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 error bars.

https://iopscience.iop.org/article/10.1088/1361-6633/aa5bc5/pdf

Status and future of nuclear matrix elements for neutrinoless double-beta decay: a review.

Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review

Current status of the relativistic two nucleon one boson exchange potential

Low-energy πN partial wave analysis

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 into account when deriving bounds on the extra parameters. Conversely, the extra states can also have a significant impact, canceling the Standard Model neutrino contribution for masses lighter than the nuclear scale and leading to unobservable neutrinoless double beta decay amplitudes even if neutrinos are Majorana particles. In particular, the decay rate is reduced by at least six orders of magnitude for masses of the extra states below 1 MeV in absence of extra contributions. We also discuss how seesaw models could reconcile large rates of neutrinoless double beta decay with more stringent cosmological bounds on neutrino masses.

Neutrinoless double beta decay in seesaw models

Compilation of coupling constants and low-energy parameters

Compilation of Coupling Constants and Low-Energy Parameters. 1976 Edition

Coulomb corrections in non-relativistic scattering

Electromagnetic corrections to hadron - hadron scattering

We present a method of studying the strong baryonic decays of resonances (or analogously the couplings of bound states) which places emphasis on the dynamics of the decays. We introduce the idea of a total reduced width and show how broken SU(3) leads to relations and predictions for these reduced widths. We also comment on the implications of this work for the usual type of SU(3) fits, and on the values of various coupling constants.

B. Tromborg

Papers

Compilation of coupling constants and low-energy parameters

Compilation of Coupling Constants and Low-Energy Parameters. 1976 Edition

Coulomb corrections in non-relativistic scattering

Electromagnetic corrections to hadron - hadron scattering

Baryon Decays and SU(3) Breaking