Spin alignment measurements of the $K^{*0}(892)$ and $\varphi (1020)$ vector mesons in heavy ion collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV

We present the first spin alignment measurements for the $K^{*0}(892)$ and $\varphi (1020)$ vector mesons produced at midrapidity with transverse momenta up to 5 GeV/$c$ at $\sqrt{s_{\mathit{NN}}}=200$ GeV at RHIC. The diagonal spin-density matrix elements with respect to the reaction plane in $\mathrm{Au}+\mathrm{Au}$ collisions are ${\rho }_{00}=0.32\pm 0.04$ (stat) ± 0.09 (syst) for the $K^{*0}$ ($0.8<p_T<5.0$ GeV/$c$) and ${\rho }_{00}=0.34\pm 0.02$ (stat) ± 0.03 (syst) for the $\varphi$ ($0.4<p_T<5.0$ 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 $\varphi$ in $\mathrm{Au}+\mathrm{Au}$ collisions were also measured with respect to the particle's production plane. The $\varphi$ result, ${\rho }_{00}=0.41\pm 0.02$ (stat) ± 0.04 (syst), is consistent with that in $p+p$ collisions, ${\rho }_{00}=0.39\pm 0.03$ (stat) ± 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.

Figure 1

The invariant mass distribution after combinatorial background subtraction for (a) the $K^{*0}$ and (b) the $\varphi$ meson in midcentral $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV, including all values of cos${\theta }^{*}$. The continuous lines represent fits of signal, described with a Breit-Wigner function, and residual background, described with the dashed polynomial curves. Panels (c) and (e) and panels (d) and (f) represent the $\cos {\theta }^{*}$ distributions for the $K^{*0}$ and $\varphi$ yields in $\mathrm{Au}+\mathrm{Au}$ collisions, respectively. Panel (g) is the $\varphi$ yield in $p+p$ collisions, whereas panel (h) shows the control measurement of the spin-less $K_S^0$ meson $\cos {\theta }^{*}$ distribution. The error bars show statistical uncertainties. The blue dashed lines in (c)–(h) are fits of Eq. (1) to the data.

Figure 2

The spin-density matrix elements ${\rho }_{00}$ with respect to the reaction plane in midcentral $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ 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.

Figure 3

The dependence of ${\rho }_{00}$ with respect to the reaction plane on the number of participants at midrapidity in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV. The sizes of the statistical uncertainties are indicated by error bars and the systematic uncertainties by caps. The $\varphi$ data for $p_T>2$ GeV/$c$ and the $K^{*0}$ data points have been shifted slightly in $\langle N_{\mathrm{part}}\rangle$ for clarity. The dashed horizontal line indicates the unpolarized expectation ${\rho }_{00}=1/3$.

Figure 4

The spin-density matrix elements ${\rho }_{00}$ with respect to the production plane in midcentral $\mathrm{Au}+\mathrm{Au}$ and $p+p$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ 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 $\varphi$ $p+p$ data points have been shifted slightly in $p_T$ for clarity. The dashed horizontal line indicates the unpolarized expectation ${\rho }_{00}=1/3$.