We report on the measurement of the angular distributions of final state electrons in
ppbar &rarr &gamma^{*}/Z &rarr e^{+}e^{} events produced in
the Z boson region mass range of 66 to 116 GeV/c^{2} from
2.1 fb^{1} of proton antiproton
collisions at (s)^½ = 1.96 TeV taken by the CDF detector at Fermilab.
The transverse momentum (P_{T}) dependent angular coefficients A_{0},
A_{2}, A_{3}, and A_{4} are compared with several predictions based on
Quantum Chromodymnamics (QCD). The P_{T} dependence of A_{0} and A_{2}
is in agreement with the predictions of perturbative QCD and shows that the production
of Z bosons at large P_{T} proceeds via a combination of the quarkantiquark annihilation
and the quarkgluon Compton processes. We find a good agreement with the LamTung relation
(A_{0} = A_{2}), which implies that the spin of the gluon is 1.

Two high pt electrons selected with E_{T} > 25GeV(higher E_{T} leg)
and 15GeV (lower E_{T} leg) for Z(CC),
E_{T} > 20 GeV for Z(CP), and E_{T} > 25 GeV for Z(PP).
For CC events, one electron is required to pass tight electron ID cuts
and the other loose. The CC topology is required to have oppositely charged electron pairs.
For CP events, the central electron is required to pass the tight
cuts and the plug electron the standard plug ID cuts. For the PP topology, both electrons are
required to pass the standard plug ID cuts and have the same pseudorapidity direction (positive or negative direction).
All events are required to have a track on both electrons to reduce the background contamination.
138,172 ± 372 of Z boson events are selected.
This measurement is extension of d&sigma/dy analysis with 2.1 fb^{1} data.
The more details is described in the webpage or public note of d&sigma/dy analysis.
Webpage : d&sigma/dy Public webpage
Public Note : d&sigma/dy Public note
Z P_{T} spectrum. The total QCD background is 0.30 % level and the Electroweak background is 0.19 % level. .eps 
Z P_{T} distribution. yaxis corresponds to the total number of events in the bin. .eps 
Z P_{T} spectrum. The number of events in the bin is normalized by the bin width. .eps 

A_{0} in P_{T} measurement. The uncertainty is total error. (stat. and syst. error are summed in quadrature.) The dominant uncertainty is the statistical error. .eps 

A_{2} in P_{T} measurement. The uncertainty is total error. (stat. and syst. error is summed in quadrature.) The dominant uncertainty is the statistical error. .eps 

A_{3} in P_{T} measurement. The uncertainty is total error. (stat. and syst. error is summed in quadrature.) The dominant uncertainty is the statistical error. .eps 

A_{4} in P_{T} measurement. The uncertainty is total error. (stat. and syst. error is summed in quadrature.) The dominant uncertainty is the statistical error. .eps 

Table : Angular coefficients measurement in P_{T} The uncertainty is total error. (stat. and syst. error is summed in quadrature.) The dominant uncertainty is the statistical error. .pdf 

LamTung Relation ( A_{0}  A_{2} = 0 ) in P_{T} measurement. The uncertainty is total error. (stat. and syst. error is summed in quadrature.) The dominant uncertainty is the statistical error. .eps 

Table : LamTung relation in P_{T} The average A_{0}  A_{2} = 0.017 ± 0.023. 

sin^{2}(theta_{W}) vs. A_{4} in FEWZ(NNLO) and Powheg(NLO) prediction The extracted sin^{2}(theta_{W}) in FEWZ = 0.2331 ± 0.0008 The extracted sin^{2}(theta_{W}) in Powheg = 0.2328 ± 0.0008 The uncertainty corresponds to the total error of A_{4} measurement. .eps 

sin^{2}(theta_{W}) vs. A_{4} in ResBos, VBP, and Pythia prediction .eps 

The measured A_{4} = 0.1098 ± 0.0079. sin^{2}(theta_{W}) vs. A_{4} The extracted sin^{2}(theta_{W}) = 0.2329 ± 0.0008 (A_{4} total error)^{+0.0010}_{0.0009} (QCD theory) FEWZ, Powheg, ResBos, VBP, and Pythia predictions are used. .eps 