Large-$N_c$ analysis of two-nucleon neutrinoless double beta decay and charge-independence-breaking contact terms

TL;DR

This paper uses large-$N_c$ QCD analysis to justify and establish a hierarchy for charge-independence-breaking contact terms relevant to neutrinoless double beta decay, supporting effective field theory calculations.

Contribution

It provides a large-$N_c$ theoretical framework validating assumptions about CIB contact terms in neutrinoless double beta decay analysis.

Findings

Large-$N_c$ limit justifies assumptions about CIB operators.

Establishes a hierarchy among CIB nucleon-nucleon interactions.

Results align with phenomenological observations.

Abstract

The interpretation of experiments that search for neutrinoless double beta decay relies on input from nuclear theory. Cirigliano et al. recently showed that, for the light Majorana exchange formalism, effective field theory calculations require a $nn\to pp e^- e^-$ contact term at leading order. They estimated the size of this contribution by relating it to measured charge-independence-breaking (CIB) nucleon-nucleon interactions and making an assumption about the relative sizes of CIB operators. We show that the assumptions underlying this approximation are justified in the limit of the number of colors $N_c$ being large. We also obtain a large-$N_c$ hierarchy among CIB nucleon-nucleon interactions that is in agreement with phenomenological results.