Photon- and pion-nucleon interactions in a unitary and causal effective field theory based on the chiral Lagrangian

Abstract

We present and apply a novel scheme for studying photon- and pion-nucleon scattering beyond the threshold region. Partial-wave amplitudes for the $\gamma N$ and $\pi N$ states are obtained by an analytic extrapolation of subthreshold reaction amplitudes computed in chiral perturbation theory, where the constraints set by electromagnetic-gauge invariance, causality and unitarity are used to stabilize the extrapolation. Based on the chiral Lagrangian we recover the empirical s- and p-wave amplitudes up to energies $\sqrt{s}\simeq 1300$ MeV in terms of the parameters relevant at order $Q^3$.

arXiv comment76 pages, 23 figures, one additional figure, Tables 4,5 and Figure 4 are corrected, a few references and comments are added. The role of higher partial waves in pion photoproduction is clarified

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