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We present a study of the polarization of the $\Upsilon(1S)$ and$\Upsilon(2S)$ states using a $1.3 $ fb$^{-1}$ data sample collected by the D0experiment in 2002--2006 during Run II of the Fermilab Tevatron Collider. Wemeasure the polarization parameter$\alpha=(\sigma_{T}-2\sigma_{L})/(\sigma_{T}+2\sigma_{L})$, where $\sigma_{T}$and $\sigma_{L}$ are the transversely and longitudinally polarized componentsof the production cross section, as a function of the transverse momentum($p_{T}^{\Upsilon}$) for the $\Upsilon(1S)$ and $\Upsilon(2S)$. Significant$p_{T}^{\Upsilon}$-dependent longitudinal polarization is observed for the$\Upsilon(1S)$. A comparison with theoretical models is presented.

Measurement of the polarization of the $\Upsilon(1S)$ and $\Upsilon(2S)$ states in $p\bar{p}$ collisions at $\sqrt{s}=$1.96 TeV