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

D. Drechsel·M. Gorchtein·B. Pasquini·M. Vanderhaeghen
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Abstract

We present fixed-$t$ subtracted dispersion relations for Compton scattering off the nucleon at energies $E_γ\leq$ 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 $γN \to πN \to γN$ and $ππ$ intermediate states in the $t$-channel $γγ\to ππ\to N \bar N$. For the subprocess $γγ\to ππ$, 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.

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D. Drechsel, M. Gorchtein, B. Pasquini, M. Vanderhaeghen. 1999-04-09. Fixed-t subtracted dispersion relations for Compton scattering off the nucleon. https://doi.org/10.1103/physrevc.61.015204

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