Virtual Compton Scattering at High Energy

TL;DR

This dissertation develops a pQCD-based theoretical framework for non-forward virtual Compton scattering, analyzing operator expansions, renormalization group evolution, and high-energy behavior of scattering amplitudes.

Contribution

It introduces a novel operator product expansion in double moments and computes evolution kernels for non-forward virtual Compton scattering at high energies.

Findings

Derived explicit anomalous dimensions for relevant operators.

Solved RG equations to predict high-energy amplitude behavior.

Confirmed consistency with double leading logarithmic analysis.

Abstract

In this dissertation we develop a theoretical framework in the context of perturbative QuantumChromoDynamics (pQCD) for studying non-forward scattering processes. In particular, we investigate a non-forward unequal mass virtual Compton scattering 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 the invariant amplitudes in the non-forward kinematic region. We study the OPE to identify the relevant operators and their reduced matrix elements, as well as the corresponding Wilson coefficients. We find that the OPE now should be done in double moments with new moment variables. There are in the expansion new sets of leading twist operators which have overall derivatives. They mix under renormalization in a well-defined way. We compute the evolution kernels from which the anomalous dimensions for these operators can be extracted. We also obtain explicitly the lowest order Wilson coefficients. In the high energy limit we find the explicit form of the dominantly contributing anomalous dimensions. We are then able to solve the resulting renormalization group equations (RGE) and give a prediction of the high energy behavior of the invariant amplitudes. We find that it is the same as is indicated by the conventional double leading logarithmic analysis.