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

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.

34 pages, 1 figure, v2: journal version + fixed typos in eqs. (1.2) and (3.6), corrected c1 coefficients for TauBj in table 2

References in corpus (17)

• The Zero-Bin and Mode Factorization in Quantum Field Theory
• The Quark Beam Function at NNLL
• The semi-inclusive jet function in SCET and small radius resummation for inclusive jet production
• C-parameter Distribution at N${}^3$LL${}^{\prime }$ including Power Corrections
• Measurements of fiducial and differential cross sections for Higgs boson production in the diphoton decay channel at $\sqrt{s}=8$ TeV with ATLAS
• Fragmentation of a Jet with Small Radius
• Glauber Gluons and Multiple Parton Interactions
• The Gluon Beam Function at Two Loops
• Resummation of Large Endpoint Corrections to Color-Octet J/psi Photoproduction
• An Explanation of the WW Excess at the LHC by Jet-Veto Resummation
• Two-loop anomalous dimensions of generic dijet soft functions
• Automated NNLL+NLO Resummation for Jet-Veto Cross Sections
• Rapidity-Dependent Jet Vetoes
• Factorization for Jet Radius Logarithms in Jet Mass Spectra at the LHC
• Jet Vetoes Interfering with H->WW
• Exploiting jet binning to identify the initial state of high-mass resonances
• Impact of Jet Veto Resummation on Slepton Searches

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• Collinear expansion for color singlet cross sections
• Quark and gluon two-loop beam functions for leading-jet $p_T$ and slicing at NNLO
• The NNLO quark beam function for jet-veto resummation
• Sleptons without Hadrons
• Higgs Production at NNLL${}^{\prime }$+NNLO using Rapidity Dependent Jet Vetoes
• Two-loop bottom mass effects on the Higgs transverse momentum spectrum in top-induced gluon fusion
• Disentangling observable dependence in SCETI and SCETII anomalous dimensions: angularities at two loops
• Jet veto resummation for STXS $H+$1-jet bins at aNNLL${}^{\prime }$+NNLO
• The Drell-Yan Process at NNLL${}^{\prime }$+NNLO using Rapidity Dependent Jet Vetoes
• The analytic two-loop soft function for leading-jet $p_T$