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

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 image 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 image of flavour-singlet structure functions. The practical relevance of these kernels as an alternative to image 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 image with image and image, respectively, for the off-diagonal and diagonal quantities to all powers a in image.