Fixed-t subtracted dispersion relations for Compton scattering off the nucleon

TL;DR

This paper develops fixed-t subtracted dispersion relations for nucleon Compton scattering at energies up to 500 MeV, enabling extraction of nucleon polarizabilities with minimal model dependence.

Contribution

The authors introduce a formalism using fixed-t subtracted dispersion relations to determine nucleon polarizabilities with reduced model assumptions.

Findings

Good description of $\gamma o \pi o \gamma$ and $\pi o \pi$ intermediate states.

Sensitivity analysis of polarizability difference $\alpha - eta$ and spin polarizability $\gamma_\pi$.

Constructed a unitarized amplitude for $\gamma o \pi o \pi$ process.

Abstract

We present fixed-$t$ subtracted dispersion relations for Compton scattering off the nucleon at energies $E_\gamma \leq$ 500 MeV, as a formalism to extract the nucleon polarizabilities with a minimum of model dependence. The subtracted dispersion integrals are mainly saturated by $\pi N$ intermediate states in the $s$-channel $\gamma N \to \pi N \to \gamma N$ and $\pi \pi$ intermediate states in the $t$-channel $\gamma \gamma \to \pi \pi \to N \bar N$. For the subprocess $\gamma \gamma \to \pi \pi$, we construct a unitarized amplitude and find a good description of the available data. We show results for Compton scattering using the subtracted dispersion relations and display the sensitivity on the scalar polarizability difference $\alpha - \beta$ and the backward spin polarizability $\gamma_\pi$, which enter directly as fit parameters in the present formalism.