Large-$N_c$ operator analysis of hyperon-nucleon interactions in SU(3) chiral effective field theory

TL;DR

This paper uses large-$N_c$ operator analysis within SU(3) chiral effective field theory to reduce free parameters in hyperon-nucleon interactions, showing better consistency with data when applying large-$N_c$ sum rules.

Contribution

It introduces a large-$N_c$ operator framework to constrain hyperon-nucleon interaction parameters, reducing the number of free parameters and improving model-data consistency.

Findings

Number of free parameters reduced from 15 to 6 at LO of $1/N_c$ expansion.

Large-$N_c$ sum rules decrease model parameters from 5 to 3.

Relativistic covariant ChEFT fits align better with large-$N_c$ predictions.

Abstract

We study octet-octet baryon ($J^P = {\textstyle \frac12}^+$) contact interactions in SU(3) chiral effective field theory by using large-$N_c$ operator analysis. Applying the $1/N_c$ expansion of the Hartee Hamiltonian, we find 15 operators in the octet-octet baryon potential where 4 operators for leading order (LO) and 11 for and net-to-next-to-leading order (NNLO). The large-$N_c$ operator analysis of octet-octet baryon matrix elements reduces the number of free parameters from 15 to 6 at LO of the $1/N_c$ expansion. The application of large-$N_c$ sum rules to the J\"{u}lich model of hyperon-nucleon (YN) interactions at the LO of the chiral expansion reduces the model parameters to 3 from 5 at the LO of $1/N_c$ expansion. We find that the values of LECs fitted to YN scattering data in Ref. \cite{Li:2016paq} in the relativistic covariant ChEFT (EG) approach is more consistent with the predictions of large-$N_c$ than in the heavy baryon (HB) formalism approach.