Large-$N_c$ and renormalization group constraints on parity-violating low-energy coefficients for three-derivative operators in pionless effective field theory

TL;DR

This paper extends the analysis of parity-violating operators in pionless EFT to three derivatives, using large-$N_c$ expansion to relate low-energy coefficients and guide experimental and lattice QCD efforts.

Contribution

It introduces a systematic large-$N_c$ expansion for three-derivative parity-violating operators in pionless EFT, revealing relationships among low-energy coefficients.

Findings

Large-$N_c$ separates operators into different orderings.

Relationships among low-energy coefficients are established.

Discussion of scale dependence of coefficients.

Abstract

We extend from operators with one derivative to operators with three derivatives the analysis of two-body hadronic parity violation in a combined pionless effective field theory (EFT$_{\pi\!/}$) and large-$N_c$ expansion, where $N_c$ is the number of colors in quantum chromodynamics (QCD). In elastic scattering, these operators contribute to $S$-$P$ and $P$-$D$ wave transitions, with five operators and their accompanying low energy coefficients (LECs) characterizing the $S$-$P$ transitions and six operators and LECs those in $P$-$D$ transitions. We show that the large-$N_c$ analysis separates them into leading order in $N_c$, next-to-leading order in $N_c$, etc. Relationships among EFT$_{\pi\!/}$ LECs emerge in the large-$N_c$ expansion. We also discuss the renormalization scale dependence of these LECs. Our analysis can complement lattice QCD calculations and help prioritize future parity-violating experiments.