Power counting to better jet observables

Abstract

Optimized jet substructure observables for identifying boosted topologies will play an essential role in maximizing the physics reach of the Large Hadron Collider. Ideally, the design of discriminating variables would be informed by analytic calculations in perturbative QCD. Unfortunately, explicit calculations are often not feasible due to the complexity of the observables used for discrimination, and so many validation studies rely heavily, and solely, on Monte Carlo. In this paper we show how methods based on the parametric power counting of the dynamics of QCD, familiar from effective theory analyses, can be used to design, understand, and make robust predictions for the behavior of jet substructure variables. As a concrete example, we apply power counting for discriminating boosted Z bosons from massive QCD jets using observables formed from the n-point energy correlation functions. We show that power counting alone gives a definite prediction for the observable that optimally separates the background-rich from the signal-rich regions of phase space. Power counting can also be used to understand effects of phase space cuts and the effect of contamination from pile-up, which we discuss. As these arguments rely only on the parametric scaling of QCD, the predictions from power counting must be reproduced by any Monte Carlo, which we verify using Pythia 8 and Herwig++. We also use the example of quark versus gluon discrimination to demonstrate the limits of the power counting technique.

Analytic boosted boson discrimination

“…Using the power counting technique of refs. [66,67], we show that the angular exponents of the energy correlation functions, α and β, can be chosen such that the different subjet configurations occupy parametrically separated regions of this phase space, and extend to all boundaries of the phase space. This parametric separation allows for each region to be separately described by its own effective field theory.…”

“…Examples of such observables include ratios of N -subjettiness variables [63,64], ratios of energy correlation functions [65][66][67], or planar flow [68]. In general, ratios of IRC safe observables are not themselves IRC safe [69] and cannot be calculated -1 -…”

“…In this paper we will study the factorization and resummation of the jet substructure observable D 2 [66], a ratio-type observable formed from the energy correlation functions. We will give a detailed effective theory analysis using the language of soft-collinear effective theory (SCET) [79][80][81][82] in all regions of phase space required for the description of a one or two-prong jet, and will prove all-orders leading-power factorization theorems in each region.…”

A complete basis of helicity operators for subleading factorization

“…In addition to collinear and soft modes, these effective field theories typically contain (multiple) collinear-soft modes, which exhibit both a collinear, and a soft scaling. Such effective field theories have been used, for example, for the calculation [101] of the D 2 [102] jet substructure observable. While subleading power corrections to SCET + theories have not been studied, we wish to emphasize that our helicity operator approach extends also straightforwardly to such theories.…”

Soft evolution of multi-jet final states

“…Inter-jet radiation and in particular its response to the presence of a jet veto has also received a lot of attention both from the theoretical [53][54][55][56][57][58][59] and experimental [60][61][62][63] communities, primarily in the context of Higgs-boson studies [64][65][66][67][68][69][70]. All-order analytical calculations have been performed recently for an increasing number of jet-substructure observables, including jet masses [71][72][73][74], other jet shapes [75][76][77][78][79], sub-jet multiplicity [80] and grooming algorithms [81][82][83]. Recently, there has also been substantial progress towards achieving NNLL accuracy in threshold resummation for dijet production [84,85].…”