W polarisation beyond helicity fractions in top quark decays

TL;DR

This paper extends the analysis of top quark decay by introducing new W polarisation fractions, especially transverse and normal, and demonstrates their sensitivity to anomalous couplings and CP-violating effects, enabling comprehensive coupling measurements at the LHC.

Contribution

It introduces the study of transverse and normal W polarisation fractions in top decays and explores their sensitivity to anomalous couplings and CP violation, enhancing top decay analysis.

Findings

Normal W polarisation asymmetry is sensitive to complex phases in Wtb couplings.

A simple forward-backward asymmetry in the normal direction indicates normal W polarisation.

Combined analysis can measure all Wtb couplings and top polarisation at the LHC.

Abstract

We calculate the density matrix for the decay of a polarised top quark into a polarised W boson and a massive b quark, for the most general Wtb vertex arising from dimension-six gauge-invariant effective operators. We show that, in addition to the well-known W helicity fractions, for polarised top decays it is worth to define and study the transverse and normal W polarisation fractions, that is, the W polarisation along two directions orthogonal to its momentum. In particular, a rather simple forward-backward asymmetry in the normal direction is found to be very sensitive to complex phases in one of the Wtb anomalous couplings. This asymmetry, which indicates a normal W polarisation, can be generated for example by a P-odd, T-odd transition electric dipole moment. We also investigate the angular distribution of decay products in the top quark rest frame, calculating the spin analysing powers for a general Wtb vertex. Finally we show that, using a combined fit to top decay observables and the tW cross section, at LHC it will be possible to obtain model-independent measurements of all the (complex) Wtb couplings as well as the single top polarisation. Implications for spin correlations in top pair production are also discussed.