Heavy Baryon Chiral Perturbation Theory with Light Deltas

TL;DR

This work extends heavy baryon chiral perturbation theory by treating the Delta(1232) as an explicit degree of freedom within a small scale expansion that counts the nucleon–Delta mass gap as a small parameter. It develops a comprehensive 1/M expansion for both spin-1/2 and spin-3/2 sectors, including simultaneous expansions for nucleons and Deltas, and derives leading and next-to-leading order heavy-baryon Lagrangians for NN, $N\Delta$, and $\Delta\Delta$ interactions with pions and photons. The paper also formulates an all-orders Small Scale Expansion and provides the complete ${\cal O}(\epsilon^2)$ counterterm Lagrangians, clarifying the structure and interpretation of mass, magnetic, and two-pion couplings. Together, these results establish a rigorous framework for near-threshold and resonance-region hadronic processes, enabling systematic connections between QCD and low-energy observables involving the Delta resonance.

Abstract

We demonstrate how heavy mass methods, previously applied to chiral perturbation theory calculations involving the interactions of nucleons and pions, can be generalized to include interactions with the $Δ(1232)$ in a systematic formalism which we call the "small scale expansion."