The invariant mass of a jet is a benchmark variable describing the structure of jets at the LHC. We calculate the jet mass spectrum for Higgs plus one jet at the LHC at next-to-next-to-leading logarithmic (NNLL) order using a factorization formula. At this order, the cross section becomes sensitive to perturbation theory at the soft m 2 jet /p jet T scale. Our calculation is exclusive and uses the 1-jettiness global event shape to implement a veto on additional jets. The dominant dependence on the jet veto is removed by normalizing the spectrum, leaving residual dependence from non-global logarithms depending on the ratio of the jet mass and jet veto variables. For our exclusive jet cross section these non-global logarithms are parametrically smaller than in the inclusive case, allowing us to obtain a complete NNLL result. Results for the dependence of the jet mass spectrum on the kinematics, jet algorithm, and jet size R are given. Using individual partonic channels we illustrate the difference between the jet mass spectra for quark and gluon jets. We also study the effect of hadronization and underlying event on the jet mass in Pythia. To highlight the similarity of inclusive and exclusive jet mass spectra, a comparison to LHC data is presented.

Abstract. The N-jettiness event shape divides phase space into N + 2 regions, each containing one jet or beam. These jet regions are insensitive to the distribution of soft radiation and, with a geometric measure for N-jettiness, have circular boundaries. We give a factorization theorem for the cross section which is fully differential in the mass of each jet, and compute the corresponding soft function at next-to-leading order (NLO). For N-jettiness, all ingredients are now available to extend NLO cross sections to resummed predictions at next-to-next-to-leading logarithmic order.Keywords: Hadron colliders, jet production, resummation. PACS: 13.87.Ce, 12.38.Cy, 13.85.Qk Talk given by T.T. Jouttenus at the PANIC 2011 conference. Preprint: The measurement of exclusive jet cross sections, where one identifies a certain number of signal jets but vetoes additional jets, is an important aspect of Higgs and new-physics searches at the LHC and Tevatron. Since the relative contributions of various signal and background channels often vary with the number of hard jets in the event, the sensitivity of the search is improved by optimizing the analysis for each separate jet bin. Thus, reliable theoretical calculations of exclusive jet cross sections are essential.The complication compared to the calculation of an inclusive N-jet cross section, where one sums over additional jets, comes from the fact that the veto on additional jets imposes a restriction on the energetic initial-and final-state radiation off the primary hard partons, as well as the overall soft radiation in the event. This restriction on additional emissions leads to the appearance of large Sudakov double logarithms in perturbation theory. For this reason, the calculation of exclusive jet cross sections is traditionally carried out with parton-shower Monte Carlo programs, where the parton shower allows one to resum the most singular leading double logarithms.An alternative analytic approach to calculate exclusive jet cross sections is possible using factorization and the methods of soft-collinear effective theory (SCET) [1]. SCET allows one to factorize the N-jet cross section into pieces depending on only one scale and resum the large logarithmic contributions. An advantage of this approach is that the resummation can be carried out to much higher orders than is possible with parton showers. Schematically, the cross section for pp → N jets (plus some nonhadronic final state like a W , Z, or Higgs if desired) can be factorized asThis formula directly applies to observables that implement a veto on additional jets. The hard function H N encodes hard virtual corrections to the underlying partonic 2 → N process, the beam functions B a,b contain the parton distributions and perturbative collinear initial-state radiation from the colliding hard partons, and the jet functions J i describe energetic collinear final-state radiation from the primary N hard partons produced in the collision. The soft function S N describes the soft radiation in the event that couples...

The N -jettiness event shape divides phase space into N + 2 regions, each containing one jet or beam. Using a geometric measure these regions correspond to jets with circular boundaries. We give a factorization theorem for the cross section fully differential in the mass of each jet, and compute the corresponding soft function at next-to-leading order (NLO). The ultraviolet divergences are analytically extracted by exploiting hemispheres for interactions between each pair of hard partons, leaving only convergent integrals that are sensitive to the precise boundaries. This hemisphere decomposition can also be applied to other N -jet soft functions, including other observables. For N -jettiness, the final result for the soft function involves stable one-dimensional numerical integrals, and all ingredients are now available to extend NLO cross sections to resummed predictions at next-to-next-to-leading logarithmic order.

The jet function for the factorized cross section e + e − into dijets is given as a function of the jet invariant mass s and with a generic jet algorithm at O(αs). We demonstrate the results using the Sterman-Weinberg algorithm and show that the jet function is independent of the energy fraction β of the soft radiation. The anomalous dimension has the same form with and without the cone half-angle δ. The dependence of the finite part of the jet function on the cone angle is given.

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