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 (µ 2), the N-subjettiness ratio (τ (β=2) 21) and energy correlation functions (C (β=2) 2 or D (β=2) 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.
