Polarization in Quarkonium Production

Production mechanisms for quarkonium states in hadronic collisions remain difficult to understand. The decay angular distributions of J/$\psi$ or $\Upsilon(nS)$ states into $\mu^+ \mu^-$ final states are sensitive to the matrix elements in the production process and provide a unique tool to evaluate different models. This talk will focus on new results for the spin alignment of $\Upsilon(nS)$ states produced in $p\bar{p}$ collisions at $\sqrt{s}$ = 1.96 TeV using the CDF II detector at the Fermilab Tevatron. The data sample corresponds to an integrated luminosity of 6.7 fb$^{-1}$. The angular distributions are analyzed as functions of the transverse momentum of the dimuon final state in both the Collins-Soper and the s-channel helicity frames using a unique data-driven background determination method. Consistency of the analysis is checked by comparing frame-invariant quantities derived from parametrizations of the angular distributions measured in each choice of reference frame. This analysis is the first to quantify the complete three-dimensional angular distribution of $\Upsilon(1S), \Upsilon(2S)$ and $\Upsilon(3S)$ decays. The decays are nearly isotropic in all frames, even when produced with large transverse momentum.