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

We present a study of the polarization of the $\mathrm{{\rm Y}}(1S)$ and $\mathrm{{\rm Y}}(2S)$ states using a $1.3$ fb${}^{-1}$ data sample collected by the D0 experiment in 2002–2006 during Run II of the Fermilab Tevatron Collider. We measure the polarization parameter $\alpha =({\sigma }_T-2{\sigma }_L)\mathrm{/}({\sigma }_T+2{\sigma }_L)$, where ${\sigma }_T$ and ${\sigma }_L$ are the transversely and longitudinally polarized components of the production cross section, as a function of the transverse momentum ($p_T^{\mathrm{{\rm Y}}}$) for the $\mathrm{{\rm Y}}(1S)$ and $\mathrm{{\rm Y}}(2S)$. Significant $p_T^{\mathrm{{\rm Y}}}$-dependent longitudinal polarization is observed for the $\mathrm{{\rm Y}}(1S)$. A comparison with theoretical models is presented.