I will present a unified large-Nc operator analysis of two-baryon contact interactions that simultaneously includes the SU(3) flavor octet (J^P = 1⁺) and decuplet (J^P = 3⁺) sectors within chiral effective field theory (ChEFT).
Starting from the most general non-derivative four-baryon Lagrangians, we perform a systematic non-relativistic expansion of baryon bilinears up to next-to-leading order (NLO) in three-momentum, obtaining closed-form contact potentials for BB, BD, and DD channels through O(Q2). At this stage the theory contains 134 low-energy constants (LECs)—28 at leading order and 106 at NLO—arising from 104 independent chiral couplings. We then impose a Hartree Hamiltonian expansion in 1/Nc up to next-to-next-to-leading order, match spin–flavor structures between the ChEFT potentials and the large-Nc operator basis, and derive a set of large-Nc sum rules.
These relations reduce the number of independent LECs from 134 to 66 without sacrificing the chiral or SU(3) structure, substantially increasing predictivity across octet–octet, octet–decuplet, and decuplet–decuplet channels.
I will highlight phenomenological consequences for Omega N and Omega Omega scattering as benchmarks where forthcoming lattice-QCD results can directly test the sum rules, and discuss implications for hypernuclear physics and dense-matter modeling in astrophysics. The talk will emphasize the operator-level derivation, the role of SU(3) flavor in organizing contact terms, and practical pathways to incorporate the reduced parameter sets in few-baryon calculations and global fits.