The 3-Loop Non-Singlet Heavy Flavor Contributions and Anomalous Dimensions for the Structure Function $F_2(x,Q^2)$ and Transversity

J. Ablinger; A. Behring; J. Blümlein; A. De Freitas; A. Hasselhuhn; A. von Manteuffel; M. Round; C. Schneider; F. Wißbrock

Paper

The 3-Loop Non-Singlet Heavy Flavor Contributions and Anomalous Dimensions for the Structure Function $F_2(x,Q^2)$ and Transversity

Abstract

We calculate the massive flavor non-singlet Wilson coefficient for the heavy flavor contributions to the structure function

in the asymptotic region

and the associated operator matrix element

to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable

. This matrix element is associated to the vector current and axial vector current for the even and the odd moments

, respectively. We also calculate the corresponding operator matrix elements for transversity, compute the contributions to the 3-loop anomalous dimensions to

and compare to results in the literature. The 3-loop matching of the flavor non-singlet distribution in the variable flavor number scheme is derived. All results can be expressed in terms of nested harmonic sums in

space and harmonic polylogarithms in

-space. Numerical results are presented for the non-singlet charm quark contribution to