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

Abstract

We discuss the large-x behaviour of the splitting functions Pqg and Pgq and of flavour-singlet coefficient functions, such as the gluon contributions C2,g and CL,g to the structure functions F2,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 Pqg, Pgq and CL at order α 4 s can be predicted from known third-order results and present, as a first step towards a full all-order generalization, the leading-logarithmic large-x behaviour of Pqg, Pgq and C2,g at all orders in αs.

Generalized double-logarithmic large-x resummation in inclusive deep-inelastic scattering

“…Hence the conjectures of Refs. [17,28,29,54] are proven by our present calculations for the leading N −1 large-N contributions.…”

“…The complete fourth-order coefficient function (for W -exchange, i.e., without the f l g 11 = 0 part) has been predicted in Ref. [54] from the physical evolution kernel for the system (F 2 , F L ) of flavour-singlet structure functions together with the four-loop splitting-function results of Ref. [17].…”

Generalized threshold resummation in inclusive DIS and semi-inclusive electron-positron annihilation

“…Considerable progress has been made in the past seven years on the resummation of large-x (or, in Mellin space, large-N ) threshold logarithms [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51] beyond those addressed by the soft-gluon exponentiation (SGE) [25][26][27][28][29]. This holds for sub-leading contributions, in terms of powers of (1−x) or 1/N for x → 1 or N → ∞, to quantities to which the SGE is applicable for the leading terms, as well as for which the SGE is not applicable at all.…”

“…This holds for sub-leading contributions, in terms of powers of (1−x) or 1/N for x → 1 or N → ∞, to quantities to which the SGE is applicable for the leading terms, as well as for which the SGE is not applicable at all. So far most of the explicit large-x results for higher-order splitting functions and coefficient functions have been obtained by studying physical evolution kernels [36][37][38][39][40][48][49][50] and the structure of unfactorized cross sections in dimensional regularization [32][33][34][35]51] (see refs. [53,54] for an analogous small-x resummation in SIA).…”

“…The reader is referred to refs. [36][37][38][39][40] for an alternative approach (with identical results where both methods are applicable) using physical evolution kernels, which is particularly suited for deriving all-ξ results at a fixed order n. For other, partly more formal research on subleading threshold logarithms see refs. [41][42][43][44][45][46][47][48][49][50].…”