Large- Nc and renormalization group constraints on parity-violating low-energy coefficients for three-derivative operators in pionless effective field theory
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 (EFTπ/) and large-Nc expansion, where Nc 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-Nc analysis separates them into leading order in Nc, next-to-leading order in Nc, etc. Relationships among EFTπ/ LECs emerge in the large-Nc expansion. We also discuss the renormalization group (RG) scale dependence of these LECs by considering two distinct limits: one in which large-Nc 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.