Predictions of chiral perturbation theory for Compton scattering off protons

TL;DR

This paper uses covariant baryon chiral perturbation theory to compute Compton scattering off protons, revealing significant differences from heavy-baryon approaches and highlighting the impact of the Δ(1232) resonance on nucleon polarizabilities.

Contribution

It demonstrates the advantages of covariant BχPT over HBχPT in describing Compton scattering and incorporates the Δ(1232) resonance effects naturally.

Findings

Covariant BχPT results differ notably from HBχPT, especially in forward kinematics.

The covariant approach satisfies forward-Compton-scattering sum rules.

Δ(1232) resonance significantly influences 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. We find that the substantial effect of the $\Delta$-excitation on the nucleon polarizabilities can naturally be accommodated in the manifestly covariant calculation.