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

Abstract

We present all-order results for the highest three large-x logarithms of the splitting functions P qg and P gq and of the coefficient functions C φ,q , C 2,g and C L,g for structure functions in Higgs-and gauge-boson exchange DIS in massless perturbative QCD. The corresponding coefficients have been derived by studying the unfactorized partonic structure functions in dimensional regularization independently in terms of their iterative structure and in terms of the constraints imposed by the functional forms of the real-and virtual-emission contributions together with their Kinoshita-LeeNauenberg cancellations required by the mass-factorization theorem. The numerical resummation corrections are small for the splitting functions, but partly very large for the coefficient functions. The highest two (three for C L,g ) logarithms can be resummed in a closed form in terms of new special functions recently introduced in the context of the resummation of the leading logarithms.

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

“…This resummation was extended to the NLL and NNLL contributions to the splitting functions for the evolution of parton distributions and the coefficients functions for inclusive DIS in ref. [32]. However, with the exception of the longitudinal structure function, closed forms were found only for the NLL corrections.…”

“…Specifically, we complete the study of DIS in ref. [32] by deriving analytic formulae for the next-to-next-to-leading logarithmic (NNLL) ℓ = 2 corrections and present the corresponding results for SIA. A brief previous account of the latter can be found in ref.…”

“…(2.7)-(2.13) of ref. [32]. Schematically, the leading-logarithmic behaviour of Z in N -space corresponding to eqs.…”

“…[32] that the a n s contributions to the unfactorized structure functions T 2, g , T φ, q and T L, k in Mellin space can be written as…”

A complete basis of helicity operators for subleading factorization

“…The description of observables with more complicated dynamics typically relies on factorization theorems and much less is known about the structure of power corrections in these cases. Power corrections have been considered for Drell-Yan [11][12][13][14][15] at O(Λ 2 QCD /Q 2 ), for inclusive B decays in the endpoint region at O((1−z) 0 , (Λ QCD /m b ) 1,2 ) [16][17][18][19][20][21][22][23][24], for exclusive B decays at O(Λ QCD /m b ) [25][26][27][28][29][30][31][32][33], for event shapes τ in e + e − , ep, and pp collisions at O(Λ k QCD /(Qτ ) k ) [13,[34][35][36][37][38][39][40][41][42][43][44][45][46][47][48], and at O((1 − z) 0 ) for threshold resummation [49][50][51][52][53][54][55][56]…”