Higher-order predictions for large-x splitting functions and coefficient functions

Abstract

We discuss the large-x behaviour of the splitting functions P qg and P gq and of flavour-singlet coefficient functions, such as the gluon contributions C 2,g and C L,g to the structure functions F 2,L , in massless perturbative QCD. These quantities are suppressed by one or two powers of (1−x) with respect to the (1−x) −1 terms which are the subject of the well-known threshold exponentiation. We show that the double-logarithmic contributions to P qg , P gq and C L at order α 4 s can be predicted from known third-order results.

On next-to-eikonal exponentiation

“…A similar conclusion holds for the DIS case, where we could compare with 2-loop [13] and even 3-loop results [14]. Full agreement at NE accuracy is, however, not reached here, nor in other approaches [15,16,17,18,19,20,21]. To this end, a deeper understanding of exponentiation at NE accuracy is called for.…”

“…How to resum sub-leading logarithms at nextto-eikonal accuracy is an unsolved problem, relevant for phenomenological applications [16,28]. An approach based on path integrals and using the replica trick yields much insight into exponentiation of these contributions in terms of (nextto-)eikonal webs, and it is corroborated by a diagrammatic analysis.…”

Higher-order predictions from physical evolution kernels

“…Also the C F = 0 part of the gluon-gluon splitting functions is of this form [6]. The corresponding (pure-) singlet splitting functions include double-logarithmic (DL) contributions…”

“…(1.1), with the exception of c (3) L (x) in SIA, have been obtained in Refs. [2][3][4][5][6][7] (the latter two new articles deal with the only theoretically relevant Higgs-exchange structure function F φ in the heavy-top limit). The NNLO spacelike (S) splitting functions in Eq.…”

“…[8], while for the timelike (T ) case only the diagonal quantities P (2)T qq,gg (x) have been derived so far [9]. At N 3 LO only the coefficient functions for the structure functions F 1,2,3,φ are available at this point [6,10].…”