Photon- and pion-nucleon interactions in a unitary and causal effective theory

In recent years photonand pion-nucleon interactions have been successfully used as a quantitative challenge of chiral perturbation theory (χPT), which is a systematic tool to learn about low-energy QCD dynamics [1]. The application of χPT is however limited to the near threshold region. A method to extrapolate χPT results beyond the threshold region using analyticity and unitarity constraints was proposed recently in [2]. Our approach is based on the chiral Lagrangian involving pion, nucleon and photon fields including terms relevant at the order Q. The relevant counter terms of the Lagrangian are adjusted to the empirical data available for photon and pion scattering off the nucleon. We focus on the sand p-wave partial-wave amplitudes and do not consider inelastic channels with two or more pions. We recover the empirical sand p-wave pion-nucleon phase shifts (cf. Fig. 1) and pion photoproduction multipoles up to about 1300 MeV quantitatively.