Mellin Moments of Heavy Flavor Contributions to $F_2(x,Q^2)$ at NNLO
| Autor: | Klein, Sebastian Werner Gerhard |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: |
Condensed Matter::Quantum Gases
polarization High Energy Physics::Lattice thesis bibliography structure function [p] electroproduction [quark] ddc:539.72167 anomalous dimension 2 [higher-order] higher-order [perturbation theory] moment renormalization regularization deep inelastic scattering [lepton nucleon] quantum chromodynamics High Energy Physics::Experiment heavy quark Mellin transformation light cone renormalization group distribution function [parton] numerical calculations 1 [higher-order] transversity |
| Zdroj: | Berlin, Heidelberg : Springer Berlin Heidelberg 207 pp. (2012). doi:10.1007/978-3-642-23286-2 = Dissertation, Technische Universität Dortmund, 2012 |
| DOI: | 10.1007/978-3-642-23286-2 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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