Mellin moments of heavy flavor contributions to F_2(x,Q^2) at NNLO
Sebastian Klein
TL;DR
The work develops and implements a comprehensive framework to compute fixed Mellin moments of heavy flavor contributions to F_2(x,Q^2) in the NNLO regime, using massive operator matrix elements in the asymptotic limit Q^2 >> m^2. It delivers explicit 3-loop fixed moments for various OMEs, confirms fermionic parts of NNLO anomalous dimensions, and develops novel summation techniques (Sigma) and hypergeometric representations to manage infinite sums and ε-expansions. By detailing renormalization schemes (MS-bar and MOM), mass renormalization, and mass-factorization structures, the study provides a robust path to accurate heavy-flavor Wilson coefficients and supports VFNS implementations. The work also extends to polarized DIS and transversity, and outlines methods to extend all-N results from fixed moments, offering significant advances for precision QCD in DIS and related collider phenomenology.
Abstract
This thesis is concerned with the calculation of fixed moments of the O(a_s^3) heavy flavor contributions to the Wilson coefficients of the structure function F_2(x,Q^2) in the limit Q^2 >> m^2, neglecting power corrections. The massive Wilson coefficients in the asymptotic region are given as convolutions of massive operator matrix elements (OMEs) and the known light flavor Wilson coefficients. The former derive from the twist--2 operators emerging in the light--cone--expansion and are calculated at the 3--loop level for fixed moments. We also compute the massive OMEs which are needed to evaluate heavy flavor parton distributions in the variable flavor number scheme to the same order. All contributions to the Wilson coefficients and OMEs but the genuine constant terms at O(a_s^3) of the OMEs are derived in terms of quantities, which are known for general values in the Mellin variable N. For the OMEs A_{Qg}^(3), A_{qg,Q}^(3) and A_{gg,Q}^(3) the moments N = 2 to 10, for A_{Qq}^{(3), PS} to N = 12, and for A_{qq,Q}^{(3), NS}, A_{qq,Q}^{(3), PS}, A_{gq,Q}^(3)}to N=14 are computed. These terms contribute to the light flavor '+'-combinations. For the flavor non-singlet terms, we calculate as well the odd moments N=1 to 13, corresponding to the light flavor '-'-combinations. We also obtain moments of the terms ~ T_F of the 3-loop anomalous dimensions in an independent calculation, which agree with results given in the literature. The mathematical structure of the occurring momentum integrals and of the final results in terms of harmonic sums is discussed. We study applications of the same techniques to the polarized and transversity case at the NLO and NNLO level as well.