  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.
