Constraining neutrinoless double beta decay

A class of discrete flavor-symmetry-based models predicts constrained neutrino mass matrix schemes that lead to specific neutrino mass sum-rules (MSR). We show how these theories may constrain the absolute scale of neutrino mass, leading in most of the cases to a lower bound on the neutrinoless double beta decay effective amplitude.     

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.     

Nuclear moments for the neutrinoless double beta decay

A derivation of the neutrinoless double beta decay rate, specially adapted for nuclear structure calculations, is presented. It is shown that the Fourier-Bessel expansion of the hadronic currents, jointly with 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 ββ decay ⁴⁸Ca → ⁴⁸Ti, both within the QRPA and a shell-model like model.     

Mean-field effects on neutrinoless double beta decay

Mean-field effects on the nuclear matrix elements involved in the neutrinoless double beta (0νββ) decay of several double-electron and double-positron emitters have been studied within the framework of the relativistic quark-confinement model and the quasiparticle random-phase approximation. The single-particle energies of the model space have been generated both by using the standard Woods-Saxon parametrization of the mean field and adjusting the quasiparticle spectra with the data from neutron- and proton-odd nuclei. The 0νββ rates are found to be much less affected by the energies of the mean-field orbitals than the rates of the two-neutrino double beta decay. The present study suggests that the extracted effective neutrino masses vary within a factor of two when using different realistic single-particle bases in the calculations.     

Status of neutrinoless double beta decay searches

Neutrinoless double beta decay is one of the most sensitive tools in non-accelerator particle physics to probe the regime of physics beyond the standard model. It can provide in fact fundamental informations on the character of neutrinos and their absolute mass scale. The present status of experiments searching for neutrinoless double-beta decay (ββ(0ν)) is reviewed and the most relevant results discussed. Phenomenological aspects of ββ(0ν) are introduced. Given the observation of neutrino oscillations and the present knowledge of neutrino masses and mixing parameters, a possibility to observe ββ(0ν) at a neutrino mass scale m _ν in the range 10–50 meV could actually exist. The achievement of the required experimental sensitivity is a real challenge faced by a number of new proposed projects. A review of the various proposed experiments in the context of their figure-of-merit parameters is given. The most important parameters contributing to the experimental sensitivity are finally outlined. A short discussion on nuclear matrix element calculations is also given.     

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.     

Nuclear moments for the neutrinoless double beta decay II

The recently developed formalism for the evaluation of nuclear form factors in neutrinoless double beta decay is applied to ⁴⁸Ca, ⁷⁶Ge, ⁸²Se, ¹⁰⁰Mo, ¹²⁸Te and ¹³⁰Te nuclei. Explicit analytical expressions that follows from this theoretical development, in the single-mode model for the decay of ⁴⁸Ca, 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 were used. Yet, besides using the G-matrix as residual interaction, we here use a simple δ-force. Attention is paid to the connected effects of the short range nuclear correlations and the finite nucleon size. Constraints on lepton number violating terms in the weak Hamiltonian (effective neutrino Majorana mass and effective right-handed current coupling strengths) are deduced.     

Effective Majorana mass and neutrinoless double beta decay

The probability distribution for the effective Majorana mass as a function of the lightest neutrino mass in the standard three neutrino scheme is computed via a random sampling from the distributions of the involved mixing angles and squared mass differences. A flat distribution in the \([0,2\pi ]\) range for the Majorana phases is assumed, and the dependence of small values of the effective mass on the Majorana phases is highlighted. The study is then extended with the addition of the cosmological bound on the sum of the neutrino masses. Finally, the prospects for \(0\nu \beta \beta \) decay search with \(^{76}\)Ge, \(^{130}\)Te and \(^{136}\)Xe are discussed, as well as those for the measurement of the electron neutrino mass.     

Status and prospects of searches for neutrinoless double beta decay

The simultaneous beta decay of two neutrons in a nucleus without the emission of neutrinos (called neutrinoless double beta decay) is a lepton number violating process which is not allowed in the Standard Model of particle physics. More than a dozen experiments using different candidate isotopes and a variety of detection techniques are searching for this decay. Some (EXO‐200, Kamland‐Zen, and GERDA) started to take data recently. EXO and Kamland‐Zen have reported first limits of the half life for ¹³⁶Xe. After a decade of little progress in this field, these results start to scrutinize the claim from part of the Heidelberg–Moscow collaboration to have observed this decay. The sensitivities of the different proposals are reviewed.     

Present and future strategies for neutrinoless double beta decay searches

The renewed interest shown in these days towards neutrinoless double beta decay, a lepton number violating process which can take place only if neutrinos are Majorana particles (ν = \(\bar \nu \)) with a nonvanishing mass, is justified by the fact that the Majorana nature of neutrinos is expected in many theories beyond the Standard Model. We also now know, thanks to the neutrino oscillation experiments, that neutrinos are in fact massive, as expected in these theories and not requested in the Standard Model. Moreover, since neutrino oscillation experiments measure only the absolute value of the difference of the square of the neutrino masses, the discovery of neutrinoless double beta decay would help to disentangle questions that still remain unsolved: what is the absolute mass scale of the neutrinos and which mass hierarchy (normal, inverted or quasi-degenerate) is the correct one?The scope of this paper is not only to review the present results reached in the field by the different groups and technologies worldwide, but also to illustrate and comment on the (near and long-term) future strategies that experimentalists are trying to pursue to reach the needed sensitivity required to explore the inverted hierarchy neutrino mass scale.