We present a measurement of the top quark polarization in the tt pair production in pp collisions at the Fermilab Tevatron collider at √ s = 1.96 TeV. We use the full Run II data sample corresponding to 9.1fb^{1} of integrated luminosity collected with the CDF detector. We select the final state events containing two high transverse momentum leptons (electron or muon), two jets and large missing transeverse energy. We measure the top quark polarization through the two dimensional distribution of lepton angles along the spin quantization axis. In order to reconstruct the angular distribution of top quark decay products, we perform full kinematic reconstruction using predicted distributions of P_{z}^{tt}, P_{T}^{tt}, M_{tt}. We make signal templates using NLO Monte Carlo simulation and background templates from admixture of Monte Carlo simulations and databased background modellings. Then, we perform binned likelihood fit of two dimensional angular distributions of data to signal and background templates and obtain a measurement of the top quark polarization. We consider two different axis for the top quark polarization measurement: the helicity axis and transeverse axis which is normal to the tt production plane. Two measurements of αP in each basis, the product of the leptonic spin analyzing power and the top quark polarization, are performed assuming that the polarization is introduced by either a CP conserving (CPC) or a CP violating (CPV) production process. The measured top quark polarizations are consistent with standard model predictions of negligible polarization.

The double differencial distribution of polar angles of two leptons with
respect to a given quantization axis.
C and P_{±} represent the
tt spin
correlation and the polarization of top and antitop quark along the
chosen quantization axis.
In this analysis, two extreme cases are considered according to the relative sign of α_{+}P_{+} and α_{}P_{}. CP convervation has the same sign and the CP violation has the opposite sign. α_{±} is the spinanalyzing power of the final state object. â and b̂ are quantization axes. The two axis frames are used in this analysis. (1) Helicity frame : the momentum directions of the top and antitop quarks in the tt centerofmass frame are defined as the quantization axes. (2) Transverse frame : The quantization axis of the top quark in the transverse basis is defined as the cross product of the proton momentum direction and the top quark momentum direction. 
Heicity axis The signal(cosθ+ ,cosθ) templates for the helicity basis of (a) CPC and CPV at αP = 0 (b) CPC at 0.3, (c) CPC at 0.3, (d) CPV at 0.3, and (e) CPV at 0.3. The signal templates are normalized to an integrated luminosity of 9.1 fb^{1}. [pdf format] (a) (b) (c) (d) (e) 
Transeverse axis The signal(cos θ+, cos θ) templates for the transverse basis of (a) CPC and CPV at αP = 0 (b) CPC at 0.3, (c) CPC at 0.3, (d) CPV at 0.3, and (e) CPV at 0.3. The signal templates are normalized to an integrated luminosity of 9.1 fb^{1}. [pdf format] (a) (b) (c) (d) (e) 
Helicity basis : CPC cosθ+ [pdf format] Helicity basis : CPC cosθ [pdf format] Helicity basis : CPV cosθ+ [pdf format] Helicity basis : CPV cosθ [pdf format] 
Transverse basis : CPC cosθ+ [pdf format] Transverse basis : CPC cosθ [pdf format] Transverse basis : CPV cosθ+ [pdf format] Transverse basis : CPV cosθ [pdf format] 
Helicity basis [pdf format] Transverse basis [pdf format] 
Helicity basis (cos θ+, cos θ) distribution of two leptons for (a) data , (bd) signal and backgrounds for CPC, (eg) signal and backgrounds for CPV in helicity basis. [pdf format] (a) (b) (c) (d) (e) (f) (g) Transverse basis (cos θ+, cos θ) distribution of two leptons for (a) data , (bd) signal and backgrounds for CPC, (eg) signal and backgrounds for CPV in transverse basis. [pdf format] (a) (b) (c) (d) (e) (f) (g) 
[pdf format] CPCHelicicy , CPVHelicity , CPCTransverse , CPVTransverse 
CDF Run II Prelim 
[pdf format] 