Time-reversal-invariance-violating nucleon-nucleon potential in the 1/N_c expansion

TL;DR

This paper uses the large-$N_c$ expansion to analyze the structure of time-reversal-invariance-violating nucleon-nucleon potentials, identifying dominant operator structures and deriving scaling relations for couplings.

Contribution

It constructs operator structures for TV nucleon-nucleon potentials at various orders and compares them with phenomenological models to establish large-$N_c$ scaling relations.

Findings

Single operator structure at leading order for TV and parity-violating case

Two leading-order terms in TV but parity-conserving potential, suppressed by 1/$N_c$

Derived large-$N_c$ scaling relations for TV meson-nucleon and nucleon-nucleon couplings

Abstract

We apply the large-$N_c$ expansion to the time-reversal-invariance-violating (TV) nucleon-nucleon potential. The operator structures contributing to next-to-next-to-leading order in the large-$N_c$ counting are constructed. For the TV and parity-violating case we find a single operator structure at leading order. The TV but parity-conserving potential contains two leading-order terms, which however are suppressed by 1/$N_c$ compared to the parity-violating potential. Comparison with phenomenological potentials, including the chiral EFT potential in the TV parity-violating case, leads to large-$N_c$ scaling relations for TV meson-nucleon and nucleon-nucleon couplings.