CombiningQTand small-xresummations

Abstract

We analyze transverse momentum (QT ) resummation of a colorless final state, e.g. Higgs production in gluon fusion or the production of a lepton pair via the Drell-Yan mechanism, in the limit where the invariant mass of the final state is much less then the center-of-mass energy, i.e. Q 2 ≪ s. We show how the traditional resummation of logarithms of QT /Q can be supplemented with the resummation of the leading logarithmic contributions at small x = Q 2 /s and we compute the necessary ingredients to perform such joint resummation.

Higgs Transverse-Momentum Resummation in Direct Space

“…[8], and a formalism to perform a joint p H t =small-x resummation has been presented in Ref. [9]. The differential distribution in fixed-order perturbation theory has been known for several years at next-to-leading order (NLO) [10][11][12], and has been recently improved through the computation of the Higgs-plus-one-jet cross section at next-to-next-to-leading order (NNLO) [13][14][15][16].…”

The evolution of the small x gluon TMD

“…In particular, we notice that the attempts to unify the description of various types evolution of the gluon TMD have also been made in refs. [28,[39][40][41][42][43]. However, the calculations presented in refs.…”

“…However, the calculations presented in refs. [28,[39][40][41][42][43] are formulated in the very different ways. It is a non-trivial task to compare the current work with these formalisms.…”

Gluon TMD in particle production from low to moderate x

“…It would be interesting to find how the linear evolution equation (6.2) is connected with other results on the combined small-and large-x resummation, see refs. [48][49][50][51][52][53].…”