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

Understand

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 $= 12\%$.