First Measurement of the Angular Coefficients of Drell-Yan $e^{+}{e}^{-}$ Pairs in the $Z$ Mass Region from $p\overline{p}$ Collisions at $\sqrt{s}=1.96\mathrm{TeV}$

We report on the first measurement of the angular distributions of final state electrons in $p\overline{p}\to {\gamma }^{*}/Z\to e^{+}{e}^{-}+X$ events produced in the $Z$ boson mass region at $\sqrt{s}=1.96\mathrm{TeV}$. The data sample collected by the CDF II detector for this result corresponds to $2.1{\mathrm{fb}}^{-1}$ of integrated luminosity. The angular distributions are studied as a function of the transverse momentum of the electron-positron pair and show good agreement with the Lam-Tung relation, consistent with a spin-1 description of the gluon, and demonstrate that, at high values of the transverse momentum, $Z$ bosons are produced via quark-antiquark annihilation and quark-gluon Compton processes.

Figure 1

Dielectron $P_T$ spectrum of data, default (CDF tuned) pythia prediction, and backgrounds (QCD and electroweak processes). The mass range corresponds to $66<M_{ee}<116\mathrm{GeV}/c^2$.

Figure 2

The $\cos \theta$ distribution of data and default (CDF tuned) pythia prediction.

Figure 3

Comparison of the measured values of $A_0$, $A_2$, $A_3$, and $A_4$ (for $66<M_{ee}<116\mathrm{GeV}/c^2$), shown with statistical and systematic uncertainties combined in quadrature, to theory predictions. The data are plotted at the mean $P_T$ of the events for each bin. The last bin corresponds to $P_T>55\mathrm{GeV}/c$ with no upper limit. The horizontal uncertainty is the rms of the transverse momenta in each bin. Agreement [29] is found with the predictions of fewz and powheg (shown) and also with dyrad, madgraph, and pythia ($Z+1$)-jet MC simulations (not shown). The data do not favor [29] the predictions of default pythia and vbp. Also shown are the pure $q\overline{q}\to {\gamma }^{*}/ZG$ annihilation diagram prediction and the $qG\to {\gamma }^{*}/Zq$ Compton process prediction from the pythia ($Z+1$)-jet MC simulation.