The analytic two-loop soft function for leading-jet $p_T$

TL;DR

This paper computes the two-loop soft function for leading-jet transverse momentum distribution, enabling higher-precision resummation for collider physics processes involving jets and color-singlet systems.

Contribution

It provides the first analytic calculation of the two-loop soft function for leading-jet $p_T$ in soft-collinear effective theory, including rapidity divergence regularization.

Findings

Analytic two-loop soft function expressions obtained.

Results facilitate next-to-next-to-next-to-leading logarithmic resummation.

Applicable to Higgs, Z boson, and other color-singlet associated productions.

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 ancillary files with this article.