Manifestly-covariant chiral PT calculation of nucleon Compton scattering

TL;DR

This paper presents a covariant baryon chiral perturbation theory approach to nucleon Compton scattering, showing significant differences from heavy-baryon methods and including the effects of the Δ(1232) resonance on nucleon polarizabilities.

Contribution

It introduces a manifestly covariant calculation of nucleon Compton scattering that accurately incorporates the Δ(1232) resonance effects, improving upon previous heavy-baryon approaches.

Findings

Covariant approach yields different results from heavy-baryon calculations.

Forward-Compton-scattering sum rules are satisfied.

Δ(1232) resonance significantly affects nucleon polarizabilities.

Abstract

We compute the Compton scattering off the nucleons in the framework of manifestly covariant baryon chiral perturbation theory (B$\chi$PT). The results for observables differ substantially from the corresponding calculations in heavy-baryon chiral perturbation theory (HB$\chi$PT), most appreciably in the forward kinematics. We verify that the covariant $p^3$ result fulfills the forward-Compton-scattering sum rules. We also explore the effect of the $\Delta$(1232) resonance at order $p^4/\varDelta$, with $\varDelta\approx 300$ MeV, the resonance excitation energy. We find that the substantial effect of the $\Delta$-excitation on the nucleon polarizabilities can naturally be accommodated in the manifestly covariant calculation.