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We present the coefficient functions for deep-inelastic scattering (DIS) viathe exchange of a scalar phi directly coupling only to gluons, such as theHiggs boson in the limit of a very heavy top quark and n_f effectively masslesslight flavours, to the third order in perturbative QCD. The two-loop resultsare employed to construct the next-to-next-to-leading order physical evolutionkernels for the system (F_2 F_phi) of flavour-singlet structure functions. Thepractical relevance of these kernels as an alternative to MSbar factorizationis bedevilled by artificial double logarithms at small values of the scalingvariable x, where the large top-mass limit ceases to be appropriate. However,they show an only single-logarithmic enhancement at large x. Conjecturing thatthis feature persists to the next order also in the present singlet case, thethree-loop coefficient functions facilitate exact predictions (backed up bytheir particular colour structure) of the double-logarithmic contributions tothe fourth-order singlet splitting functions, i.e., of the terms (1-x)^aln^k(1-x) with k = 4, 5, 6 and k = 3, 4, 5, respectively, for the off-diagonaland diagonal quantities to all powers a in 1-x.

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