Optimal sum-rule inequalities for [formula omitted] compton scattering

Abstract

A formalism appropriate for model-independent dispersion theoretical investigations of the (not necessarily forward) Compton scattering off spin- 1 2 hadronic targets, which fully exploits the analyticity properties of the amplitudes (to lowest order in electromagnetism) in ν 2 at fixed t ( ν = 1 4 (s − u); s, t , u = Mandelstam variables), is developed. It relies on methods which are specific to boundary-value problems for analytic matrix-valued functions. An analytic factorization of the positive definite hermitian matrix associated with the bilinear expression of the unpolarized differential cross section (u.d.c.s.) in terms of the Bardeen-Tung (B.T.) invariant amplitudes is explicitly obtained. For t in a specified portion of the physical region, six new amplitudes describing the process are thereby constructed which have the same good analyticity structure in ν 2 as the (crossing symmetrized) B.T. amplitudes, while their connection with the usual helicity amplitudes is given by a matrix which is unitary on the unitarity cut. A bound on a certain integral over the u.d.c.s. above the first inelastic threshold, established in terms of the target's charge and anomalous magnetic moment, improves a previous weaker result, being now optimal under the information accepted as known.