Double Beta Decay, Nuclear Structure and Physics beyond the Standard Model

TL;DR

This paper reviews the significance of neutrinoless double beta decay ($0 uetaeta$) in understanding neutrino properties, compares theoretical models for calculating decay matrix elements, and explores how experimental data can reveal underlying mechanisms and CP violation.

Contribution

It provides a comprehensive review of theoretical methods for calculating $0 uetaeta$ matrix elements and discusses how to determine the decay mechanism from experimental data.

Findings

Comparison of QRPA, Shell Model, PHFB, IBM2 methods for matrix elements

Explicit formulas for transition matrix elements in $0 uetaeta$

Potential to test CP violation through interference terms

Abstract

Neutrinoless Double Beta Decay ($0\nu\beta\beta$) is presently the only known experiment to distinguisch between Dirac neutrinos, different from their antiparticles, and Majorana neutrinos, identical with their antiparticles. In addition $0\nu\beta\beta$ allows to determine the absolute scale of the neutrino masses. This is not possible with neutrino oscillations. To determine the neutrino masses one must assume, that the light Majorana neutrino exchange is the leading mechanism for $0\nu\beta\beta$ and that the matrix element of this transition can ba calculated reliably. The experimental $0\nu\beta\beta$ transition amplitude in this mechanism is a product of the light left handed effective Majorana neutrino mass and of this transition matrix element. The different methods, Quasi-particle Random Phase Approximation (QRPA), Shell Model (SM), Projected Hartree-Fock-Bogoliubov (PHFB) and Interacting Boson Model (IBM2) used in the literature and the reliability of the matrix elements in these approaches are reviewed. In the second part it is investigated how one can determine the leading mechanism or mechanisms from the data of the $0\nu\beta\beta$ decay in different nuclei. Explicite expressions are given for the transition matrix elements. is shown, that possible interference terms allow to test CP (Charge and Parity conjugation) violation.