Evaluation of the forward Compton scattering off protons: I. Spin-independent amplitude

TL;DR

This paper evaluates the spin-independent forward Compton scattering amplitude off protons using dispersion relations and photoabsorption data, deriving polarizability sum rules and comparing results with existing data and models.

Contribution

It introduces two new fits to photoabsorption data and evaluates the proton's polarizability sum rules using these fits, providing updated estimates for polarizabilities.

Findings

Average sum of electric and magnetic polarizabilities: 14.0(2) x 10^{-4} fm^3

Evaluation of quadrupole polarizability sum rule

Comparison with previous evaluations and experimental data point at 2.2 GeV

Abstract

We evaluate the forward Compton scattering off the proton, based on Kramers-Kronig kind of relations which express the Compton amplitudes in terms of integrals of total photoabsorption cross sections. We obtain two distinct fits to the world data on the unpolarized total photoabsorption cross section, and evaluate the various spin-independent sum rules using these fits. For the sum of proton electric and magnetic dipole polarizabilities, governed by the Baldin sum rule, we obtain the following average (between the two fits): $\alpha_{E1}+\beta_{M1}=14.0(2)\times 10^{-4}\,\mathrm{fm}^3$. An analogous sum rule involving the quadrupole polarizabilities of the proton is evaluated too. The spin-independent forward amplitude of proton Compton scattering is evaluated in a broad energy range. The results are compared with previous evaluations and the only experimental data point for this amplitude (at 2.2 GeV). We remark on sum rules for the elastic component of polarizabilities.