We introduce a new jet substructure technique called "soft drop declustering", which recursively removes soft wide-angle radiation from a jet. The soft drop algorithm depends on two parameters -a soft threshold z cut and an angular exponent β -with the β = 0 limit corresponding roughly to the (modified) mass drop procedure. To gain an analytic understanding of soft drop and highlight the β dependence, we perform resummed calculations for three observables on soft-dropped jets: the energy correlation functions, the groomed jet radius, and the energy loss due to soft drop. The β = 0 limit of the energy loss is particularly interesting, since it is not only "Sudakov safe" but also largely insensitive to the value of the strong coupling constant. While our calculations are strictly accurate only to modified leading-logarithmic order, we also include a discussion of higher-order effects such as multiple emissions and (the absence of) non-global logarithms. We compare our analytic results to parton shower simulations and find good agreement, and we also estimate the impact of non-perturbative effects such as hadronization and the underlying event. Finally, we demonstrate how soft drop can be used for tagging boosted W bosons, and we speculate on the potential advantages of using soft drop for pileup mitigation.

We show how generalized energy correlation functions can be used as a powerful probe of jet substructure. These correlation functions are based on the energies and pair-wise angles of particles within a jet, with (N + 1)-point correlators sensitive to N -prong substructure. Unlike many previous jet substructure methods, these correlation functions do not require the explicit identification of subjet regions. In addition, the correlation functions are better probes of certain soft and collinear features that are masked by other methods. We present three Monte Carlo case studies to illustrate the utility of these observables: 2-point correlators for quark/gluon discrimination, 3-point correlators for boosted W /Z/Higgs boson identification, and 4-point correlators for boosted top quark identification. For quark/gluon discrimination, the 2-point correlator is particularly powerful, as can be understood via a next-to-leading logarithmic calculation. For boosted 2-prong resonances the benefit depends on the mass of the resonance.

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Jet grooming algorithms are widely used in experimental analyses at hadron colliders to remove contaminating radiation from within jets. While the algorithms perform a great service to the experiments, their intricate algorithmic structure and multiple parameters has frustrated precision theoretic understanding. In this paper, we demonstrate that one particular groomer called soft drop actually makes precision jet substructure easier. In particular, we derive a factorization formula for a large class of soft drop jet substructure observables, including jet mass. The essential observation that allows for this factorization is that, without the soft wide-angle radiation groomed by soft drop, all singular contributions are collinear. The simplicity and universality of the collinear limit in QCD allows us to show that to all orders, the normalized differential cross section has no contributions from non-global logarithms. It is also independent of process, up to the relative fraction of quark and gluon jets. In fact, soft drop allows us to define this fraction precisely. The factorization theorem also explains why soft drop observables are less sensitive to hadronization than their ungroomed counterparts. Using the factorization theorem, we resum the soft drop jet mass to next-to-next-to-leading logarithmic accuracy. This requires calculating some clustering effects that are closely related to corresponding effects found in jet veto calculations. We match our resummed calculation to fixed order results for both e + e − → dijets and pp → Z + j events, producing the first jet substructure predictions (groomed or ungroomed) to this accuracy for the LHC. arXiv:1603.09338v2 [hep-ph] 11 Jul 2016 Contents 1. Recluster the jet with a sequential k T -type [45-47] jet algorithm. This produces an infrared and collinear (IRC) safe branching history of the jet. The k T clustering metric 1 While we will not do it in this paper, one could use the results of Ref. [36] which calculates the anomalous dimension of the soft function for event-wide (recoil-free) angularities [37-40] or energy correlation functions with arbitrary angular exponent. This would enable us to extend our results to the case with α = 2. 2 The jet mass has been calculated at NNLL using other methods [41-43] as has 2-subjettiness [44]. However, without grooming the jets, there are non-global logarithms which are not resummed (and which may or may not be quantitatively important) and uncontrollable sensitivity to pileup (which is very quantitatively important).

In this paper, we review recent theoretical progress and the latest experimental results in jet substructure from the Tevatron and the LHC. We review the status of and outlook for calculation and simulation tools for studying jet substructure. Following up on the report of the Boost 2010 workshop, we present a new set of benchmark comparisons of substructure techniques, focusing on the set of variables and grooming methods that are collectively known as 'top taggers'. To facilitate further exploration, we have attempted to collect, harmonize and publish software implementations of these techniques.