Leading large- x logarithms of the quark–gluon contributions to inclusive Higgs-boson and lepton-pair production

Abstract

We present all-order expressions for the leading double-logarithmic threshold contributions to the quark-gluon coefficient functions for inclusive Higgs-boson production in the heavy top-quark limit and for Drell-Yan lepton-pair production. These results have been derived using the structure of the unfactorized cross sections in dimensional regularization and the large-x resummation of the gluon-quark and quark-gluon splitting functions. The resummed coefficient functions, which are identical up to colour factor replacements, are similar to their counterparts in deep-inelastic scattering but slightly more complicated.

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).…”

“…It is worthwhile to note that the different phase-space structure of the Drell-Yan process and Higgs production prevents a direct generalization of this approach to these cases beyond the leading-logarithmic ℓ = 0 accuracy of ref. [35]. The reader is referred to refs.…”

Non-abelian factorisation for next-to-leading-power threshold logarithms

“…[16]. Since then, and following early studies in [17,18], several groups have attempted to construct a systematic formalism for understanding NLP logarithms, using a variety of methods, ranging from path integral techniques [19], to diagrammatic approaches [20], physical evolution kernels [21][22][23][24][25][26], effective field theories [27,28], and other techniques [29][30][31]. Interestingly, the study of next-to-soft contributions to scattering amplitudes in both gauge theory and gravity from a more formal point of view, based on asymptotic symmetries of the S matrix, has also received a great deal of attention (see for example [32][33][34][35][36][37][38]).…”

On the Higgs cross section at N3LO+N3LL and its uncertainty

“…The resummation of the leading logarithms of this class of NS contributions has been performed in ref. [51]. However, these contributions are not yet implemented in the current version of TROLL.…”