Partial-wave analysis of proton Compton scattering data below the pion-production threshold

TL;DR

This study performs a partial-wave analysis of proton Compton scattering data below the pion-production threshold to better understand proton polarizabilities and address discrepancies between theoretical models and experimental data.

Contribution

It introduces a partial-wave analysis approach to analyze proton Compton scattering data, highlighting the impact of data outliers on polarizability extraction and suggesting directions for future experiments.

Findings

The analysis shows high sensitivity to a few data outliers.

The difference between models is likely due to experimental data issues.

Proton scalar polarizability difference constrained to (6.8, 10.9)×10^{-4} fm^3.

Abstract

Low-energy Compton scattering off the proton is used for determination of the proton polarizabilities. However, the present empirical determinations rely heavily on the theoretical description(s) of the experimental cross sections in terms of polarizabilities. The most recent determinations are based on either the fixed-$t$ dispersion relations (DR) or chiral perturbation theory in the single-baryon sector ($\chi$PT). The two approaches obtain rather different results for proton polarizabilities, most notably for $\beta_{M1}$ (magnetic dipole polarizability). We attempt to resolve this discrepancy by performing a partial-wave analysis of the world data on proton Compton scattering below threshold. We find a large sensitivity of the extraction to a few "outliers", leading us to conclude that the difference between DR and $\chi$PT extraction is a problem of the experimental database rather than of "model-dependence". We have specific suggestions for new experiments needed for an efficient improvement of the database. With the present database, the difference of proton scalar polarizabilities is constrainedto a rather broad interval: $\alpha_{E1}-\beta_{M1} = (6.8\, \ldots \, 10.9)\times 10^{-4}$ fm$^3$, with their sum fixed much more precisely [to $14.0(2)$] by the Baldin sum rule.