Precision Jet Substructure from Boosted Event Shapes

TL;DR

This work demonstrates that systematic higher-order QCD computations of jet substructure can be carried out by boosting global event shapes by a large momentum Q and accounting for effects due to finite jet size, initial-state radiation (ISR), and the underlying event (UE) as 1/Q corrections.

Abstract

Jet substructure has emerged as a critical tool for LHC searches, but studies so far have relied heavily on shower Monte Carlo simulations, which formally approximate QCD at leading-log level. We demonstrate that systematic higher-order QCD computations of jet substructure can be carried out by boosting global event shapes by a large momentum Q, and accounting for effects due to finite jet size, initial-state radiation (ISR), and the underlying event (UE) as 1/Q corrections. In particular, we compute the 2-subjettiness substructure distribution for boosted Z -> q qbar events at the LHC at next-to-next-to-next-to-leading-log order. The calculation is greatly simplified by recycling the known results for the thrust distribution in e+ e- collisions. The 2-subjettiness distribution quickly saturates, becoming Q independent for Q > 400 GeV. Crucially, the effects of jet contamination from ISR/UE can be subtracted out analytically at large Q, without knowing their detailed form. Amusingly, the Q=infinity and Q=0 distributions are related by a scaling by e, up to next-to-leading-log order.

Figures (4)

• Figure 1: Kinematics of boosted $Z$ decay.
• Figure 2: Results of the N$^3$LL analytic calculation for $\tau_{21}$ with $\Phi = 0$. The distribution saturates for $Q \gtrsim 400$ GeV.
• Figure 3: Comparison of theory prediction (bands) for $\tau_{21}$ to baseline Pythia (histograms). The heavier (lighter) band is N$^3$LL (NNLL), with widths given by factor of two variations of the hard, jet, and soft scales. Here, $\Phi = 700$ MeV. Arrows indicate the approximate range of validity of \ref{['eq:Ufact']}.
• Figure 4: a) Effect of finite jet cone and ISR/UE in Pythia. The $\Delta \tau'$ correction mitigates ISR/UE jet contamination. b) Fractional effect of adding finite cone and ISR/UE to the Pythia baseline distribution. With the $\Delta \tau'$ correction, these effects are smaller than 5% for $Q \gtrsim 400$ GeV, and scale as $1/Q$ as expected. c) Effect of finite $Z$ width. d) $e$-scaling between $Q = 0$ (thrust) and $Q = \infty$.