Jet substructures of boosted polarized hadronic top quarks

Abstract

We study jet substructures of a boosted polarized top quark, which undergoes the hadronic decay $t\to b u\bar d$, in the perturbative QCD framework, focusing on the energy profile and the differential energy profile. These substructures are factorized into the convolution of a hard top-quark decay kernel with a bottom-quark jet function and a $W$-boson jet function, where the latter is further factorized into the convolution of a hard $W$-boson decay kernel with two light-quark jet functions. Computing the hard kernels to leading order in QCD and including the resummation effect in the jet functions, we show that the differential jet energy profile is a useful observable for differentiating the helicity of a boosted hadronic top quark: a right-handed top jet exhibits quick descent of the differential energy profile with the inner test cone radius $r$, which is attributed to the $\mbox{V-A}$ structure of weak interaction and the dead-cone effect associated with the $W$-boson jet. The above helicity differentiation may help to reveal the chiral structure of physics beyond the Standard Model at high energies.