Proton scalar dipole polarizabilities from real Compton scattering data, using fixed-t subtracted dispersion relations and the bootstrap method

Abstract

We perform a fit of the real Compton scattering (RCS) data below pion-production threshold to extract the electric ($\alpha_{E1}$) and magnetic ($\beta_{M1}$) static scalar dipole polarizabilities of the proton, using fixed-$t$ subtracted dispersion relations and a bootstrap-based fitting technique. The bootstrap method provides a convenient tool to include the effects of the systematic errors on the best values of $\alpha_{E1}$ and $\beta_{M1}$ and to propagate the statistical errors of the model parameters fixed by other measurements. We also implement various statistical tests to investigate the consistency of the available RCS data sets below pion-production threshold and we conclude that there are not strong motivations to exclude any data point from the global set. Our analysis yields $\alpha_{E1} = (12.03^{+0.48}_{-0.54})\times 10^{-4} \text{fm}^3$ and $\beta_{M1} = (1.77^{+0.52}_{-0.54})\times 10^{-4} \text{fm}^3$, with p-value $= 12\%$.