W polarisation beyond helicity fractions in top quark decays

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 W tb 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 defining and studying 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 W tb 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 W tb 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) W tb couplings as well as the single top polarisation. Implications for spin correlations in top pair production are also discussed.

Measurements of the top quark properties at decay with CMS

“…Values different from zero are then an indication of deviations from the SM. By fixing the two vector couplings to their SM expectation (V L = 1, V R = 0), limits are derived on the tensor couplings, using the theoretical relations between the helicity fractions and the couplings [6]. The values allowed for Re(g L ) and Re(g R ) are shown as contour plots in Fig.…”

Anomalous couplings in single top and searches for rare top quark couplings with the ATLAS detector

“…[2,7]: S 1,2,3 , T 0 and A 1,2 . The observables S 1,2 and A 1,2 are proportional to P. The observables S 3 and T 0 are related the W -boson helicity fractions: F R ,F L and F 0 .…”

“…Moreover, complex values of these couplings would imply that the top-quark decay has a CP-violating component [2]. On the other hand, searches for rare topquark decays are interesting because a wide variety of models of physics beyong the SM predicts a strong enhancement of the branching ratios of flavor-violating top quark decays [3], that are highly suppressed in the SM.…”

Top mass and properties at the LHC and Tevatron

“…However, if the top quark is polarised (as occurs in the case of top quarks produced via the single top t-channel process) two additional directions can be considered: the transverse T and the normal N as defined in Ref. [18]. Therefore, three different angles can be defined between the charged lepton momentum in the W rest frame and each of the three mentioned directions q, T and N, as θ * , θ T and θ N respectively.…”

“…Concerning the lepton angular distributions defined in the normal direction, it is in particular interesting to measure the forward-background asymmetry A FB , as proposed in Ref. [18], because of its sensitivity to Im(g R ). A nonzero value of this asymmetry would automatically lead to a sign of CP violation in top quark decays.…”