$v_{2}(p_{T})$ for $K_{S}^{0}$ (Centrality:0-80%)

$v_{3}(p_{T})$ for $K_{S}^{0}$ (Centrality:0-10%)

$v_{3}(p_{T})$ for $K_{S}^{0}$ (Centrality:10-40%)

$v_{3}(p_{T})$ for $K_{S}^{0}$ (Centrality:40-80%)

$v_{3}(p_{T})$ for $K_{S}^{0}$ (Centrality:0-80%)

$v_{2}(p_{T})$ for $\Lambda$ (Centrality:0-10%)

$v_{2}(p_{T})$ for $\Lambda$ (Centrality:10-40%)

$v_{2}(p_{T})$ for $\Lambda$ (Centrality:40-80%)

$v_{2}(p_{T})$ for $\Lambda$ (Centrality:0-80%)

$v_{3}(p_{T})$ for $\Lambda$ (Centrality:0-10%)

$v_{3}(p_{T})$ for $\Lambda$ (Centrality:10-40%)

$v_{3}(p_{T})$ for $\Lambda$ (Centrality:40-80%)

$v_{3}(p_{T})$ for $\Lambda$ (Centrality:0-80%)

$v_{2}(p_{T})$ for $\bar{\Lambda}$ (Centrality:0-10%)

$v_{2}(p_{T})$ for $\bar{\Lambda}$ (Centrality:10-40%)

$v_{2}(p_{T})$ for $\bar{\Lambda}$ (Centrality:40-80%)

$v_{2}(p_{T})$ for $\bar{\Lambda}$ (Centrality:0-80%)

$v_{3}(p_{T})$ for $\bar{\Lambda}$ (Centrality:0-10%)

$v_{3}(p_{T})$ for $\bar{\Lambda}$ (Centrality:10-40%)

$v_{3}(p_{T})$ for $\bar{\Lambda}$ (Centrality:40-80%)

$v_{3}(p_{T})$ for $\bar{\Lambda}$ (Centrality:0-80%)

$v_{2}(p_{T})$ for $\phi$ (Centrality:0-10%)

$v_{2}(p_{T})$ for $\phi$ (Centrality:10-40%)

$v_{2}(p_{T})$ for $\phi$ (Centrality:40-80%)

$v_{2}(p_{T})$ for $\phi$ (Centrality:0-80%)

$v_{3}(p_{T})$ for $\phi$ (Centrality:0-10%)

$v_{3}(p_{T})$ for $\phi$ (Centrality:10-40%)

$v_{3}(p_{T})$ for $\phi$ (Centrality:0-80%)

$v_{2}(p_{T})$ for $\Xi^{-}$ (Centrality:0-10%)

$v_{2}(p_{T})$ for $\Xi^{-}$ (Centrality:10-40%)

$v_{2}(p_{T})$ for $\Xi^{-}$ (Centrality:40-80%)

$v_{2}(p_{T})$ for $\Xi^{-}$ (Centrality:0-80%)

$v_{3}(p_{T})$ for $\Xi^{-}$ (Centrality:0-10%)

$v_{3}(p_{T})$ for $\Xi^{-}$ (Centrality:10-40%)

$v_{3}(p_{T})$ for $\Xi^{-}$ (Centrality:0-80%)

$v_{2}(p_{T})$ for $\bar{\Xi^{+}}$ (Centrality:0-10%)

$v_{2}(p_{T})$ for $\bar{\Xi^{+}}$ (Centrality:10-40%)

$v_{2}(p_{T})$ for $\bar{\Xi^{+}}$ (Centrality:40-80%)

$v_{2}(p_{T})$ for $\bar{\Xi^{+}}$ (Centrality:0-80%)

$v_{3}(p_{T})$ for $\bar{\Xi^{+}}$ (Centrality:0-10%)

$v_{3}(p_{T})$ for $\bar{\Xi^{+}}$ (Centrality:10-40%)

$v_{3}(p_{T})$ for $\bar{\Xi^{+}}$ (Centrality:0-80%)

$v_{2}(p_{T})$ for $\Omega^{-}$ (Centrality:0-10%)

$v_{2}(p_{T})$ for $\Omega^{-}$ (Centrality:10-40%)

$v_{2}(p_{T})$ for $\Omega^{-}$ (Centrality:40-80%)

$v_{2}(p_{T})$ for $\Omega^{-}$ (Centrality:0-80%)

$v_{3}(p_{T})$ for $\Omega^{-}$ (Centrality:0-10%)

$v_{3}(p_{T})$ for $\Omega^{-}$ (Centrality:10-40%)

$v_{3}(p_{T})$ for $\Omega^{-}$ (Centrality:0-80%)

$v_{2}(p_{T})$ for $\bar{\Omega^{+}}$ (Centrality:0-10%)

$v_{2}(p_{T})$ for $\bar{\Omega^{+}}$ (Centrality:10-40%)

$v_{2}(p_{T})$ for $\bar{\Omega^{+}}$ (Centrality:40-80%)

$v_{2}(p_{T})$ for $\bar{\Omega^{+}}$ (Centrality:0-80%)

$v_{3}(p_{T})$ for $\bar{\Omega^{+}}$ (Centrality:0-10%)

$v_{3}(p_{T})$ for $\bar{\Omega^{+}}$ (Centrality:10-40%)

$v_{3}(p_{T})$ for $\bar{\Omega^{+}}$ (Centrality:0-80%)

$v_{2}$ of $\phi$ to $\bar{p}$ ratio

Difference of $v_{2}$ between particle and anti-particle

Difference of $v_{3}$ between particle and anti-particle

Example of combinatorial background subtracted invariant mass distributions and the extracted yields as a function of $\cos \theta^*$ for $\phi$ and $K^{*0}$ mesons. \textbf{a)} example of $\phi \rightarrow K^+ + K^-$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{b)} example of $K^{*0} (\overline{K^{*0}}) \rightarrow K^{-} \pi^{+} (K^{+} \pi^{-})$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{c)} extracted yields of $\phi$ as a function of $\cos \theta^*$; \textbf{d)} extracted yields of $K^{*0}$ as a function of $\cos \theta^*$.

Example of combinatorial background subtracted invariant mass distributions and the extracted yields as a function of $\cos \theta^*$ for $\phi$ and $K^{*0}$ mesons. \textbf{a)} example of $\phi \rightarrow K^+ + K^-$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{b)} example of $K^{*0} (\overline{K^{*0}}) \rightarrow K^{-} \pi^{+} (K^{+} \pi^{-})$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{c)} extracted yields of $\phi$ as a function of $\cos \theta^*$; \textbf{d)} extracted yields of $K^{*0}$ as a function of $\cos \theta^*$.

Example of combinatorial background subtracted invariant mass distributions and the extracted yields as a function of $\cos \theta^*$ for $\phi$ and $K^{*0}$ mesons. \textbf{a)} example of $\phi \rightarrow K^+ + K^-$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{b)} example of $K^{*0} (\overline{K^{*0}}) \rightarrow K^{-} \pi^{+} (K^{+} \pi^{-})$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{c)} extracted yields of $\phi$ as a function of $\cos \theta^*$; \textbf{d)} extracted yields of $K^{*0}$ as a function of $\cos \theta^*$.

Efficiency corrected $\phi$-meson yields as a function of cos$\theta$* and corresponding fits with Eq.1 in the method section.

Efficiency and acceptance corrected $K^{*0}$-meson yields as a function of cos$\theta$* and corresponding fits with Eq.4 in the method section.

$\phi$-meson $\rho_{00}$ obtained from 1st- and 2nd-order event planes. The red stars (gray squares) show the $\phi$-meson $\rho_{00}$ as a function of beam energy, obtained with the 2nd-order (1st-order) EP.

$\phi$-meson $\rho_{00}$ with respect to different quantization axes. $\phi$-meson $\rho_{00}$ as a function of beam energy, for the out-of-plane direction (stars) and the in-plane direction (diamonds). Curves are fits based on theoretical calculations with a $\phi$-meson field. The corresponding $G_s^{(y)}$ values obtained from the fits are shown in the legend.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

Global spin alignment measurement of $\phi$ and $K^{*0}$ vector mesons in Au+Au collisions at 0-20\% centrality. The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for $K^{*0}$-meson, obtained with the 2nd-order EP.

Global spin alignment measurement of $\phi$ and $K^{*0}$ vector mesons in Au+Au collisions at 0-20\% centrality. The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for $K^{*0}$-meson, obtained with the 2nd-order EP.

(Color Online) Variation of $N_{ch}$ normalized to the number of collisions in the FTPC coverage $(2.9 \leq \eta \leq 3.9)$ and $N_{\gamma}$ normalized to number of collisions, in the PMD coverage $(2.3 \leq \eta \leq 3.7)$ as a function of $N_{coll}$. The lower band shows the uncertainty in the ratio due to uncertainties in $N_{coll}$ calculations.

(Color Online) $dN/d\eta$ for charged particles and photons for Au + Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV for various event centrality classes.

(Color Online) $dN/d\eta$ for charged particles and photons for Au + Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV for various event centrality classes.

(Color Online) Half width at half maximum of the pseudorapidity distributions ($\eta_{h}$) of charged particles as a function of total charged particle multiplicity ($N_{T}$) normalized to the center of mass energy. The Au + Au collision data are from the PHOBOS [8] experiment and p + p collision data are from the ISR [31] experiments.

(Color Online) Half width at half maximum of the pseudorapidity distributions ($\eta_{h}$) of charged particles as a function of total charged particle multiplicity ($N_{T}$) normalized to the center of mass energy. The Au + Au collision data are from the PHOBOS [8] experiment and p + p collision data are from the ISR [31] experiments.

(Color Online) Variation of $dN_{ch}/d\eta$ normalized to $N_{part}$ with $\eta – y_{beam}$ for central and peripheral collisions for positively charged hadrons ($h^{+}$) and negatively charged hadrons ($h^{−}$).

(Color Online) The top panel shows the variation of pion rapidity density normalized to $N_{part}$ with $y – y_{beam}$ for central collisions at various collision energies. Also shown is the estimated $dN_{\pi^{0}}/dy$ obtained from $dN\_{\gamma}/dy$ normalized to $N_{part}$. The bottom panel shows the variation of net proton rapidity density normalized to $N_{part}$ with $y – y_{beam}$ for central collisions at various collision energies.

(Color Online) The top panel shows the variation of pion rapidity density normalized to $N_{part}$ with $y – y_{beam}$ for central collisions at various collision energies. Also shown is the estimated $dN_{\pi^{0}}/dy$ obtained from $dN\_{\gamma}/dy$ normalized to $N_{part}$. The bottom panel shows the variation of net proton rapidity density normalized to $N_{part}$ with $y – y_{beam}$ for central collisions at various collision energies.

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