Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2009-12-02
Physics
High Energy Physics
High Energy Physics - Phenomenology
75 pages, LaTeX, 13 figures (.eps). FORM and Fortran files of main results appended to source
Scientific paper
10.1016/j.nuclphysb.2010.02.003
We present the coefficient functions for deep-inelastic scattering (DIS) via the exchange of a scalar phi 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_phi) of flavour-singlet structure functions. The practical relevance of these kernels as an alternative to MSbar 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.
Moch Sven
Soar G.
Vermaseren J.
Vogt Adam
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