W polarisation beyond helicity fractions in top quark decays
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Aguilar-Saavedra, J.A.; Bernabéu, J. W polarisation beyond helicity fractions in top quark decays. Nuclear Physics B, 840(1-2): 439-378 (2010). [http://hdl.handle.net/10481/30585]
SponsorshipThis work has been partially supported by projects FPA 2006-05294 and FPA 2008-02878 (MICINN), FQM 101 and FQM 437 (Junta de Andalucía), PROMETEO 2008/004 (Generalitat Valenciana), CERN/FP/83588/2008 (FCT), and by the European Community's Marie-Curie Research Training Network under contract MRTN-CT-2006-035505 “Tools and Precision Calculations for Physics Discoveries at Colliders”. The work of J.A.A.S. has been supported by a MICINN Ramón y Cajal contract.
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 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 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.