Virtual Compton Scattering at High Energy

Virtual Compton Scattering at High EnergyZHANG CHEN In this dissertation we develop a theoretical framework in the context of per-turbative QuantumChromoDynamics (pQCD) for studying non-forward scatteringprocesses. In particular, we investigate a non-forward unequal mass virtual Comptonscattering amplitude by performing the general operator product expansion (OPE)and the formal renormalization group (RG) analysis.We discuss the general tensorial decomposition of the amplitude to obtain theinvariant amplitudes in the non-forward kinematic region. We study the OPE toidentify the relevant operators and their reduced matrix elements, as well as the cor-responding Wilson coefficients. We find that the OPE now should be done in doublemoments with new moment variables. There are in the expansion new sets of leadingtwist operators which have overall derivatives. They mix under renormalization ina well-defined way. We compute the evolution kernels from which the anomalousdimensions for these operators can be extracted. We also obtain explicitly the lowestorder Wilson coefficients.In the high energy limit we find the explicit form of the dominantly contributinganomalous dimensions. We are then able to solve the resulting renormalization groupequations (RGE) and give a prediction of the high energy behavior of the invariantamplitudes. We find that it is the same as is indicated by the conventional doubleleading logarithmic analysis.