On Higgs-exchange DIS, physical evolution kernels and fourth-order splitting functions at large x

We present the coefficient functions for deep-inelastic scattering (DIS) via the exchange of a scalar ϕ directly coupling only to gluons, such as the Higgs boson in the limit of a very heavy top quark and nf effectively massless light flavours, to the third order in perturbative QCD. The two-loop results are employed to construct the next-to-next-to-leading order physical evolution kernels for the system (F2,Fϕ) of flavour-singlet structure functions. The practical relevance of these kernels as an alternative to MS¯ factorization is bedevilled by artificial double logarithms at small values of the scaling variable x, where the large top-mass limit ceases to be appropriate. However, they show an only single-logarithmic enhancement at large x. Conjecturing that this feature persists to the next order also in the present singlet case, the three-loop coefficient functions facilitate exact predictions (backed up by their particular colour structure) of the double-logarithmic contributions to the fourth-order singlet splitting functions, i.e., of the terms (1−x)alnk(1−x) with k=4,5,6 and k=3,4,5, respectively, for the off-diagonal and diagonal quantities to all powers a in (1−x).