A measurement of the correlations between the polar angles of leptons from the decay of pair-produced $t$ and $\bar{t}$ quarks in the helicity basis is reported, using proton-proton collision data collected by the ATLAS detector at the LHC. The dataset corresponds to an integrated luminosity of 4.6fb$^{-1}$ at a center-of-mass energy of $\sqrt{s}=7$TeV collected during 2011. Candidate events are selected in the dilepton topology with large missing transverse momentum and at least two jets. The angles $\theta_1$ and $\theta_2$ between the charged leptons and the direction of motion of the parent quarks in the $t\bar{t}$ rest frame are sensitive to the spin information, and the distribution of {\mbox{$\cos\theta_1\cdot\cos\theta_2$}} is sensitive to the spin correlation between the $t$ and $\bar{t}$ quarks. The distribution is unfolded to parton level and compared to the next-to-leading order prediction. A good agreement is observed.
The numerical summary of the unfolded $\cos\theta_1\cdot\cos\theta_2$ distribution, with statistical and systematic uncertainties.
The correlation factors for the statistical uncertainties between any two bins of the unfolded distribution.
We report a measurement of the differential cross section, d{\sigma}/d(cos {\theta}t), for top-quark-pair production as a function of the top-quark production angle in proton-antiproton collisions at sqrt{s} = 1.96 TeV. This measurement is performed using data collected with the CDF II detector at the Tevatron, corresponding to an integrated luminosity of 9.4/fb. We employ the Legendre polynomials to characterize the shape of the differential cross section at the parton level. The observed Legendre coefficients are in good agreement with the prediction of the next-to-leading-order standard-model calculation, with the exception of an excess linear-term coefficient, a1 = 0.40 +- 0.12, compared to the standard-model prediction of a1 = 0.15^{+0.07}_{-0.03}.
The parton-level Legendre moments for the measured angular distribution of the momentum direction of the t-quark from the momentum direction of the incoming proton.
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