Constraints from a large-N_c analysis on meson-baryon interactions at chiral order Q^3

TL;DR

This paper derives constraints on meson-baryon interactions at chiral order Q^3 using large-N_c QCD analysis, reducing the number of unknown parameters for practical applications.

Contribution

It constructs the complete set of Q^3 order counter terms for meson-baryon interactions and establishes 22 sum rules for low-energy constants based on large-N_c QCD.

Findings

24 chiral order Q^3 counter terms identified

22 sum rules reduce free parameters to 2

Only 2 parameters need experimental or lattice determination

Abstract

We consider the chiral Lagrangian for baryon fields with J^P =\frac{1}{2}^+ or J^P =\frac{3}{2}^+ quantum numbers as constructed from QCD with up, down and strange quarks. The specific class of counter terms that are of chiral order Q^3 and contribute to meson-baryon interactions at the two-body level is constructed. Altogether we find 24 terms. In order to pave the way for realistic applications we establish a set of 22 sum rules for the low-energy constants as they are implied by QCD in the large-N_c limit. Given such a constraint there remain only 2 independent unknown parameters that need to be determined by either Lattice QCD simulations or directly from experimental cross section measurements. At subleading order we arrive at 5 parameters.