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

Abstract 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 n f 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 ( F 2 , F ϕ ) 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 ) a ln k ( 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 ) .