Measurement of ttbar Spin Correlations Coefficient in 5.1 fb-1 Dilepton Candidates
Analysis Public Web Page

Dec. 6, 2011
Public Analysis Note

Authors:Kenichi Takemasa, Shinhong Kim, Yuji Takeuchi (Univ. of Tsukuba) for the CDF collaboration
    One of the most remarkable properties of the top quark is its extremely short lifetime, which allows us to observe the top quark spin at its production. That means spin correlations at ttbar production is possible to be observed.
In this page, we report on a measurement of the spin spin correlation coefficient of top and anit-top in the beam basis at ttbar production in ppbar collisions at √s=1.96 TeV using ∫Ldt=5.1 fb-1 dilepton candidates.

What are we going to measure?
=> Spin Correlation Parameter: κ
    Correlation parameter κ is defined as the correlation coefficient between top and anti-top spin polarizations. The top quark is expected to decay before losing spin polarization at its production, and the flight directions of decay products in the top rest frame are correlated with the top polarization. Therefore we could see the spin-spin correlation at ttbar production through correlations between flight directions of decay products.

    In this analysis, we measure κ at the ttbar decay in the dilepton channel, where ttbar is supposed to decay with the following differential cross-section and decay rate:


where θ+-) denotes angle of a decay product flight direction in top (anti-top) rest frame with respect to a choosen quantization axis for top (anti-top). We suppose that ttbar is produced with standard model spin correlations, but we don't assume the top and anti-top polarizations are kept until their decays, i.e. we consider κ as a free parameter that is what we are going to measure.
  The spin correlation depends on the quantization basis of top and anti-top spin. We select the beam basis. Beam basis is the direction of the incident coliding particles. In this basis, standard model predicts κ∼0.8.
  If we observe non-zero correlation coefficient κ in ttbar production and decay, that consequently indicates the direct evidence that top and anti-top are produced with their spins correlated and decay before losing their spin polarizations as bare quarks.
How do we measure κ
=> Using angular distribution (cosθl+, cosθl-) and (cosθb, cosθbbar)
Due to P-violating weak decay of the top (anti-top) quark, the flight direction of decay products has some portion of information on the spin polarization of the parent top quark. Hence the spin correlation between top and anti-top manifests itself on the angular distributions of the decay products. We use the distributions of (cosθl+, cosθl-) and (cosθb, cosθbbar) to extract the spin correlation coefficient, where the angle θl+, θl-, θb, and θbbar are defined as the angle of the flight direction of each decay products with respect to the quantization basis (beam basis) in the top and anti-top rest frame, respectively.
    In this analysis, we used 334 ttbar candidates in dilepton channel observed in 5.1 fb-1 data.
angular distribution
Signal Templates
Upper: The expected distributions of ( cosθl+, cosθl-) and (cosθb, cosθbbar) reconstructed with CDF-II detector  by the Monte Carlo simulation for dilepton channel candidates in ttbar Monte Carlo (κ=-1.0, 0.0 and 1.0).
Lower: Fits of the distributions to a 2 dimensional polynomial function.
Background Templates
Upper: The expected distributions of ( cosθl+, cosθl-) and (cosθb, cosθbbar) reconstructed with CDF-II detector  by the Monte Carlo simulation for Background (WW/WZ/ZZ, Drell-Yan(Z/γ*)->ττ, ee, μμ, W+QCD fake).
Middle: 1σ uncertainty of each bin of the distributions
Lower: Fits of the distributions to a 2 dimensional polynomial function.

Reconstructed cosθl+, cosθb Distribution
Cross: Dilepton candidates in data of 5.1 fb-1 integrated luminosity.
Histogram: Expected signal+background distirbution with 1σ uncertainty

Statistic and Systematic Uncertainties on measured κ
By performing pseudo experiments, we obtain statistical uncertainty on measured κ as a fucntion of assumed κ.
As for systematic uncertainty, we consider uncertainties from Monte Carlo sample statistics, shape of signal/background templates, jet energy scale, initial/final state radiation, parton distribution function, gluon fusion fraction, effect of next leading order and color reconnection.

Observed (cosθl+, cosθl-) and (cosθb, cosθbbar) Distributions in 5.1 fb-1 Data
Lower: -2 Δ Log(Likelihood) as a function of assumed κ. We observed κ = 0.042 which gives maximum likelihood for observed distributions.

Feldman-Cousins Interval for κ
Feldman-Cousisns Intervals based on the statistical and systematic uncertainty for measured κ.
From this intervals and observed κ = 0.042, we set 68% confidence interval for κ on the assumed Mt=172.5 GeV/c2.

Top Mass Dependence of Confidence Interval for κ
We measure 68% confidence interval for κ on assumptions of different top quark mass (167.5, 170.0, 175.0, and 177.5 GeV/c2).

-0.520<κ<0.605 (68% C.L.)
κ = 0.042+0.563-0.562
for Mt = 172.5 GeV/c2

Last modified: Tuesday Dec. 6 03:48 JST 2011 by Kenichi Takemasa