Crossing symmetric potential model of pion-nucleon scattering

Abstract

A crossing symmetric $\pi N$ scattering amplitude is constructed through a complete attachment of two external pions to the dressed nucleon propagator of an underlying $\pi N$ potential model. Our formulation automatically provides expressions also for the crossing symmetric and gauge invariant pion photoproduction and Compton scattering amplitudes. We show that our amplitudes are unitary if they coincide on-shell with the amplitudes obtained by attaching one pion to the dressed $\pi NN$ vertex of the same potential model.Comment: 6 pages, 2 figures; contribution to the proceedings of "Achievements and New Directions in Subatomic Physics: Workshop in Honour of Tony Thomas's 60th Birthday", Special Centre for the Subatomic Structure of Matter, Adelaide, South Australia, February 15 - February 19, 2010

Unified description of hadron-photon and hadron-meson scattering in the Dyson-Schwinger approach

“…Some of the terms cancel when summing up Eqs. (34) and (35), and the remainder is 37), ( 41) and (44), that enters the scattering amplitude. For each of the first three graphs on the r.h.s.…”

“…The method has been used for computing nucleon form factors both in the quark-diquark model [32] and from the covariant three-body equation [33]. The scope of the approach is however more general: the same formalism can be exploited to derive generalized parton distributions from their quark-gluon substructure [34], and it has been recently applied to obtain the scattering amplitudes for N π scattering and pion electroproduction at a hadronic level, i.e., from chiral effective field theories [35,36].…”