Jet shapes for boosted jet two-prong decays from first-principles

TL;DR

This paper provides a first-principles analytical study of jet shape variables used to distinguish boosted two-prong decays from QCD backgrounds, offering new insights into their performance and application.

Contribution

It offers the first analytical calculations of key jet shape variables for both background and signal jets, including effects of recursive cuts and axis choices.

Findings

Analytic expressions for jet shape distributions in QCD background jets.

Comparison of jet shape variables' effectiveness for boosted object identification.

Insights into the impact of axis choice and recursive cuts on jet shape performance.

Abstract

Several boosted jet techniques use jet shape variables to discriminate the multi-pronged signal from Quantum Chromodynamics backgrounds. In this paper, we provide a first-principles study of an important class of jet shapes all of which put a constraint on the subjet mass: the mass-drop parameter ($\mu^2$), the $N$-subjettiness ratio ($\tau_{21}^{(\beta=2)}$) and energy correlation functions ($C_2^{(\beta=2)}$ or $D_2^{(\beta=2)}$). We provide analytic results both for QCD background jets as well as for signal processes. We further study the situation where cuts on these variables are applied recursively with Cambridge-Aachen de-clustering of the original jet. We also explore the effect of the choice of axis for $N$-subjettiness and jet de-clustering. Our results bring substantial new insight into the nature, gain and relative performance of each of these methods, which we expect will influence their future application for boosted object searches.