Next-to-leading logarithmic final-state resummed predictions have traditionally been calculated, manually, separately for each observable. In this article we derive NLL resummed results for generic observables. We highlight and discuss the conditions that the observable should satisfy for the approach to be valid, in particular continuous globalness and recursive infrared and collinear safety. The resulting resummation formula is expressed in terms of certain well-defined characteristics of the observable. We have written a computer program, caesar, which, given a subroutine for an arbitrary observable, determines those characteristics, enabling full automation of a large class of final-state resummations, in a range of processes.

We consider interjet observables in hard QCD processes given by the energy flow E out in a region away from all hard jets. Here the QCD radiation is depleted (E out ≪ Q), and therefore these observables provide ideal means to study non-perturbative effects. We derive an evolution equation (in the large N c limit) which resums, for large Q/E out , all leading terms arising from large angle soft emission (double logarithms are absent). We discuss the analytical features of the result and identify universal and geometry-dependent contributions. Our analysis confirms features found using numerical methods by Dasgupta and Salam.

We derive first next-to-next-to-leading logarithmic resummations for jet-veto efficiencies in Higgs and Z-boson production at hadron colliders. Matching with next-to-next-to-leading order results allows us to provide a range of phenomenological predictions for the LHC, including cross-section results, detailed uncertainty estimates and comparisons to current widely-used tools.In searches for new physics at hadron colliders such as the Tevatron and CERN's Large Hadron Collider (LHC), in order to select signal events and reduce backgrounds, events are often classified according to the number of hadronic jets -collimated bunches of energetic hadrons -in the final state. A classic example is the search for Higgs production via gluon fusion with a subsequent decay to. A severe background comes from tt production, whose decay products also include a W + W − pair. However, this background can be separated from the signal because its W + W − pair usually comes together with hard jets, since in each top decay the W is accompanied by an energetic (b) quark.Relative to classifications based on objects such as leptons (used e.g. to identify the W decays), one of the difficulties of hadronic jets is that they may originate not just from the decay of a heavy particle, but also as Quantum Chromodynamic (QCD) radiation. This is the case in our example, where the incoming gluons that fuse to produce the Higgs quite often radiate additional partons. Consequently, while vetoing the presence of jets eliminates much of the tt background, it also removes some fraction of signal events. To fully interpret the search results, including measuring Higgs couplings, it is crucial to be able to predict the fraction of the signal that survives the jet veto, which depends for example on the transverse momentum threshold p t,veto used to identify vetoed jets.One way to evaluate jet-veto efficiencies is to use a fixed-order perturbative expansion in the strong coupling α s , notably to next-next-to-leading order (NNLO), as in the Higgs-boson production calculations of [3][4][5]. Such calculations however become unreliable for p t,veto ≪ M , with M the boson mass, since large terms α n s L 2n appear (L = ln(M/p t,veto )) in the cross-section to all orders in the coupling constant. These enhanced classes of terms can, however, be resummed to all orders in the coupling, often involving a functional form .).There exist next-to-next-to-leading logarithmic (NNLL) resummations, involving the g n (α s L) functions up to and including g 3 , for a number of quantities that are more inclusive than a jet veto: e.g. a Higgs or vector-boson transverse momentum [6][7][8][9], the beam thrust [10], and related observables [11,12]. To obtain estimates for jet vetoes, some of these calculations have been compared to or used to reweight [10,[13][14][15][16] parton-shower predictions [17,18] matched to NLO results [19,20]. However, with reweighting, neither the NNLO nor NNLL accuracy of the original calculation carry through to the jet veto prediction.Recently ther...

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 α 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.

It is common, in both theoretical and experimental studies, to separately discuss quark and gluon jets. However, even at parton level, widely-used jet algorithms fail to provide an infrared safe way of making this distinction. We examine the origin of the problem, and propose a solution in terms of a new 'flavour-k t ' algorithm. As well as being of conceptual interest this can be a powerful tool when combining fixed-order calculations with multi-jet resummations and parton showers. It also has applications to studies of heavy-quark jets.