Transverse-momentum resummation and the structure of hard factors at the NNLO

TL;DR

This paper explores the relationship between hard factors and virtual amplitudes in QCD for high-mass system production, enabling precise calculations at NNLO and beyond through a universal formula.

Contribution

It explicitly evaluates the universal relation between hard factors and virtual amplitudes up to two-loop level, facilitating NNLO and higher-order resummations.

Findings

Derived a universal relation between hard factors and virtual amplitudes.

Explicitly evaluated the relation up to two-loop level.

Enabled NNLO calculations using the derived hard factors.

Abstract

In this proceeding we consider QCD radiative corrections to the production of colourless high-mass systems in hadron collisions. At small transverse momentum the logarithmically-enhanced contributions can be organized to all perturbative orders by a universal resummation formula that depends on a single process-dependent hard factor. We show that the hard factor is directly related to the all-order virtual amplitude of the corresponding partonic process by a universal (process independent) formula, which we explicitly evaluate up to two-loop level. Once the next-to-next-to-leading order (NNLO) scattering amplitude is available, the corresponding hard factor is directly determined. It can be used in fully-exclusive perturbative calculations (via q$_T$ subtraction formalism) up to NNLO, in resummed calculations at full next-to-next-to-leading logarithmic (NNLL) accuracy, and also, it's a necessary ingredient to the next subsequent logarithmic order (N$^3$LL).