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.

Calculation of two-photon exchange effects for Δ production in electron–proton collisions

“…[17]). An inherent property of the minimal substitution is that it yields unambiguously only the contact term longitudinal to the photons' four-momenta (which is sufficient for current conservation).…”

K-Λ and K-Σ photo-production in a coupled channels framework

“…To be more specific, the loop corrections generated in the K-matrix procedure include only diagrams that correspond to two on-mass-shell particles in the loop [16,17]. This is the minimal set of diagrams one has to include to ensure two-particle unitarity.…”

“…The omitted real parts are important to guarantee analyticity of the amplitude and may have complicated cusp-like structures at energies where other reaction channels open. In principle these can be included as form factors as is done in the dressed-K-matrix procedure [16,18]. For reasons of simplicity we have chosen to work with purely phenomenological form factors in the present calculations.…”

“…In the current work we limit ourselves to the spin-1 2 and 3 2 resonances as in this energy regime higher-spin resonances are known [23] to give only a minor contribution to the strange channels, which are of primary interest here. Spin 3/2 resonances are included with so-called gaugeinvariant vertices which have the property that the coupling to the spin-1/2 pieces in the Rarita-Schwinger propagator vanish [16,24]. We have chosen for this prescription since it reduces the number of parameters as we do not have to deal with the off-shell couplings.…”

“…A second reason are intermediate-range effects due to meson-loop corrections which are not generated through the K-matrix formalism. Examples of these are given in refs [16,18].…”