Compton scattering from chiral dynamics with unitarity and causality

TL;DR

This paper analyzes proton Compton scattering using chiral Lagrangian techniques, employing unitarity and causality constraints to improve predictions of spin observables and polarizabilities, highlighting rescattering effects.

Contribution

It introduces an analytic extrapolation method for partial-wave amplitudes in chiral perturbation theory constrained by fundamental principles, enhancing the understanding of proton polarizabilities.

Findings

Rescattering significantly affects diagonal polarizabilities.

Predictions align with strict chiral perturbation theory for transition polarizabilities.

Method stabilizes amplitude extrapolation using gauge invariance, causality, and unitarity.

Abstract

Proton Compton scattering is analyzed with the chiral Lagrangian. Partial-wave amplitudes are obtained by an analytic extrapolation of subthreshold reaction amplitudes computed in chiral perturbation theory, where the constraints set by electromagnetic-gauge invariance, causality and unitarity are used to stabilize the extrapolation. We present and discuss predictions for various spin observables and polarizabilties of the proton. While for the transition polarizabilities $\gamma_{E1M2}, \gamma_{M1E2}$ we recover the results of strict chiral perturbation theory, for the diagonal $\gamma_{E1E1}, \gamma_{M1M1}$ elements we find significant effects from rescattering.