Combined threshold and transverse momentum resummation for inclusive observables

TL;DR

This paper introduces a combined resummation method for the transverse momentum distribution of a colorless final state in perturbative QCD, unifying transverse momentum and threshold resummation to improve predictions across all pt values.

Contribution

It presents a novel combined resummation framework that smoothly interpolates between transverse momentum and threshold resummation, with explicit NNLL coefficients for Higgs production.

Findings

Resummation reduces to standard transverse momentum resummation as pt->0.

Resummation reduces to threshold resummation as x->1.

Integration over pt reproduces total cross section resummation.

Abstract

We present a combined resummation for the transverse momentum distribution of a colorless final state in perturbative QCD, expressed as a function of transverse momentum pt and the scaling variable x. Its expression satisfies three requirements: it reduces to standard transverse momentum resummation to any desired logarithmic order in the limit pt-> 0 for fixed x, up to power suppressed corrections in pt; it reduces to threshold resummation to any desired logarithmic order in the limit x-> 1 for fixed pt, up to power suppressed correction in 1-x; upon integration over transverse momentum it reproduces the resummation of the total cross cross at any given logarithmic order in the threshold x->1 limit. Its main ingredient, and our main new result, is a modified form of transverse momentum resummation, which leads to threshold resummation upon integration over pt, and for which we provide a simple closed-form analytic expression in Fourier-Mellin (b,N) space. We give explicit coefficients up to NNLL order for the specific case of Higgs production in gluon fusion in the effective field theory limit. Our result allows for a systematic improvement of the transverse momentum distribution through threshold resummation which holds for all pt, and elucidates the relation between transverse momentum resummation and threshold resummation at the inclusive level, specifically by providing within perturbative QCD a simple derivation of the main consequence of the so-called collinear anomaly of SCET.