Analytic Boosted Boson Discrimination

TL;DR

This paper presents an all-orders factorization framework for the two-prong jet discriminant $D_2$, built within soft-collinear effective theory (SCET) and extended by a novel zero-bin merging procedure to coherently combine background and signal descriptions across soft/hard subjet regions. By using a basis of energy correlation observables $e_{2}^{( ext{α})}$, $e_{2}^{( ext{β})}$, and $e_{3}^{( ext{α})}$, it derives region-specific factorization theorems (soft haze, collinear subjets, soft subjet) and demonstrates Sudakov safety for $D_2$ with a jet-mass cut. The authors compare analytic predictions, including non-perturbative shape functions to model hadronization, with parton- and hadron-level Monte Carlo simulations for boosted $Z$ discrimination at $e^+e^-$ colliders, showing good overall agreement and pinpointing MC sensitivities to soft radiation modeling. They also discuss LEP tests, LHC extensions, and potential uses in Monte Carlo tuning and NNLL improvements. Overall, the work provides a systematic, calculable, and improvable path to understanding jet substructure observables and boosting the precision of boosted-boson tagging at current and future colliders.

Abstract

Observables which discriminate boosted topologies from massive QCD jets are of great importance for the success of the jet substructure program at the Large Hadron Collider. Such observables, while both widely and successfully used, have been studied almost exclusively with Monte Carlo simulations. In this paper we present the first all-orders factorization theorem for a two-prong discriminant based on a jet shape variable, $D_2$, valid for both signal and background jets. Our factorization theorem simultaneously describes the production of both collinear and soft subjets, and we introduce a novel zero-bin procedure to correctly describe the transition region between these limits. By proving an all orders factorization theorem, we enable a systematically improvable description, and allow for precision comparisons between data, Monte Carlo, and first principles QCD calculations for jet substructure observables. Using our factorization theorem, we present numerical results for the discrimination of a boosted $Z$ boson from massive QCD background jets. We compare our results with Monte Carlo predictions which allows for a detailed understanding of the extent to which these generators accurately describe the formation of two-prong QCD jets, and informs their usage in substructure analyses. Our calculation also provides considerable insight into the discrimination power and calculability of jet substructure observables in general.

Figures (35)

• Figure 1: Comparison of our analytic calculation with Vincia Monte Carlo predictions for the two prong discriminant, $D_2$. Predictions for both boosted $Z$ bosons and massive QCD jets at a 1 TeV $e^+e^-$ collider are shown. The Monte Carlo is fully hadronized, and non-perturbative effects have been included in the analytic calculation through a shape function. In a) we show the complete distribution, and in b) we zoom in to focus on the region relevant for boosted $Z$ discrimination.
• Figure 2: Regions of interest for studying the two-prong substructure of a jet. a) Soft haze region in which no subjets are resolved. b) Collinear subjets with comparable energy and a small opening angle. c) Soft subjet carrying a small fraction of the total energy, and at a wide angle from the hard subjet.
• Figure 3: a) Schematic of a one-prong soft haze jet, dominated by collinear (blue) and soft (green) radiation. The angular size of the collinear radiation is $\theta_{cc}$ and the energy fraction of the soft radiation is $z_s$. b) Schematic of a jet resolved into two collinear subjets, dominated by collinear (blue), soft (green), and collinear-soft (orange) radiation emitted from the dipole formed by the two subjets. The subjets are separated by an angle $\theta_{12}$ and the energy fraction of the collinear-soft radiation is $z_{cs}$.
• Figure 4: Monte Carlo distributions in the $e_{2}^{(1)},e_{3}^{(1)}$ plane, for QCD quark jets (left) and boosted $Z\to q\bar{q}$ jets (right). The parametric scalings predicted by the power counting analysis are shown as dashed lines, and the one- and two-prong regions of phase space are labelled, and extend between the parametric boundaries. Note the upper boundary is constrained to have a maximal value of $\frac{1}{2}(e_{2}^{(\alpha)})^2=e_{3}^{(\alpha)}$.
• Figure 5: a) Table summarizing the defining relations for the different subjet configurations in terms of the energy correlation functions $e_{2}^{(\alpha)}, e_{2}^{(\beta)},e_{3}^{(\alpha)}$. b) The one- and two-prong jets regions in the $e_{2}^{(\beta)}, e_{3}^{(\alpha)}$ phase space. Jets with a two-prong structure lie in the lower (orange) region of phase space, while jets with a one-prong structure lie in the upper (purple) region of phase space. c) The projection onto the $e_{2}^{(\alpha)}, e_{2}^{(\beta)}$ phase space in which the soft subjet and collinear subjets are separated.