Spin analyzing power for polarized top decays with jets

TL;DR

This paper develops a perturbative QCD framework to analyze the spin analyzing power in polarized top quark decays involving jets, predicting a potential doubling of sensitivity when jet dynamics are considered.

Contribution

It introduces a factorization approach combining a heavy-quark kernel and a jet function to study spin analyzing power dependence on jet invariant mass.

Findings

Spin analyzing power can be enhanced by a factor of 2 with jet mass consideration.

The approach predicts how spin sensitivity varies with jet invariant mass.

Experimental tests of the jet effect on spin analysis are encouraged.

Abstract

We perform perturbative QCD factorization of infrared radiations associated with an energetic $b$ quark from a polarized top quark decay, taking the semi-leptonic channel as an example. The resultant formula is expressed as a convolution of an infrared-finite heavy-quark kernel with a $b$-quark jet function. Evaluating the heavy-quark kernel up to leading order in the coupling constant and adopting the jet function from QCD resummation, we predict the dependence of the spin analyzing power for a polarized top quark on the invariant mass of the $b$-quark jet. It is observed that the spin analyzing power could be enhanced by a factor 2 compared to the inclusive case with the jet mass being integrated over. It is worthwhile to test experimentally the enhancement of the spin analyzing power due to the inclusion of jet dynamics.