Small x resummation of rapidity distributions: the case of Higgs production

TL;DR

This paper develops a method for all-order small x resummation of rapidity distributions, applied specifically to Higgs production, providing explicit expressions and approximations for higher-order corrections.

Contribution

It generalizes high energy factorization to rapidity distributions and applies this to Higgs production, deriving all-order resummed expressions and finite-mass corrections.

Findings

Derived all-order resummed expressions for Higgs rapidity distributions.

Provided explicit small x terms up to NNLO for finite and infinite top mass.

Constructed approximate analytic NLO rapidity distribution with finite-mass effects.

Abstract

We provide a method for the all order computation of small x contributions at the leading logarithmic level to cross-sections which are differential in rapidity. The method is based on a generalization to rapidity distributions of the high energy (or k_T) factorization theorem hitherto proven for inclusive cross-sections. We apply the method to Higgs production in gluon-gluon fusion, both with finite top mass and in the infinite mass limit: in both cases, we determine all-order resummed expressions, as well as explicit expressions for the leading small x terms up to NNLO. We use our result to construct an explicit approximate analytic expression of the finite-mass NLO rapidity distribution and an estimate of finite-mass corrections at NNLO.