We present the first spin alignment measurements for the $K^{*0}(892)$ and $\phi(1020)$ vector mesons produced at mid-rapidity with transverse momenta up to 5 GeV/c at $\sqrt{s_{NN}}$ = 200 GeV at RHIC. The diagonal spin density matrix elements with respect to the reaction plane in Au+Au collisions are $\rho_{00}$ = 0.32 $\pm$ 0.04 (stat) $\pm$ 0.09 (syst) for the $K^{*0}$ ($0.8<p_T<5.0$ GeV/c) and $\rho_{00}$ = 0.34 $\pm$ 0.02 (stat) $\pm$ 0.03 (syst) for the $\phi$ ($0.4<p_T<5.0$ GeV/c), and are constant with transverse momentum and collision centrality. The data are consistent with the unpolarized expectation of 1/3 and thus no evidence is found for the transfer of the orbital angular momentum of the colliding system to the vector meson spins. Spin alignments for $K^{*0}$ and $\phi$ in Au+Au collisions were also measured with respect to the particle's production plane. The $\phi$ result, $\rho_{00}$ = 0.41 $\pm$ 0.02 (stat) $\pm$ 0.04 (syst), is consistent with that in p+p collisions, $\rho_{00}$ = 0.39 $\pm$ 0.03 (stat) $\pm$ 0.06 (syst), also measured in this work. The measurements thus constrain the possible size of polarization phenomena in the production dynamics of vector mesons.
The spin-density matrix elements $\rho_{00}$ with respect to the reaction plane in midcentral $Au+Au$ collisions at $\sqrt{s_{NN}}=200$ GeV versus $p_{T}$ of the vector meson. The sizes of the statistical uncertainties are indicated by error bars, and the systematic uncertainties by caps. The $K^{∗0}$ data points have been shifted slightly in $p_{T}$ for clarity. The dashed horizontal line indicates the unpolarized expectation $\rho_{00}=1/3$. The bands and continuous horizontal lines show predictions discussed in the text.
The dependence of $\rho_{00}$ with respect to the reaction plane on the number of participants at midrapidity in $Au+Au$ collisions at $\sqrt{s_{NN}}=200$ GeV. The sizes of the statistical uncertainties are indicated by error bars and the systematic uncertainties by caps. The $\phi$ data for $p_{T} > 2$ GeV/$c$ and the $K^{∗0}$ data points have been shifted slightly in $\langle N_{\scriptsize{\mbox{part}}}\rangle$ for clarity. The dashed horizontal line indicates the unpolarized expectation $\rho_{00}=1/3$.
The spin-density matrix elements $\rho_{00}$ with respect to the production plane in midcentral $Au+Au$ and $p+p$ collisions at $\sqrt{s_{NN}}=200$ GeV versus $p_{T}$ of the vector meson. The sizes of the statistical uncertainties are indicated by error bars and the systematic uncertainties by caps. The $K^{*0}$ and the $\phi$ $p+p$ data points have been shifted slightly in $p_{T}$ for clarity. The dashed horizontal line indicates the unpolarized expectation $\rho_{00}=1/3$.
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