The analytic two-loop soft function for leading-jet pT

Abstract

We present the calculation of the two-loop soft function for the transverse momentum distribution of the leading jet produced in association with any colour-singlet system (e.g. a Higgs or a Z boson). This constitutes a central ingredient for the resummation of the above distribution as well as the jet-vetoed cross section at the next-to-next-to-next-to-leading logarithmic order, both of which play an important role in the precision physics programme at the Large Hadron Collider. The calculation is performed in soft-collinear effective theory with an appropriate regularisation of the rapidity divergences that occur in the phase-space integrals. We obtain analytic results by employing an exponential regulator and by taking a Laurent expansion in the jet radius R. All expressions are presented as supplementary material attached to this article.

Two-loop bottom mass effects on the Higgs transverse momentum spectrum in top-induced gluon fusion

“…For measurements that put different weights on the one-and two-particle final states like the ones in refs. [53][54][55], however, the contributions from fig. 2i must cancel with similar terms from diagrams 2g and 2h related by gauge symmetry (just like the corresponding rapidity divergences in the soft function).…”

Transverse momentum resummation at N3LL+NNLO for diboson processes

“…Beam-and soft-functions are taken from refs. [40,41] and the rapidity anomalous dimension at the two-loop level is taken from refs. [39,42].…”

“…Reducing the background from top production to an acceptable level currently requires the imposition of a veto on jet activity. We have implemented jet-veto resummation for all single boson and boson pair processes at the level of N 3 LL p +NNLO based on the collinear anomaly formalism [39] and the ingredients available in the literature [40,41]. Here we only present results for W + W − production and leave a detailed jet-veto study for a future publication [44].…”

Jet-veto resummation at N3LLp + NNLO in boson production processes

“…The quantity ν is a supplementary scale necessitated by the rapidity divergences present in beam and soft functions. The main process-independent ingredients are the beam and soft functions for both incoming quarks and gluons which have been published recently at the two-loop level [24,25]. The hard function is process specific.…”

“…The jet veto soft function has been calculated using an exponential regulator [27] in ref. [25]. The calculation is divided into the sum of the soft function for a reference observable and a correction factor,…”