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).

On higher-order flavour-singlet splitting and coefficient functions at large x

“…The coefficients of the highest three powers of ln (1−x) have been derived for the four-loop contributions to the splitting functions P qg and P gq from the three-loop coefficient functions and the singlelogarithmic enhancement of the physical evolution kernel for the system (F 2 , F φ ) of flavoursinglet structure functions at order α 4 s [24]. In the present contribution we have employed these results to derive also the leading three large-x logarithms for the fourth-order gluon coefficient function C L,g for the longitudinal structure function from the analogous kernel for (F 2 , F L ).…”

“…The coefficient functions C φ,i have been determined recently in Refs. [23] and [24] to the second and third order in α s , respectively.…”

“…(5)) and to order α 3 s for the singlet contribution, is that the physical kernel K is only single-log enhanced [24], i.e.,…”

“…This implies a cancellation between the doublelogarithmic contributions to the, so far unknown, off-diagonal l = 3 splitting functions (6) and the known [4,24] coefficient functions to order α 3 s from which the former can be deduced. The results are…”

“…C of Ref. [24], given for W -exchange, i.e., without the f l g 11 contribution for the photon case [4] -have also been derived, but not explicitly written down, in Ref. [17].…”