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 pTj of jets. Alternatively, one can also consider jet observables for which pTj is weighted by a smooth function of the jet rapidity yj that vanishes as |yj| → ∞. 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.
Highlights
The default jet variable by which jets are currently classified and vetoed is the transverse momentum pT j of a jet
One way to get around this problem is by introducing a hard cut on the jetrapidity and only consider jets at |ηj| < ηcut. Such a cut changes the logarithmic structure [1], and none of the extant resummations of pT j take account of such a rapidity cut. Another way one might try to avoid the problem is to raise the cut on pT j, but one loses the potential benefits of a tight jet veto
In refs. [1, 3], the factorization of the color-singlet production cross sections with a TBj or TCj veto, involving jet-dependent beam and soft functions, was formulated within soft collinear effective theory (SCET) [6,7,8,9,10,11], and the resummation of the two observables was performed to the NLL +NLO order [3]
Summary
The default jet variable by which jets are currently classified and vetoed is the transverse momentum pT j of a jet. In addition to the above practical considerations, given the importance of jet binning it is highly desirable to have several different options for performing jet vetoes, both experimentally and theoretically This avoids having to rely exclusively on pT j, and provides important complementary information on the pattern of additional jets produced, for example in Higgs production [4]. TBj gives the plus (minus) momentum of the jet j if the jet lies in the right (left) hemisphere with p−j (+) > p+j (−) That is, it has the same rapidity weighting as the global beam thrust hadronic event shape [5]. These corrections provide the necessary fixed-order boundary conditions for the N3LL resummation, with the remaining missing ingredients being the three-loop clustering correction to the noncusp and the fourloop correction to the cusp anomalous dimensions
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