Nucleon resonances in Compton scattering

TL;DR

This paper calculates nucleon resonance contributions to Compton scattering using a gauge-invariant tensor basis, deriving form factors and analyzing their impact on nucleon polarizabilities, with a focus on resonance states like Delta(1232) and N(1520).

Contribution

It introduces a Lorentz-invariant framework for nucleon resonance contributions to Compton scattering, including offshell transition vertices and simple form factor fits.

Findings

Resonance contributions to scalar and spin polarizabilities are generally small.

The N(1520) resonance may influence the proton's magnetic polarizability.

The Delta(1232) resonance significantly impacts nucleon polarizabilities.

Abstract

We calculate the nucleon resonance contributions to nucleon Compton scattering, including all states with J^P = 1/2^{+-} and J^P = 3/2^{+-} where experimental data for their electromagnetic transition form factors exist. To this end, we construct a tensor basis for the Compton scattering amplitude based on electromagnetic gauge invariance, crossing symmetry and analyticity. The corresponding Compton form factors provide a Lorentz-invariant description of the process in general kinematics, which reduces to the static and generalized polarizabilities in the appropriate kinematic limits. We derive the general forms of the offshell nucleon-to-resonance transition vertices that implement electromagnetic and spin-3/2 gauge invariance, which automatically also defines onshell transition form factors that are free of kinematic constraints. We provide simple fits for those form factors, which we use to analyze the resulting Compton form factors and extract their contributions to the nucleon's polarizabilities. Apart from the Delta(1232), the resonance contributions to the scalar and spin polarizabilites are very small, although the N(1520) could play a role for the proton's magnetic polarizability.