Fixed-t subtracted dispersion relations for Compton scattering off the nucleon

Abstract

We present fixed-$t$ subtracted dispersion relations for Compton scattering off the nucleon at energies $E_{\hat{I}}^3\le$ 500 MeV, as a formalism to extract the nucleon polarizabilities with a minimum of model dependence. The subtracted dispersion integrals are mainly saturated by $\ddot{I}€N$ intermediate states in the $s$-channel ${\hat{I}}^{3}N\to \ddot{I}€N\to {\hat{I}}^{3}N$ and $\ddot{I}€\ddot{I}€$ intermediate states in the $t$-channel ${\hat{I}}^3{\hat{I}}^3\to \ddot{I}€\ddot{I}€\to N\bar{N}$. For the subprocess ${\hat{I}}^3{\hat{I}}^3\to \ddot{I}€\ddot{I}€$, we construct a unitarized amplitude and find a good description of the available data. We show results for Compton scattering using the subtracted dispersion relations and display the sensitivity on the scalar polarizability difference $\hat{I}\pm -{\hat{I}}^2$ and the backward spin polarizability ${\hat{I}}_{\ddot{I}}^3€$, which enter directly as fit parameters in the present formalism.