Large-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>N</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math> analysis of two-nucleon neutrinoless double-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math> decay and charge-independence-breaking contact terms
Thomas R. Richardson, Matthias R. Schindler, Saori Pastore, Roxanne P. Springer
Abstract
The interpretation of experiments that search for neutrinoless double-$\ensuremath{\beta}$ decay relies on input from nuclear theory. Cirigliano et al. [Phys. Rev. Lett. 120, 202001 (2018)] recently showed that, for the light Majorana exchange formalism, effective field theory calculations require a $nn\ensuremath{\rightarrow}pp{e}^{\ensuremath{-}}{e}^{\ensuremath{-}}$ 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.