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 (${\mathrm{EFT}}_{\pi /}$) and large-$N_c$ expansion, where $N_c$ is the number of colors in quantum chromodynamics (QCD). In elastic scattering, these operators contribute to $S\text{−}P$ and $P\text{−}D$ wave transitions, with five operators and their accompanying low energy coefficients (LECs) characterizing the $S\text{−}P$ transitions and six operators and LECs those in $P\text{−}D$ 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 ${\mathrm{EFT}}_{\pi /}$ LECs emerge in the large-$N_c$ expansion. We also discuss the renormalization group (RG) scale dependence of these LECs by considering two distinct limits: one in which large-$N_c$ relationships among LECs hold but RG-related approximate expansions do not, and vice versa. Our analysis can complement lattice QCD calculations and help prioritize future parity-violating experiments.

• Received 9 December 2020
• Revised 20 March 2021
• Accepted 12 April 2021

DOI:https://doi.org/10.1103/PhysRevC.103.054004

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Published by the American Physical Society