[en] 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

[en] The pion-nucleon amplitude is considered in the vicinity of the elastic scattering threshold within a relativistic dynamical model dressing the πNN and πNΔ vertices self-consistently with an infinite number of meson loops. The dressing is formulated as solution of a system of coupled integral equations incorporating unitarity, crossing symmetry and analyticity constraints. The calculated scattering lengths and the sigma-term agree with recent data analyses. The dressing is important in this model both below and at threshold. The contribution of the Δ resonance is discussed, including effects of the consistent dressing of the πNΔ vertex. A comparison with the approaches of chiral perturbation theory and the Bethe-Salpeter equation is outlined

[en] We solve the Bethe-Salpeter equation for two-particle scattering in a field-theoretical model using two lagrangians related by a field transformation. The kernel of the equation consists of the sum of all tree-level diagrams for each lagrangian. The solutions differ even if all four external particles are put on the mass shell, which implies that observables calculated by solving the Bethe-Salpeter equation depend on the representation of the theory. We point out that this violation of the equivalence theorem has a simple explanation and should be expected for any Bethe-Salpeter equation with a tree-level kernel. Implications for dynamical models of hadronic interactions are discussed. (author)

[en] We calculate the effects on the elastic electron-proton scattering cross section of the two-photon exchange contribution with an intermediate Δ resonance. The Δ two-photon exchange contribution is found to be smaller in magnitude than the previously evaluated nucleon contribution, with an opposite sign at backward scattering angles. The sum of the nucleon and Δ two-photon exchange corrections has the angular dependence compatible with both the polarization transfer and the Rosenbluth methods of measuring the nucleon electromagnetic form factors

[en] 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

[en] A microscopic coupled-channels model for Compton and pion scattering off the nucleon is introduced which is applicable at the lowest energies (polarizabilities) as well as at GeV energies. To introduce the model first the conventional K-matrix approach is discussed to extend this in a following chapter to the 'Dressed K-Matrix' model. The latter approach restores causality, or analyticity, of the amplitude to a large extent. In particular, crossing symmetry, gauge invariance and unitarity are satisfied. The extent of violation of analyticity (causality) is used as an expansion parameter. (author)

[en] We calculate contributions of hadron resonances to two-photon exchange effects in electron-proton scattering. In addition to the nucleon and P33 resonance, the following heavier resonances are included as intermediate states in the two-photon exchange diagrams: D13,D33,P11,S11, and S31. We show that the corrections due to the heavier resonances are smaller than the dominant nucleon and P33 contributions. We also find that there is a partial cancellation between the contributions from the spin 1/2 and spin 3/2 resonances, which results in a further suppression of their aggregate two-photon exchange effect

[en] Since the existing calculations of the effective meson mass in nuclear medium involve approximations, it is important to examine whether they satisfy the general requirement of the equivalence theorem that the physical observables should be independent of the choice of field variables. We study here consequences of nucleon field transformations. As an illustrative case we consider the in-medium effective pion mass calculated for the s-wave pion-nucleon interaction in the linear-density approximation. We demonstrate that it is necessary to include the Born term explicitly in order that the effective pion mass should obey the equivalence theorem

[en] The Gerasimov-Drell-Hearn and Baldin-Lapidus sum rules are evaluated in the dressed K-matrix model for photon-induced reactions on the nucleon. For the first time the sum α+β of the electric and magnetic polarizabilities and the forward spin polarizability γ₀ are explicitly calculated in two alternative ways--from the sum rules and from the low-energy expansion of the real Compton scattering amplitude--within the same framework. The two methods yield compatible values for α+β but differ somewhat for γ₀. Consistency between the two ways of determining the polarizabilities is a measure of the extent to which basic symmetries of the model are obeyed

[en] The form factor of the parity and time-reversal violating (PTV) pion-nucleon interaction is calculated from one-loop vertex diagrams. The degrees of freedom included in the effective Lagrangian are nucleons, pions, η, ρ and ω mesons. We show that by studying the form factor one can constrain the PTV meson-nucleon coupling constants. We evaluate the mean square radius associated with the PTV πNN vertex. Using the mean square radius, we estimate the effect of the PTV πNN vertex on the neutron electric dipole moment, and find a very small correction. We also extract the renormalisation group β function and use it to discuss evolution of the PTV πNN coupling constant beyond the hadronic mass scale