Massive two- and three-loop calculations in QED and QCD

Abstract

This thesis is devoted to the study of mass effects in higher order radiative corrections within QEDand QCD. The first part of the thesis deals with the process of deep-inelastic scattering. We computethe full mass dependence of the pure singlet Wilson coefficient in the polarized and unploarized case to next-to-leading order using iterated integrals over square root valued letters. Through explicit expansion in the asymptotic limit we proof the factorization of the heavy Wilson coefficient into massless Wilson coefficient and massive operator matrix element and additionally derive improved asymptotic expressions. We then turn to the calculation of massive operator matrix elements with two masses. We compute missing two-mass contributions to unpolarized operator matrix elements at next-to-next-to-leading order and extend the calculation to polarized operator matrix elements at next-to-leading and next-to-next-to-leading order in the single and two-mass case. For the calculation of these processes we set up new calculational methods.In the second part of the thesis we deal with QED initial state radiation in electron-positronannihilation into a neutral vector boson at next-to-next-to-leading order. With the new calculation, which is based on an exact integration of the phase space and a subsequent expansion, we proof the asymptotic factorization of massive external particles for this process and clarify results in the literature.