Towards an understanding of jet substructure

TL;DR

The paper delivers analytic, resummed calculations for how popular jet-substructure taggers—trim, prune, MDT—and two new variants perform on QCD jets. By framing emissions in a small-R, single-log accuracy context and introducing Lund-diagram-inspired reasoning, it uncovers the distinct log structures and Sudakov behavior across methods, highlighting mMDT’s unique absence of non-global logarithms and its favorable perturbative stability. Comprehensive comparisons with Monte Carlo data validate the analytic results and emphasize how tagger choice shapes background shapes, non-perturbative effects, and signal-background discrimination. The work provides a robust foundation for interpreting substructure tools and for guiding parameter choices in future studies and experimental analyses.

Abstract

We present first analytic, resummed calculations of the rates at which widespread jet substructure tools tag QCD jets. As well as considering trimming, pruning and the mass-drop tagger, we introduce modified tools with improved analytical and phenomenological behaviours. Most taggers have double logarithmic resummed structures. The modified mass-drop tagger is special in that it involves only single logarithms, and is free from a complex class of terms known as non-global logarithms. The modification of pruning brings an improved ability to discriminate between the different colour structures that characterise signal and background. As we outline in an extensive phenomenological discussion, these results provide valuable insight into the performance of existing tools and help lay robust foundations for future substructure studies.

Figures (19)

• Figure 1: The distribution of $\rho = m^2/(p_t^2 R^2)$ for tagged jets, with three taggers/groomers: trimming, pruning and the mass-drop tagger (MDT). The results have been obtained from Monte Carlo simulation with Pythia 6.425 Pythia6 in the DW tune DW (virtuality-ordered shower), with a minimum $p_t$ cut in the generation of $3\,\mathrm{TeV}$, for $14\,\mathrm{TeV}$$pp$ collisions, at parton level, including initial and final-state showering, but without the underlying event (multiple interactions). The left-hand plot shows $qq \to qq$ scattering, the right-hand plot $gg \to gg$ scattering. In all cases, the taggers have been applied to the two leading Cambridge/Aachen Dokshitzer:1997inWobisch:1998wt jets ($R=1.0$). The parameters chosen for mass-drop ($y_\text{cut}=0.09$, $\mu=0.67$), pruning ($z_\text{cut}=0.1$, $R_\text{fact}=0.5$) and trimming ($z_\text{cut}=0.05$, $R_\text{sub}=0.3$) all correspond to widely-used choices.
• Figure 2: Lund diagrams Andersson:1988gp represent emission kinematics in terms of two variables: vertically, the logarithm of an emission's transverse momentum $k_t$ with respect to the jet axis, and horizontally, the logarithm of the inverse of the emission's angle $\theta$ with respect to the jet axis, i.e. its rapidity with respect to the jet axis. Here the diagram shows a line of constant jet mass, together with a shaded region corresponding to the part of the kinematic plane where emissions are vetoed, leading to a Sudakov form factor.
• Figure 3: Lund kinematic diagrams for trimming, considering three different possible values of $\rho$. In each case, to obtain the given value of $\rho$, there must be an emission somewhere along the thick (red) line, and there must be no emissions in the shaded region. Emissions in the unshaded regions have no impact on the trimmed jet mass. Dotted lines serve to indicate transition regions in the kinematic plane and their relation to the parameters of the trimmer.
• Figure 4: Comparison of Monte Carlo (left panels) and analytic results (right panels) for trimming. The upper panels are for quark jets, the lower panels for gluon jets. Two sets of trimming parameters are illustrated. In the upper left panel, arrows indicate the expected transition points, at $\rho = r^2 z_\text{cut}$ (in black) and $\rho = z_\text{cut}$ (in grey), where $r = R_\text{sub}/R$. The details of the MC event generation are as for Fig. \ref{['fig:tagged-mass-MC']}.
• Figure 5: Configuration that illustrates generation of double logs in pruning at ${\cal O}\left(\alpha_s^2\right)$. Soft gluon $p_3$ dominates the jet mass, thus determining the pruning radius. However, because of $p_3$'s softness, it is then pruned away, leaving only the central core of the jet, which has a usual double-logarithmic type mass distribution.