Polarization of top produced in particle decays in an arbitrary frame

Abstract

In most of the models beyond the Standard Model, the top quark is expected to be polarized when produced in the decay of some heavier particle, like the gluino or the stop. The polarization is constructed, in an experiment or in simulations, through the distribution of top decay products. Here, we propose an estimator of top quark polarization that depends only on the kinematics of it's mother particle, apart from its decay couplings to top quarks, and is given in terms of the top polarization expected in the rest frame of the decaying particle. This estimator allows one to estimate the top polarization without performing a full simulation. We find this estimator is independent of the production angle of the mother, top decay angle (for unpolarized mother), and the spin of the mother particle. We study the quality of the estimator with finite width of the mother particle via examples of gluinos and stops decaying into top quark at LHC. We also point out how for the mass spectra of gluinos and top squarks currently expected in a `natural' scenario, the polarization of the top quarks produced in the gluino decays can uniquely track the mixing angle in the stop sector.