ar X iv : h ep - p h / 99 04 29 0 v 1 9 A pr 1 99 9 Fixed - t subtracted dispersion relations for Compton scattering off the nucleon

We present fixed-t subtracted dispersion relations for Compton scattering off the nucleon at energies E γ ≤ 500 MeV, as a formalism to extract the nucleon polarizabilities with a minimum of model dependence. The subtracted dispersion integrals are mainly saturated by πN intermediate states in the s-channel γN → πN → γN and ππ intermediate states in the t-channel γγ → ππ → N ¯ N. For the subprocess γγ → ππ, 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 α − β and the backward spin polarizability γ π , which enter directly as fit parameters in the present formalism.