Optimal jet radius in kinematic dijet reconstruction

Obtaining a good momentum reconstruction of a jet is a compromise between taking it large enough to catch the perturbative final-state radiation and small enough to avoid too much contamination from the underlying event and initial-state radiation. In this paper, we compute analytically the optimal jet radius for dijet reconstructions and study its scale dependence. We also compare our results with previous Monte-Carlo studies.Comment: 30 pages, 11 figures; minor corrections; published in JHE

The mass area of jets

We introduce a new characteristic of jets called mass area. It is defined so as to measure the susceptibility of the jet's mass to contamination from soft background. The mass area is a close relative of the recently introduced catchment area of jets. We define it also in two variants: passive and active. As a preparatory step, we generalise the results for passive and active areas of two-particle jets to the case where the two constituent particles have arbitrary transverse momenta. As a main part of our study, we use the mass area to analyse a range of modern jet algorithms acting on simple one and two-particle systems. We find a whole variety of behaviours of passive and active mass areas depending on the algorithm, relative hardness of particles or their separation. We also study mass areas of jets from Monte Carlo simulations as well as give an example of how the concept of mass area can be used to correct jets for contamination from pileup. Our results show that the information provided by the mass area can be very useful in a range of jet-based analyses.Comment: 36 pages, 12 figures; v2: improved quality of two plots, added entry in acknowledgments, nicer form of formulae in appendix A; v3: added section with MC study and pileup correction, version accepted by JHE

Non-global logarithms and jet algorithms in high-pT jet shapes

We consider jet-shape observables of the type proposed recently, where the shapes of one or more high-pT jets, produced in a multi-jet event with definite jet multiplicity, may be measured leaving other jets in the event unmeasured. We point out the structure of the full next-to-leading logarithmic resummation specifically including resummation of non-global logarithms in the leading-Nc limit and emphasising their properties. We also point out differences between jet algorithms in the context of soft gluon resummation for such observables.Comment: 22 pages, 4 figures. Title and a few words changed. Several typos corrected. Version accepted by JHE

Phenomenology of event shapes at hadron colliders

We present results for matched distributions of a range of dijet event shapes at hadron colliders, combining next-to-leading logarithmic (NLL) accuracy in the resummation exponent, next-to-next-to leading logarithmic (NNLL) accuracy in its expansion and next-to-leading order (NLO) accuracy in a pure alpha_s expansion. This is the first time that such a matching has been carried out for hadronic final-state observables at hadron colliders. We compare our results to Monte Carlo predictions, with and without matching to multi-parton tree-level fixed-order calculations. These studies suggest that hadron-collider event shapes have significant scope for constraining both perturbative and non-perturbative aspects of hadron-collider QCD. The differences between various calculational methods also highlight the limits of relying on simultaneous variations of renormalisation and factorisation scale in making reliable estimates of uncertainties in QCD predictions. We also discuss the sensitivity of event shapes to the topology of multi-jet events, which are expected to appear in many New Physics scenarios.Comment: 70 pages, 25 figures, additional material available from http://www.lpthe.jussieu.fr/~salam/pp-event-shapes

Non-global Structure of the O({\alpha}_s^2) Dijet Soft Function

High energy scattering processes involving jets generically involve matrix elements of light- like Wilson lines, known as soft functions. These describe the structure of soft contributions to observables and encode color and kinematic correlations between jets. We compute the dijet soft function to O({\alpha}_s^2) as a function of the two jet invariant masses, focusing on terms not determined by its renormalization group evolution that have a non-separable dependence on these masses. Our results include non-global single and double logarithms, and analytic results for the full set of non-logarithmic contributions as well. Using a recent result for the thrust constant, we present the complete O({\alpha}_s^2) soft function for dijet production in both position and momentum space.Comment: 55 pages, 8 figures. v2: extended discussion of double logs in the hard regime. v3: minor typos corrected, version published in JHEP. v4: typos in Eq. (3.33), (3.39), (3.43) corrected; this does not affect the main result, numerical results, or conclusion

Pure Samples of Quark and Gluon Jets at the LHC

Having pure samples of quark and gluon jets would greatly facilitate the study of jet properties and substructure, with many potential standard model and new physics applications. To this end, we consider multijet and jets+X samples, to determine the purity that can be achieved by simple kinematic cuts leaving reasonable production cross sections. We find, for example, that at the 7 TeV LHC, the pp {\to} {\gamma}+2jets sample can provide 98% pure quark jets with 200 GeV of transverse momentum and a cross section of 5 pb. To get 10 pb of 200 GeV jets with 90% gluon purity, the pp {\to} 3jets sample can be used. b+2jets is also useful for gluons, but only if the b-tagging is very efficient.Comment: 19 pages, 16 figures; v2 section on formally defining quark and gluon jets has been adde

Double Non-Global Logarithms In-N-Out of Jets

We derive the leading non-global logarithms (NGLs) of ratios of jet masses m_{1,2} and a jet energy veto \Lambda due to soft gluons splitting into regions in and out of jets. Such NGLs appear in any exclusive jet cross section with multiple jet measurements or with a veto imposed on additional jets. Here, we consider back-to-back jets of radius R produced in e^+e^- collisions, found with a cone or recombination algorithm. The leading NGLs are of the form \alpha_s^2 \ln^2(\Lambda/m_{1,2}) or \alpha_s^2\ln^2(m_1/m_2). Their coefficients depend both on the algorithm and on R. We consider cone, \kt, anti-\kt, and Cambridge-Aachen algorithms. In addition to determining the full algorithmic and R dependence of the leading NGLs, we derive new relations among their coefficients. We also derive to all orders in \alpha_s a factorized form for the soft function S(k_L,k_R,\Lambda) in the cross section \sigma(m_1,m_2,\Lambda) in which dependence on each of the global logs of \mu/k_L, \mu/k_R and \mu/\Lambda determined by the renormalization group are separated from one another and from the non-global logs. The same kind of soft function, its associated non-global structure, and the algorithmic dependence we derive here will also arise in exclusive jet cross sections at hadron colliders, and must be understood and brought under control to achieve precise theoretical predictions.Comment: 19 pages, 10 figures. v2: minor edits, additional discussion in Introduction. v3: version published in JHE

Jet Shapes and Jet Algorithms in SCET

Jet shapes are weighted sums over the four-momenta of the constituents of a jet and reveal details of its internal structure, potentially allowing discrimination of its partonic origin. In this work we make predictions for quark and gluon jet shape distributions in N-jet final states in e+e- collisions, defined with a cone or recombination algorithm, where we measure some jet shape observable on a subset of these jets. Using the framework of Soft-Collinear Effective Theory, we prove a factorization theorem for jet shape distributions and demonstrate the consistent renormalization-group running of the functions in the factorization theorem for any number of measured and unmeasured jets, any number of quark and gluon jets, and any angular size R of the jets, as long as R is much smaller than the angular separation between jets. We calculate the jet and soft functions for angularity jet shapes \tau_a to one-loop order (O(alpha_s)) and resum a subset of the large logarithms of \tau_a needed for next-to-leading logarithmic (NLL) accuracy for both cone and kT-type jets. We compare our predictions for the resummed \tau_a distribution of a quark or a gluon jet produced in a 3-jet final state in e+e- annihilation to the output of a Monte Carlo event generator and find that the dependence on a and R is very similar.Comment: 62 pages plus 21 pages of Appendices, 13 figures, uses JHEP3.cls. v2: corrections to finite parts of NLO jet functions, minor changes to plots, clarified discussion of power corrections. v3: Journal version. Introductory sections significantly reorganized for clarity, classification of logarithmic accuracy clarified, results for non-Mercedes-Benz configurations adde

NLL+NNLO predictions for jet-veto efficiencies in Higgs-boson and Drell-Yan production

Using the technology of the CAESAR approach to resummation, we examine the jet-veto efficiency in Higgs-boson and Drell-Yan production at hadron colliders and show that at next-to-leading logarithmic (NLL) accuracy the resummation reduces to just a Sudakov form factor. Matching with NNLO calculations results in stable predictions for the case of Drell-Yan production, but reveals substantial uncertainties in gluon-fusion Higgs production, connected in part with the poor behaviour of the perturbative series for the total cross section. We compare our results to those from POWHEG with and without reweighting by HqT, as used experimentally, and observe acceptable agreement. In an appendix we derive the part of the NNLL resummation corrections associated with the radius dependence of the jet algorithm.Comment: 30 pages, 8 figures; v2 as published in JHE

Non--global logs and clustering impact on jet mass with a jet veto distribution

There has recently been much interest in analytical computations of jet mass distributions with and without vetos on additional jet activity [1-6]. An important issue affecting such calculations, particularly at next-to-leading logarithmic (NLL) accuracy, is that of non-global logarithms as well as logarithms induced by jet definition, as we pointed out in an earlier work [3]. In this paper, we extend our previous calculations by independently deriving the full jet-radius analytical form of non-global logarithms, in the anti-\kt jet algorithm. Employing the small-jet radius approximation, we also compute, at fixed-order, the effect of jet clustering on both \CF^{2} and \CF\CA colour channels. Our findings for the \CF\CA channel confirm earlier analytical calculations of non-global logarithms in soft-collinear effective theory [5]. Moreover, all of our results, as well as those of [3], are compared to the output of the numerical program \texttt{EVENT2}. We find good agreement between analytical and numerical results both with and without final state clustering.Comment: 33 pages, 15 figures. Version accepted by JHE