Jet Veto Clustering Logarithms Beyond Leading Order

Many experimental analyses separate events into exclusive jet bins, using a jet algorithm to cluster the final state and then veto on jets. Jet clustering induces logarithmic dependence on the jet radius R in the cross section for exclusive jet bins, a dependence that is poorly controlled due to the non-global nature of the clustering. At jet radii of experimental interest, the leading order (LO) clustering effects are numerically significant, but the higher order effects are currently unknown. We rectify this situation by calculating the most important part of the next-to-leading order (NLO) clustering logarithms of R for any 0-jet process, which enter as $O(\alpha_s^3)$ corrections to the cross section. The calculation blends subtraction methods for NLO calculations with factorization properties of QCD and soft-collinear effective theory (SCET). We compare the size of the known LO and new NLO clustering logarithms and find that the impact of the NLO terms on the 0-jet cross section in Higgs production is small. This brings clustering effects under better control and may be used to improve uncertainty estimates on cross sections with a jet veto.Comment: 39 pages, 5 figures. v2: journal version. v3: added missing term in calculation, conclusions unchange

N-jettiness Subtractions for NNLO QCD Calculations

We present a subtraction method utilizing the N-jettiness observable, Tau_N, to perform QCD calculations for arbitrary processes at next-to-next-to-leading order (NNLO). Our method employs soft-collinear effective theory (SCET) to determine the IR singular contributions of N-jet cross sections for Tau_N -> 0, and uses these to construct suitable Tau_N-subtractions. The construction is systematic and economic, due to being based on a physical observable. The resulting NNLO calculation is fully differential and in a form directly suitable for combining with resummation and parton showers. We explain in detail the application to processes with an arbitrary number of massless partons at lepton and hadron colliders together with the required external inputs in the form of QCD amplitudes and lower-order calculations. We provide explicit expressions for the Tau_N-subtractions at NLO and NNLO. The required ingredients are fully known at NLO, and at NNLO for processes with two external QCD partons. The remaining NNLO ingredient for three or more external partons can be obtained numerically with existing NNLO techniques. As an example, we employ our method to obtain the NNLO rapidity spectrum for Drell-Yan and gluon-fusion Higgs production. We discuss aspects of numerical accuracy and convergence and the practical implementation. We also discuss and comment on possible extensions, such as more-differential subtractions, necessary steps for going to N3LO, and the treatment of massive quarks.Comment: 51 pages, 10 figures, v2: journal versio

Recombination Algorithms and Jet Substructure: Pruning as a Tool for Heavy Particle Searches

We discuss jet substructure in recombination algorithms for QCD jets and single jets from heavy particle decays. We demonstrate that the jet algorithm can introduce significant systematic effects into the substructure. By characterizing these systematic effects and the substructure from QCD, splash-in, and heavy particle decays, we identify a technique, pruning, to better identify heavy particle decays into single jets and distinguish them from QCD jets. Pruning removes protojets typical of soft, wide angle radiation, improves the mass resolution of jets reconstructing a heavy particle decay, and decreases the QCD background. We show that pruning provides significant improvements over unpruned jets in identifying top quarks and W bosons and separating them from a QCD background, and may be useful in a search for heavy particles.Comment: 33 pages, 42 figure

Factorization and Resummation for Dijet Invariant Mass Spectra

Multijet cross sections at the LHC and Tevatron are sensitive to several distinct kinematic energy scales. When measuring the dijet invariant mass m_jj between two signal jets produced in association with other jets or weak bosons, m_jj will typically be much smaller than the total partonic center-of-mass energy Q, but larger than the individual jet masses m, such that there can be a hierarchy of scales m << m_jj << Q. This situation arises in many new-physics analyses at the LHC, where the invariant mass between jets is used to gain access to the masses of new-physics particles in a decay chain. At present, the logarithms arising from such a hierarchy of kinematic scales can only be summed at the leading-logarithmic level provided by parton-shower programs. We construct an effective field theory, SCET+, which is an extension of soft-collinear effective theory that applies to this situation of hierarchical jets. It allows for a rigorous separation of different scales in a multiscale soft function and for a systematic resummation of logarithms of both m_jj/Q and m/Q. As an explicit example, we consider the invariant mass spectrum of the two closest jets in e+e- -> 3 jets. We also give the generalization to pp -> N jets plus leptons relevant for the LHC.Comment: 37 pages, 6 figures; v2: journal versio

Jet p_T Resummation in Higgs Production at NNLL'+NNLO

We present predictions for Higgs production via gluon fusion with a p_T veto on jets and with the resummation of jet-veto logarithms at NNLL'+$NNLO order. These results incorporate explicit O(alphas^2) calculations of soft and beam functions, which include the dominant dependence on the jet radius R. In particular the NNLL' order accounts for the correct boundary conditions for the N3LL resummation, for which the only unknown ingredients are higher-order anomalous dimensions. We use scale variations in a factorization theorem in both rapidity and virtuality space to estimate the perturbative uncertainties, accounting for both higher fixed-order corrections as well as higher-order towers of jet-p_T logarithms. This formalism also predicts the correlations in the theory uncertainty between the exclusive 0-jet and inclusive 1-jet bins. At the values of R used experimentally, there are important corrections due to jet algorithm clustering that include logarithms of R. Although we do not sum logarithms of R, we do include an explicit contribution in our uncertainty estimate to account for higher-order jet clustering logarithms. Precision predictions for this H+0-jet cross section and its theoretical uncertainty are an integral part of Higgs analyses that employ jet binning.Comment: 24 pages, 11 figure

Drell-Yan Production at NNLL'+NNLO Matched to Parton Showers

We present results for Drell-Yan production from the GENEVA Monte-Carlo framework. We combine the fully-differential NNLO calculation with higher-order resummation in the 0-jettiness resolution variable. The resulting parton-level events are further combined with parton showering and hadronization provided by PYTHIA8. The 0-jettiness resummation is carried out to NNLL', which consistently incorporates all singular virtual and real NNLO corrections. It thus provides a natural perturbative connection between the NNLO calculation and the parton shower regime, including a systematic assessment of perturbative uncertainties. In this way, inclusive observables are correct to NNLO, up to small power corrections in the resolution cutoff. Furthermore, the perturbative accuracy of 0-jet-like resummation variables is significantly improved beyond the parton shower approximation. We provide comparisons with LHC measurements of Drell-Yan production at 7 TeV from ATLAS, CMS, and LHCb. As already observed in $e^+e^-$ collisions, for resummation-sensitive observables, the agreement with data is noticeably improved by using a lower value of $\alpha_s(M_Z) = 0.1135$.Comment: 26 pages, 20 figure