The O(α_s^3) Massive Operator Matrix Elements of O(n_f) for the Structure Function F_2(x,Q^2) and Transversity

Details The O(α_s^3) Massive Operator Matrix Elements of O(n_f) for the Structure Function F_2(x,Q^2) and Transversity The O(α_s^3) Massive Operator Matrix Elements of O(n_f) for the Structure Function F_2(x,Q^2) and Transversity

2010-08-19

arxiv.org/abs/1008.3347v1

Nucl.Phys.B844:26-54,2011

Physics

High Energy Physics

High Energy Physics - Phenomenology

29 pages, 1 style file

Scientific paper

10.1016/j.nuclphysb.2010.10.021

The contributions $\propto n_f$ to the $O(\alpha_s^3)$ massive operator matrix elements describing the heavy flavor Wilson coefficients in the limit $Q^2 \gg m^2$ are computed for the structure function $F_2(x,Q^2)$ and transversity for general values of the Mellin variable $N$. Here, for two matrix elements, $A_{qq,Q}^{\sf PS}(N)$ and $A_{qg,Q}(N)$, the complete result is obtained. A first independent computation of the contributions to the 3--loop anomalous dimensions $\gamma_{qg}(N)$, $\gamma_{qq}^{\sf PS}(N$ and $\gamma_{qq}^{\sf NS,(TR)}(N)$ is given. In the computation advanced summation technologies for nested sums over products of hypergeometric terms with harmonic sums have been used. For intermediary results generalized harmonic sums occur, while the final results can be expressed by nested harmonic sums only.

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