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 $E_{\gamma }\le$ 500 MeV, as a formalism to extract the nucleon polarizabilities with a minimum of model dependence. The subtracted dispersion integrals are mainly saturated by $\pi N$ intermediate states in the $s$-channel $\gamma N\to \pi N\to \gamma N$ and $\pi \pi$ intermediate states in the $t$-channel $\gamma \gamma \to \pi \pi \to N\bar{N}$. For the subprocess $\gamma \gamma \to \pi \pi$, 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 $\alpha -\beta$ and the backward spin polarizability ${\gamma }_{\pi }$, which enter directly as fit parameters in the present formalism.

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