S. Kondratyuk

Dressing the nucleon in a dispersion approach

We present a model for dressing the nucleon propagator and vertices. In the model the use of a K-matrix approach (unitarity) and dispersion relations (analyticity) are combined. The principal application of the model lies in pion-nucleon scattering where we discuss effects of the dressing on the phase shifts.

Compton scattering in a unitary approach with causality constraints

Abstract Pion-loop corrections for Compton scattering are calculated in a novel approach based on the use of dispersion relations in a formalism obeying unitarity. The basic framework is presented, including an application to Compton scattering. In the approach the effects of the non-pole contribution arising from pion dressing are expressed in terms of (half-off-shell) form factors and the nucleon self-energy. These quantities are constructed through the application of dispersion integrals to the pole contribution of loop diagrams, the same as those included in the calculation of the amplitudes through a K-matrix formalism. The prescription of minimal substitution is used to restore gauge invariance. The resulting relativistic-covariant model combines constraints from unitarity, causality, and crossing symmetry.

Electromagnetic off-shell effects in proton-proton bremsstrahlung

Abstract We study the influence of the off-shell structure of the nucleon electromagnetic vertex on proton-proton bremsstrahlung observables. Realistic choices for the off-shell behavior are found to have considerable influences on observables such as cross sections and analyzing powers. The rescattering contribution diminishes the effects of off-shell modifications in negative-energy states.

Consistent off-shell pi NN vertex and nucleon self-energy

Form factors in the nucleon-photon vertex with one off-shell nucleon are calculated by dressing the vertex with pion loops up to infinite order. Cutting rules and dispersion relations are implemented in the model. Using the prescription of minimal substitution we construct a \gamma \pi N N vertex and show that it has to be included in the model in order that the Ward-Takahashi identity for the \gamma N N vertex be fulfilled. The vertex is to be applied in a coupled-channel K-matrix formalism for Compton scattering, pion photoproduction and pion scattering. The form factors show a pronounced cusp structure at the pion threshold. As an illustration of a consistent application of the model, we calculate the cross section of Compton scattering. To provide gauge invariance in Compton scattering, a four-point \gamma \gamma N N contact term is constructed using minimal substitution.We present a consistent calculation of half-off-shell form factors in the pion-nucleon vertex and the nucleon self-energy. Numerical results are presented. Near the on-shell point the pion-nucleon vertex is dominated by the pseudovector coupling, while at large nucleon invariant masses we find a sizable pseudoscalar admixture. [S0556-2813(99)02002-6].

The Adler-Weisberger and Goldberger-Miyazawa-Oehme sum rules as probes of constraints from analyticity and chiral symmetry in dynamical models for pion-nucleon scattering

Abstract The Adler–Weisberger and Goldberger–Miyazawa–Oehme sum rules are calculated within a relativistic, unitary and crossing symmetric dynamical model for pion–nucleon scattering using two different methods: (1) by evaluating the scattering amplitude at the corresponding low-energy kinematics and (2) by evaluating the sum-rule integrals with the calculated total cross section. The discrepancy between the results of the two methods provides a measure of the breaking of analyticity and chiral symmetry in the model. The contribution of the Δ resonance, including its dressing with meson loops, is discussed in some detail and found to be small.

Non-perturbative model for the half-off-shell

Form factors in the nucleon-photon vertex with one off-shell nucleon are calculated by dressing the vertex with pion loops up to infinite order. Cutting rules and dispersion relations are implemented in the model. Using the prescription of minimal substitution we construct a \gamma \pi N N vertex and show that it has to be included in the model in order that the Ward-Takahashi identity for the \gamma N N vertex be fulfilled. The vertex is to be applied in a coupled-channel K-matrix formalism for Compton scattering, pion photoproduction and pion scattering. The form factors show a pronounced cusp structure at the pion threshold. As an illustration of a consistent application of the model, we calculate the cross section of Compton scattering. To provide gauge invariance in Compton scattering, a four-point \gamma \gamma N N contact term is constructed using minimal substitution.We present a consistent calculation of half-off-shell form factors in the pion-nucleon vertex and the nucleon self-energy. Numerical results are presented. Near the on-shell point the pion-nucleon vertex is dominated by the pseudovector coupling, while at large nucleon invariant masses we find a sizable pseudoscalar admixture. [S0556-2813(99)02002-6].