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

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 quantum chromodynamics (QCD). These expressions for the hard scattering coefficients contain case distinctions in the kinematic <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mo stretchy="false">(</a:mo> <a:mi>x</a:mi> <a:mo>,</a:mo> <a:mi>z</a:mi> <a:mo stretchy="false">)</a:mo> </a:mrow> </a:math> -plane, splitting the analytic result into four regions. By reexpressing the coefficient functions in terms of single-valued polylogarithms, we remove these case distinctions and can present a unified result valid across the entire kinematic range of SIDIS. This reduces the length of the overall expressions by 30% to 60%.