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

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.

16 pages, 1 figure, version accepted for publication in Physical Review C

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• Neutrinoless double-beta decay: combining quantum Monte Carlo and the nuclear shell model with the generalized contact formalism
• Ab-initio electroweak corrections to superallowed $\beta$ decays and their impact on $V_{ud}$
• Nuclear Effective Field Theories: Reverberations of the early days
• Light Sterile Neutrinos, Left-Right Symmetry, and $0\nu \beta \beta$ Decay
• Correlations Between Neutrinoless Double-Beta, Double Gamow-Teller and Double-Magnetic Decays in the pnQRPA Framework
• Neutrinoless double beta decay rates in the presence of light sterile neutrinos
• Recent progress in the electroweak structure of light nuclei using quantum Monte Carlo methods
• Light sterile neutrinos and lepton-number-violating kaon decays in effective field theory
• Impact of nuclear matrix element calculations for current and future neutrinoless double beta decay searches
• Large-$N_c$ constraints for elastic dark matter-light nucleus scattering in pionless effective field theory
• Building models of quarks and gluons with an arbitrary number of colors using Cartan-Polyakov loops
• Impact of dim-6 $\nu$SMEFT operators on low-scale leptogenesis