O(α 3 s) contributions to the heavy flavor Wilson coefficients of the structure function F 2(χ, Q²) at Q² >> m²

Abstract

At $O(\alpha_s^3)$ the contribution of a single heavy quark to the unpolarized structure function $F_2(x,Q^2)$ in the asymptotic region $Q^2\gg m^2$ is written as a convolution of the light flavor Wilson coefficents and the process independent massive operator matrix elements. This thesis extends the present description to allow for the presence of two heavy quark flavors and presents the respective renormalization prescription and first analytic results for these contributions. Furthermore the remaining $O(C_{A,F} T_F^2 N_F)$ contributions and various diagrams of more complex topologies have been computed analytically. On the mathematical side different evaluation techniques based on representations in terms of special functions, Mellin-Barnes representations and Hyperlogarithms have been worked out.