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

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 21 ( = 2) ) and energy correlation functions (c 2 ( = 2) or d 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.