The $1/N_c$ Operator Analysis of the Combined Octet and Decuplet Baryons Contact Interactions in SU(3) Chiral Effective Field Theory

TL;DR

This work develops a comprehensive framework to describe two-baryon contact interactions involving octet and decuplet baryons within SU(3) chiral EFT and the large-$N_c$ expansion. By performing a non-relativistic reduction and organizing the interactions with a $1/N_c$ Hartree Hamiltonian, the authors derive extensive operator structures and then match them to the chiral Lagrangian, obtaining sum rules that dramatically reduce the number of independent LECs from 134 to 13 at LO and to 24 at NNLO (up to $1/N_c^2$ corrections). The resulting constraints connect many sectors (BBBB, BBDB, DBDB, BBDD, DBDD, DDDD) and enable predictive relations for hyperon-containing channels, notably Omega–N and Omega–Omega scatterings, using lattice QCD inputs and KSW-like partial-wave analyses. The findings suggest strong cross-channel interdependencies among octet-octet LECs that can be tested against lattice data, providing a more economical and testable description of baryon-baryon forces in the SU(3) sector.

Abstract

In this work, we construct the non-derivative four-point interactions for Octet and Decuplet baryons in the SU(3) Chiral Effective Field Theory (ChEFT) framework, and there are 104 coupling constant terms. The non-relativistic expansion of the baryon fields has been considered up to the Next-to-Leading Order (NLO) of the three-momentum expansion. We find 28 and 106 Low-Energy Constants (LECs) for Leading Order (LO) and NLO, respectively. Using the Hartree Hamiltonian of the $1/N_c$ expansion of the operator product up to Next-to-Next-to-Leading Order (NNLO), we can reduce the free parameters (LECs) of the ChEFT from 134 down to 24 up to NLO of the three-momentum expansion. Moreover, we will discuss the implications of the $1/N_c$ sum rules in $ΩΩ$ and $ΩN$ scatterings, where the future results from lattice QCD can be used to test our sum rules.