Polarization of $\Upsilon$~Mesons Produced in $p\bar p$~Collisions at $\sqrt{s} = 1.96$~TeV

We measure the polarization of $\Upsilon$~mesons in the $\Upsilon(1S)$, $\Upsilon(2S)$ and $\Upsilon(3S)$ states as a function of their transverse momentum $p_T$ in the $s$-channel helicity frame. The analysis uses $\Upsilon$~mesons produced in the rapidity range $|y|<0.6$. The measurement is performed using a data sample of $p\bar{p}$ collisions at $\sqrt{s} = 1.96$~TeV with an integrated luminosity of $>3$~fb$^{-1}$ collected with the CDF\,II detector at the Fermilab Tevatron. The results are compared to theoretical predictions.