading one for the neutrinoless double-beta decay and one has to be able to calculate reliably the corresponding nuclear matrix elements. In the present contribution, one discusses the accuracy of the present status of calculating the nuclear matrix elements and the corresponding limits of GUTs and supersymmetric parameters.     

Structure of nuclear transition matrix elements for neutrinoless double-<Emphasis Type="Italic">β</Emphasis> decay

The structure of nuclear transition matrix elements (NTMEs) required for the study of neutrinoless double-β decay within light Majorana neutrino mass mechanism is disassembled in the PHFB model. The NTMEs are calculated using a set of HFB intrinsic wave functions, the reliability of which has been previously established by obtaining an overall agreement between the theoretically calculated spectroscopic properties and the available experimental data. Presently, we study the role of short-range correlations, radial evolution of NTMEs and deformation effects due to quadrupolar correlations. In addition, limits on effective light neutrino mass 〈m _ν 〉 are extracted from the observed limits on half-lives T ₁^2/0ν of neutrinoless double-β decay.     

Majorana neutrino masses and the neutrinoless double-beta decay

Neutrinoless double-beta decay is forbidden in the Standard Model of electroweak and strong interaction but allowed in most Grand Unified Theories (GUTs). Only if the neutrino is a Majorana particle (identical with its antiparticle) and if it has a mass is neutrinoless double-beta decay allowed. Apart from one claim that the neutrinoless double-beta decay in ⁷⁶Ge is measured, one has only upper limits for this transition probability. But even the upper limits allow one to give upper limits for the electron Majorana neutrino mass and upper limits for parameters of GUTs and the minimal R-parity-violating supersymmetric model. One further can give lower limits for the vector boson mediating mainly the right-handed weak interaction and the heavy mainly right-handed Majorana neutrino in left-right symmetric GUTs. For that, one has to assume that the specific mechanism is the leading one for neutrinoless double-beta decay and one has to be able to calculate reliably the corresponding nuclear matrix elements. In the present work, one discusses the accuracy of the present status of calculating of the nuclear matrix elements and the corresponding limits of GUTs and supersymmetric parameters. The text was submitted by the author in English.     

A study of neutrinoless double-beta decay in the framework of QRPA

A study concerning the valence space dependence of neutrinoless doubleβ ⁻ decay observables is performed for several nuclei in the framework of QRPA using the multiple commutator method (MCM). Calculations and comparison to earlier results show that at least for the ground state to ground state transition the dependence is much weaker than in the two neutrino doubleβ ⁻ decay. It is still a difficult task to extract the parameters of the neutrinoless doubleβ ⁻ decay since the half-life expression contains products of the parameters 〈m _ν 〉 〈η〉 and 〈λ〉. Presented by M. Aunola at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997.     

Limits of Majorana neutrino mass from combined analysis of data from <Superscript>76</Superscript>Ge and <Superscript>136</Superscript>Xe neutrinoless double beta decay experiments

We present effective Majorana neutrino mass limits <m _ββ> 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 <m _ββ> less than [85.4–197.0] meV are much closer to the inverse neutrino mass hierarchy region.     

Neutrinoless double beta decay and a new limit on the lepton number violation

We have calculated the neutrinoless double beta decay rate of ⁷⁶Ge. We take into account for the first time a relativistic correction to the nuclear current including weak magnetism. Its effect is to cancel a considerable part of the decay amplitude and we obtain less stringent upper limits on the neutrino Majorana mass and the right-handed weak leptonic current compared with previous calculations.     

Suppression of the neutrinoless ββ decay?

The neutrinoless ββ decay rates of ⁷⁶Ge, ⁸²Se, ^{128, 130}Te are calculated in the quasi-particle random appproximation using a realistic effective NN interaction. The reduction of the 0νββ decay nuclear matrix elements due to ground-state correlations is much weaker than that of the 2νββ decay matrix elements, and we can deduce stringent limits on the Majorana neutrino mass and the right-handed leptonic currents from experimental data on νββ decay.     

Extended operator expansion method for neutrinoless double beta decay

Reliable calculations of nuclear matrix elements are a prerequisite for the determination of the effective neutrino mass and other particle physics parameters from neutrinoless double beta decay. Here, the operator expansion method is improved by including Coulomb, tensor and central interactions simultaneously. Furthermore, the formalism of the OEM is extended to those matrix elements necessary to extract the right-handed parameters and from 0 decay. OEM includes the dependence of the nuclear matrix elements on the intermediate states implicitly and can therefore be understood as a step beyond the closure approximation. Numerical studies are carried out for the isotope⁷⁶Ge combining the OEM expressions with ground-state wave functions calculated within a proton-neutron quasiparticle Random Phase Approximation (pn-QRPA) model. The influence and relative importance of central, tensor and Coulomb interactions is investigated. Within the OEM, contributions from the Coulomb force are found to be negligible in 0 decay, while the tensor force leads to a moderate change of the results, of the order of (10–30)%, giving a better agreement between sets of calculations which employ different NN-interactions. Generally, results of the OEM+QRPA calculation are similar to previous calculations of 0 decay matrix elements, indicating that 0 decay is not sensitive to model approximations and might therefore be more accurately calculated than the strongly suppressed 2 decay matrix elements.     

Neutrinoless double-β decay: Status and future

A brief summary of the status of neutrino masses, mixing, and oscillations is presented. Neutrinoless double β decay is considered. Predictions for the effective Majorana mass are reviewed. A possible test of the calculations of nuclear matrix elements of the 0νββ decay is proposed. The text was submitted by the authors in English.     

No-go for detecting CP violation via neutrinoless double beta decay

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 0νββ decay are calculable, it will be impossible to detect neutrino CP violation arising from Majorana phases.     

Dooble beta decay: Operator expasion method revisited

The Operator Expansion Method (OEM) for the calculation of two-neutrino double beta decay (2ν2β-decay) is reconsidered. The assumed two-body Hamiltonian, in contrast to the ones considered previously, allows a consistent derivation of the OEM transition operators. The OEM is combined with the renormalized proton-neutron QRPA (pn-RQRPA) ground state wave functions and the 2ν2β-decay of⁷⁶Ge is calculated. The influence and relative importance of the central, tensor and Coulomb interactions are investigated. We have found that the strong suppression of the nuclear matrix elementM _GT has its origin in the choice of the pn-RQRPA ground state wave functions of the initial and final nuclei. Presented by M. Veselsky at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997.     

Nuclear structure effects on the neutrinoless double beta decay

The nuclear matrix elements of the 0ν ββ decay of⁷⁶Ge,⁸²Se,¹⁰⁰Mo,^128,130Te,¹³⁶Xe and¹⁵⁰Nd are calculated in the proton-neutron quasiparticle RPA with theG-matrix of the Paris potential. It is shown that the matrix elements are not sensitive to details of nuclear structure, in contrast to the 2ν ββ decay. We investigate effects of ground-state correlations and those of short-range correlations on the suppression of the nuclear matrix elements. We also discuss effective values of the neutrino mass which are deduced from experimental 0ν ββ decay half-lives.     

Neutrinoless ββ decay and the electron neutrino mass

We discuss the nuclear structure elements participant in the calculation of the half-life of the neutrinoless double beta decay, and the consequences upon the adopted limits of the electron-neutrino mass. Presented by O. Civitarese at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’05), Corfu, Greece, September 26–29, 2005.     

Neutrinoless Double Beta Decay-A New Formalism

A new method-the operator expansion method is used in neutrinoless double beta decay processes. Both the neutrino mass and mixing of right-handed leptonic current are included. It is shown that for nuclear neutrinoless double beta decay in 2n mechanism, there appear some new terms besides the terms given by the conventional treatment based on closure approximation. The ββ with a Majoron emission is also discussed.     

Uncertainties in the 0νββ-decay nuclear matrix elements

The nuclear matrix elements M ^0ν of the neutrinoless double-beta decay (0νβ β) of most nuclei with known 2νββ-decay rates are systematically evaluated using the Quasiparticle Random Phase Approximation (QRPA) and Renormalized QRPA (RQRPA). The experimental 2νβ β-decay rate is used to adjust the most relevant parameter, the strength of the particle-particle interaction. With such procedure the M ^0ν values become essentially independent of single-particle basis size, the axial vector quenching factor, etc. Theoretical arguments in favor of the adopted way of determining the interaction parameters are presented. It is suggested that most of the spread among the published M ^0ν ’s can be ascribed to the choices of implicit and explicit parameters, inherent to the QRPA method. Presented by V. Rodin at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’05), Corfu, Greece, September 26–29, 2005.     

Neutrinoless Double-Beta Decay to Excited 0+ States Mediated by Light Majorana Neutrinos

The neutrinoless double-beta decay (0 decay) to the first excited 0⁺ collective final state is examined for A = 76, 82, 100 and 136 nuclei by assuming light Majorana neutrino exchange mechanism. Realistic calculations of nuclear matrix elements are 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. It is found that the ¹⁰⁰Mo is a good candidate for experimental study of the 0 decay to excited 0⁺ state due to small suppression of this transition relative to the transition to the ground state.     

Neutrinoless double beta decay and heavy sterile neutrinos

The experimental rate of neutrinoless double beta decay can be saturated by the exchange of virtual sterile neutrinos, that mix with the ordinary neutrinos and are heavier than 200 MeV. Interestingly, this hypothesis is subject only to marginal experimental constraints, because of the new nuclear matrix elements. This possibility is analyzed in the context of the Type I seesaw model, performing also exploratory investigations of the implications for heavy neutrino mass spectra, rare decays of mesons as well as neutrino-decay search, LHC, and lepton flavor violation. The heavy sterile neutrinos can saturate the rate only when their masses are below some 10 TeV, but in this case, the suppression of the light-neutrino masses has to be more than the ratio of the electroweak scale and the heavy-neutrino scale; i.e., more suppressed than the naive seesaw expectation. We classify the cases when this condition holds true in the minimal version of the seesaw model, showing its compatibility (1) with neutrinoless double beta rate being dominated by heavy neutrinos and (2) with any light neutrino mass spectra. The absence of excessive fine-tunings and the radiative stability of light neutrino mass matrices, together with a saturating sterile neutrino contribution, imply an upper bound on the heavy neutrino masses of about 10 GeV. We extend our analysis to the Extended seesaw scenario, where the light and the heavy sterile neutrino contributions are completely decoupled, allowing the sterile neutrinos to saturate the present experimental bound on neutrinoless double beta decay. In the models analyzed, the rate of this process is not strictly connected with the values of the light neutrino masses, and a fast transition rate is compatible with neutrinos lighter than 100 meV.     

First results of the search for neutrinoless double-beta decay with the NEMO 3 detector

The NEMO 3 detector, which has been operating in the Fréjus underground laboratory since February 2003, is devoted to the search for neutrinoless double-beta decay (beta beta 0v). The half-lives of the two neutrino double-beta decay (beta beta 2v) have been measured for 100Mo and 82Se. After 389 effective days of data collection from February 2003 until September 2004 (phase I), no evidence for neutrinoless double-beta decay was found from approximately 7 kg of 100Mo and approximately 1 kg of 82Se. The corresponding limits are T1/2(beta beta0v) > 4.6 x 10(23) yr for 100Mo and T1/2(beta beta 0v) > 1.0 x 10(23) yr for 82Se (90% C.L.). Depending on the nuclear matrix element calculation, the limits for the effective Majorana neutrino mass are < 0.7-2.8 e/v for 100Mo and < 1.7-4.9 eV for 82Se.