Dispersive Methods and QCD Sum Rules for γγCollisions

Abstract

It has been shown, in the case of meson photoproduction, that the power-law falloff of these reactions can be described by lowest order (real) sum rules, at moderate momentum transfer. The phases of these processes, in this regime, are usually thought to be non-perturbative. In a sum rule framework, however, they can possibly be described by radiative corrections to the hadronic spectral densities of the corresponding helicities, which become complex functions to order $α_s$, and the effects of interference can be strongly enhanced by the presence of the vacuum condensates in the dispersion relation. It is shown that the imaginary parts of these complex corrections have a factorized form and can be evaluated in a systematic fashion, while their real parts, at the same perturbative order, are down by at least 2 powers of momentum transfer. The analysis is done at two loop level, combining dimensional regularization and light-cone methods. The calculations are performed for all the independent set of scalar diagrams generated by the OPE. The analytical bounds are identified and discussed.