On measurement of top polarization as a probe of $ t\bar{t} $ production mechanisms at the LHC

In this note we demonstrate the use of top polarization in the study of $ t\bar{t} $ resonances at the LHC, in the possible case where the dynamic s implies a non-zero top polarization. As a probe of top polarization we construct an asymmetry in the decay-lepton azimuthal angle distribution (corresponding to the sign of cos ϕℓ) in the laboratory. The asymmetry is non-vanishing even for a symmetric collider li ke the LHC, where a positive z axis is not uniquely defined. The angular distribution of the leptons has the advantage of being a faithful top-spin analyzer, unaffected by possible anomalous tbW couplings, to linear order. We study, for purposes of demonstration, the case of a Z′ as might exist in the little Higgs models. We identify kinematic cuts which ensure that our asymmetry reflects the polarization in sign and magnitude. We investigate poss ibilities at the LHC with two energy options: $ \sqrt {s} = 14\;{\text{TeV}} $ and $ \sqrt {s} = 7\;{\text{TeV}} $, as well as at the Tevatron. At the LHC the model predicts net top quark polarization of the order of a fe w per cent for MZ′ ≃ 1200 GeV, being as high as 10% for a smaller mass of the Z′ of 700 GeV and for the largest allowed coupling in the model, the values being higher for the 7 TeV op tion. These polarizations translate to a deviation from the standard-model value of az imuthal asymmetry of up to about 4% (7%) for 14 (7) TeV LHC, whereas for the Tevatron, val ues as high as 12% are attained. For the 14 TeV LHC with an integrated luminosity of 10 fb−1, these numbers translate into a 3σ sensitivity over a large part of the range 500 ≲ MZ′ ≲ 1500 GeV.