The 3-loop non-singlet heavy flavor contributions and anomalous dimensions for the structure function F2(x,Q2) and transversity

Abstract

We calculate the massive flavor non-singlet Wilson coefficient for the heavy flavor contributions to the structure function F2(x,Q2) in the asymptotic region Q2≫m2 and the associated operator matrix element Aqq,Q(3),NS(N) to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable N. This matrix element is associated with the vector current and axial vector current for the even and the odd moments N, respectively. We also calculate the corresponding operator matrix elements for transversity, compute the contributions to the 3-loop anomalous dimensions to O(NF) 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 N space and harmonic polylogarithms in x-space. Numerical results are presented for the non-singlet charm quark contribution to F2(x,Q2).