Two-Loop Beam and Soft Functions for Rapidity-Dependent Jet Vetoes

TL;DR

This paper calculates two-loop beam and soft functions for rapidity-dependent jet vetoes, enabling higher-order resummation techniques crucial for precise LHC analyses involving jet vetoes.

Contribution

It provides the first complete two-loop calculations of beam and soft functions for specific rapidity-dependent jet veto observables, advancing resummation accuracy.

Findings

Analytical results for dominant contributions.

Numerical integrals for subleading corrections.

Foundation for NNLL' and N3LL resummation.

Abstract

Jet vetoes play an important role in many analyses at the LHC. Traditionally, jet vetoes have been imposed using a restriction on the transverse momentum $p_{Tj}$ of jets. Alternatively, one can also consider jet observables for which $p_{Tj}$ is weighted by a smooth function of the jet rapidity $y_j$ that vanishes as $|y_j| \to \infty$. Such observables are useful as they provide a natural way to impose a tight veto on central jets but a looser one at forward rapidities. We consider two such rapidity-dependent jet veto observables, $\mathcal{T}_{Bj}$ and $\mathcal{T}_{Cj}$, and compute the required beam and dijet soft functions for the jet-vetoed color-singlet production cross section at two loops. At this order, clustering effects from the jet algorithm become important. The dominant contributions are computed fully analytically while corrections that are subleading in the limit of small jet radii are expressed in terms of finite numerical integrals. Our results enable the full NNLL' resummation and are an important step towards N3LL resummation for cross sections with a $\mathcal{T}_{Bj}$ or $\mathcal{T}_{Cj}$ jet veto.