Polarizations of $J/\psi$ and $\psi (2S)$ Mesons Produced in $p\overline{p}$ Collisions at $\sqrt{s}=1.96\mathrm{TeV}$

We have measured the polarizations of $J/\psi$ and $\psi (2S)$ mesons as functions of their transverse momentum $p_T$ when they are produced promptly in the rapidity range $|y|<0.6$ with $p_T\ge 5\mathrm{GeV}/c$. The analysis is performed using a data sample with an integrated luminosity of about $800{\mathrm{pb}}^{-1}$ collected by the CDF II detector. For both vector mesons, we find that the polarizations become increasingly longitudinal as $p_T$ increases from 5 to $30\mathrm{GeV}/c$. These results are compared to the predictions of nonrelativistic quantum chromodynamics and other contemporary models. The effective polarizations of $J/\psi$ and $\psi (2S)$ mesons from $B$-hadron decays are also reported.

Figure 1

Invariant mass distributions for (a) $J/\psi$ and (b) $\psi (2S)$ candidates. The curves are fits to the data. The solid (dashed) lines indicate the signal (sideband) regions.

Figure 2

Sideband-subtracted $ct$ distributions for (a) $J/\psi$ and (b) $\psi (2S)$ events. The prompt Gaussian peak, positive excess from $B$-hadron decays, and negative tail from mismeasured events are shown. The dotted line is the reflection of the negative $ct$ histogram about zero.

Figure 3

$\cos {\theta }^{*}$ distribution of data (points) and polarization fit for the worst ${\chi }^2$ probability bin in the $J/\psi$ data. The dotted (dashed) line is the template for fully $L$ ($T$) polarization. The fit describes the overall trend of the data well.

Figure 4

Prompt polarizations as functions of $p_T$: (a) $J/\psi$ and (b) $\psi (2S)$. The band (line) is the prediction from NRQCD [4] (the $k_T$-factorization model [9]).