Single-valued representation of unpolarized and polarized semi-inclusive deep inelastic scattering at next-to-next-to-leading order

Abstract

We revisit the recently published analytic results for unpolarized and polarized semi-inclusive deep inelastic scattering (SIDIS) at next-to-next-to-leading order (NNLO) in QCD. These expressions for the hard scattering coefficients contain case distinctions in the kinematic $(x,z)$ plane splitting the analytic result in four regions. By re-expressing the coefficient functions in terms of single-valued polylogarithms we remove these case distinctions and can present a unified result valid in the entire kinematic range of SIDIS. This reduces the length of the overall expressions by 30% to 60%.

Comments: 12 pages, 5 figures, 3 ancillary files containing the results in Mathematica readable format and a numerical implementation of single-valued polylogarithms, special functions C++ library BEAVER available from https://github.com/fabianwunder/beaver , updated to match journal version