Quark Cluster Model Equations for $\beta\beta$ Decay

TL;DR

This paper develops a formalism to evaluate the energy of six-quark cluster configurations relevant to double-beta decay, using symmetries like $SU_{cs}(6)$, $SU_{o}(6)$, and $SU_I(2)$, to understand their impact on decay rates.

Contribution

It introduces a new formalism for calculating energies of six-quark clusters in the context of double-beta decay, incorporating specific symmetry groups.

Findings

Formalism for six-quark cluster energy evaluation

Use of combined symmetries $SU_{cs}(6)$, $SU_{o}(6)$, $SU_I(2)$

Potential implications for double-beta decay rates

Abstract

In a separate paper we have discussed the possibility that six quark clusters can affect the rate of double-beta decay. In this article we develop the formalism needed in the evaluation of the energy of all six-quark cluster configurations, which can arise in a harmonic oscillator basis up to $2 \hbar \omega$ excitations. The symmetries that were found useful for this purpose were the combined spin color symmetry $SU_{cs}(6)$, the orbital symmetry $SU_{o}(6)$ and the isospin symmetry $SU_I(2)$.