On the next-to-next-to-leading order QCD corrections to heavy-quark production in deep-inelastic scattering

The contribution of quarks with masses m≫ΛQCD is the only part of the structure functions in deep-inelastic scattering (DIS) which is not yet known at the next-to-next-to-leading order (NNLO) of perturbative QCD. We present improved partial NNLO results for the most important structure function F2(x,Q2) near the partonic threshold, in the high-energy (small-x) limit and at high scales Q2≫m2; and employ these results to construct approximations for the gluon and quark coefficient functions which cover the full kinematic plane. The approximation uncertainties are carefully investigated, and found to be large only at very small values, x≲10−3, of the Bjorken variable.