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>?</mml:mi></mml:math> decay and charge-independence-breaking contact terms

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, 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 size this contribution by relating it to measured charge-independence-breaking (CIB) nucleon-nucleon interactions and making an assumption about relative sizes CIB operators. We show assumptions underlying approximation are justified in limit number colors, ${N}_{c}$, being large. also obtain large-${N}_{c}$ hierarchy among is agreement with phenomenological results.