Model-independent dispersion approach to proton Compton scattering

The proton Compton scattering at low and intermediate energies is studied by means of a dispersion framework which exploits in an optimal way the (fixed-momentum-transfer) analyticity properties of the amplitudes in conjunction with the consequences of the ($s$-channel) unitarity. The mathematical background of the work consists in methods specific to boundary-value problems for analytic vector-valued functions and interpolation theory. In comparison with previous related work, the extremal problems to be solved now are much more difficult because of the inclusion of the photoproduction input and also lead to additional computational complications. The lower bounds on the differential cross section, obtained without any reference to subtractions and annihilation-channel contributions, appear sufficiently restrictive to provide rigorous evidence of some inconsistencies between results of single-pion-photoproduction multipole extractions and proton Compton-scattering data.