Subtracted Dispersion Relations for Virtual Compton Scattering off the Proton

TL;DR

This paper develops a refined dispersion relation formalism for virtual Compton scattering off protons, enabling more accurate extraction of nucleon polarizabilities from experimental data, especially near the $ riangle(1232)$ resonance.

Contribution

It introduces a once-subtracted dispersion relation approach that improves upon previous models by using data-driven methods for calculating dispersive integrals in the relevant energy region.

Findings

The formalism accurately reproduces VCS data.

Sensitivity analysis shows observables depend on scalar polarizabilities.

The approach enhances extraction precision of nucleon polarizabilities.

Abstract

We present a once-subtracted dispersion relation (DR) formalism for the virtual Compton scattering (VCS) process from threshold up to the $\Delta(1232)$ energy region. The formalism aims at extracting the nucleon's electric and magnetic generalized polarizabilities from the $e^- p \to e^- \gamma p$ process, in view of the precision goals of the present and near future experiments at Jefferson Lab. The present work improves upon the existing unsubtracted DR formalism in several ways. The required $s$- and $t$-channel discontinuities in the subtracted dispersion integrals are obtained in a largely data-driven manner in this energy region. The $s$-channel dispersive integrals are reconstructed from $\gamma^\ast p \to \pi N \to \gamma p$ using pion photo- and electro-production data, while the $t$-channel dispersion integrals are evaluated from $\gamma^\ast \gamma \to \pi \pi \to N \bar N$ using recent dispersive analyses of both the $\gamma^\ast \gamma \to \pi \pi$ and $\pi \pi \to N \bar N$ processes. We compare our results to VCS data and show the sensitivity of the observables to the nucleon's scalar generalized polarizabilities, which enter the present formalism as subtraction constants.