The K$\pi$ pair invariant mass distribution integrated over the $K^{*0}$ $p_T$ for minimum bias Cu+Cu collisions at $\sqrt{s_{NN}}$ =62.4 GeV after mixed-event background subtraction.

The Kπ pair invariant mass distribution for various pT bins (top left) pT = 0.4–0.6 GeV/c in Au+Au collisions at √sNN = 200 GeV after the mixed-event background subtraction.

The Kπ pair invariant mass distribution for various pT bins (top right) pT = 0.6–0.8 GeV/c in Au+Au collisions at √sNN = 62.4 GeV after the mixed-event background subtraction.

The Kπ pair invariant mass distribution for various pT bins (bottom left) pT = 0.8–1.0 GeV/c in Au+Au collisions at √sNN = 200 GeV after the mixed-event background subtraction.

The Kπ pair invariant mass distribution for various pT bins (bottom right) pT = 1.0–1.2 GeV/c in Au+Au collisions at √sNN = 62.4 GeV after the mixed-event background subtraction.

The signal-to-background ratio for $K^{*0}$ measurements as a function of $p_T$ for different collision centrality bins (0-10%, 10-40%, 40-60%, 60-80%) in Au+Au collisions at 200 GeV.

$K^{*0}$ mass as a function of $p_T$ for minimum bias Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV.

$K^{*0}$ mass as a function of $p_T$ for minimum bias Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.

$K^{*0}$ mass as a function of $p_T$ for minimum bias Cu+Cu collisions at $\sqrt{s_{NN}}$ = 62.4 GeV

$K^{*0}$ mass as a function of $p_T$ for minimum bias Cu+Cu collisions at $\sqrt{s_{NN}}$ = 200 GeV

$K^{*0}$ width as a function of $p_T$ for minimum bias Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV

$K^{*0}$ width as a function of $p_T$ for minimum bias Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV

$K^{*0}$ width as a function of $p_T$ for minimum bias Cu+Cu collisions at $\sqrt{s_{NN}}$ = 62.4 GeV

$K^{*0}$ width as a function of $p_T$ for minimum bias Cu+Cu collisions at $\sqrt{s_{NN}}$ = 200 GeV

The $K^{*0}$ reconstruction efficiency multiplied by the detector acceptance as a function of $p_T$ in Au+Au (|$\eta$| < 0.8) collisions at 200 GeV for different collision centrality bins (0-20% ,20-40% , 40-60%)

The $K^{*0}$ reconstruction efficiency multiplied by the detector acceptance as a function of $p_T$ in Cu+Cu (|$\eta$| < 1.0) collisions at 200 GeV for different collision centrality bins (0-20% ,20-40% , 40-60%)

Mid-rapidity $K^{*0}$ $p_T$ spectra for various collision centrality bins (0-20%, 20-40%, 40-60%, 60-80%) in Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV

Mid-rapidity $K^{*0}$ $p_T$ spectra for various collision centrality bins (0-20%, 20-40%, 40-60%) in Cu+Cu collisions at $\sqrt{s_{NN}}$ = 62.4 GeV

Mid-rapidity $K^{*0}$ $p_T$ spectra for various collision centrality bins (0-20%, 20-40%, 40-60%, 60-80%) in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV

Mid-rapidity $K^{*0}$ $p_T$ spectra for various collision centrality bins (0-20%, 20-40%, 40-60%) in Cu+Cu collisions at $\sqrt{s_{NN}}$ = 200 GeV

The mid-rapidity yields dN/dy of $K^{*0}$ as a function of the average number of participating nucleons, $⟨N_{part}⟩$, for Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV

The mid-rapidity yields dN/dy of $K^{*0}$ as a function of the average number of participating nucleons, $⟨N_{part}⟩$, for Cu+Cu collisions at $\sqrt{s_{NN}}$ = 62.4 GeV

The mid-rapidity yields dN/dy of $K^{*0}$ as a function of the average number of participating nucleons, $⟨N_{part}⟩$, for Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV

The mid-rapidity yields dN/dy of $K^{*0}$ as a function of the average number of participating nucleons, $⟨N_{part}⟩$, for Cu+Cu collisions at $\sqrt{s_{NN}}$ = 200 GeV

The mid-rapidity $K^{*0}$ $⟨p_T⟩$ as a function $⟨N_{part}⟩$ for Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV

The mid-rapidity $K^{*0}$ $⟨p_T⟩$ as a function $⟨N_{part}⟩$ for Cu+Cu collisions at $\sqrt{s_{NN}}$ = 62.4 GeV

The mid-rapidity $K^{*0}$ $⟨p_T⟩$ as a function $⟨N_{part}⟩$ for Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV

The mid-rapidity $K^{*0}$ $⟨p_T⟩$ as a function $⟨N_{part}⟩$ for Cu+Cu collisions at $\sqrt{s_{NN}}$ = 200 GeV

The mid-rapidity $⟨p_T⟩$ of $\pi$, K, p and $K^{*0}$ as a function of $⟨N_{part}⟩$ for Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV.

Mid-rapidity $N(K^{*0})/N(K^-)$ ratio for Au+Au at $\sqrt{s_{NN}}$ = 62.4 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $N(K^{*0})/N(K^-)$ ratio for Cu+Cu at $\sqrt{s_{NN}}$ = 62.4 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $N(K^{*0})/N(K^-)$ ratio for Au+Au at $\sqrt{s_{NN}}$ = 200 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $N(K^{*0})/N(K^-)$ ratio for Cu+Cu at $\sqrt{s_{NN}}$ = 200 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $N(K^{*0})N(K^-)$ in Au+Au collisions divided by $N(K^{*0})N(K^-)$ ratio in p+p collisions at $\sqrt{s_{NN}}$=200 GeV as a function of $⟨N_{part}⟩$.

Mid-rapidity $N(K^{*0})N(K^-)$ in Cu+Cu collisions divided by $N(K^{*0})N(K^-)$ ratio in p+p collisions at $\sqrt{s_{NN}}$=200 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $N(K^{*0})N(K^-)$ in d+Au collisions divided by $N(K^{*0})N(K^-)$ ratio in d+Au collisions at $\sqrt{s_{NN}}$=200 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $N(K^{*0})/N(K^-)$ ratio in minimum bias Au+Au collisions as a function of $\sqrt{s_{NN}}.

Mid-rapidity $N(K^{*0})/N(K^-)$ ratio in minimum bias Cu+Cu collisions as a function of $\sqrt{s_{NN}}.

Mid-rapidity $N(K^{*0})/N(K^-)$ ratio in minimum bias p+p collisions as a function of $\sqrt{s_{NN}}.

Mid-rapidity $N(K^{*0})/N(K^-)$ ratio in minimum bias Au+Au collisions as a function of $\sqrt{s_{NN}}.

Mid-rapidity $N(K^{*0})/N(K^-)$ ratio in minimum bias Cu+Cu collisions as a function of $\sqrt{s_{NN}}.

Mid-rapidity $N(K^{*0})/N(K^-)$ ratio in minimum bias p+p collisions as a function of $\sqrt{s_{NN}}.

Mid-rapidity $N(\phi)/N(K^{*0})$ ratio for Au+Au at $\sqrt{s_{NN}}$ = 62.4 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $N(\phi)/N(K^{*0})$ ratio for Cu+Cu at $\sqrt{s_{NN}}$ = 62.4 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $N(\phi)/N(K^{*0})$ ratio for Au+Au at $\sqrt{s_{NN}}$ = 200 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $N(\phi)/N(K^{*0})$ ratio for Cu+Cu at $\sqrt{s_{NN}}$ = 200 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $[N(\phi)/N(K^{*0})]$ in Au+Au collisions divided by $[N(\phi)/N(K^{*0})]$ ratio in p+p collisions at $\sqrt{s_{NN}}$=200 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $[N(\phi)/N(K^{*0})]$ in Cu+Cu collisions divided by $[N(\phi)/N(K^{*0})]$ ratio in p+p collisions at $\sqrt{s_{NN}}$=200 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $[N(\phi)/N(K^{*0})]$ in d+Au collisions divided by $[N(\phi)/N(K^{*0})]$ ratio in p+p collisions at $\sqrt{s_{NN}}$=200 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $N(\phi)/N(K^{*0})$ ratio in minimum bias Au+Au collisions as a function of $\sqrt{s_{NN}}$.

Mid-rapidity $N(\phi)/N(K^{*0})$ ratio in minimum bias Cu+Cu collisions as a function of $\sqrt{s_{NN}}$.

Mid-rapidity $N(\phi)/N(K^{*0})$ ratio in minimum bias p+p collisions as a function of $\sqrt{s_{NN}}$.

Mid-rapidity $N(\phi)/N(K^{*0})$ ratio in minimum bias Au+Au collisions as a function of $\sqrt{s_{NN}}$.

Mid-rapidity $N(\phi)/N(K^{*0})$ ratio in minimum bias Cu+Cu collisions as a function of $\sqrt{s_{NN}}$.

Mid-rapidity $N(\phi)/N(K^{*0})$ ratio in minimum bias p+p collisions as a function of $\sqrt{s_{NN}}$.

The $K^{*0}$ $v_2$ (Run IV) as a function of $p_T$ in minimum bias Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.

The $K^{*0}$ $v_2$ (Run II) as a function of $p_T$ in minimum bias Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.

The $K^{*0}$ $R_{CP}$ as a function of $p_T$ in Au+Au collisions at 62.4 and 200 GeV compared to the $R_{CP}$ of $K^0_S$ and $\Lambda$ at 200 GeV.

The $K^{*0}$ $R_{CP}$ as a function of $p_T$ in Au+Au collisions at 62.4 and 200 GeV compared to the $R_{CP}$ of $K^0_S$ and $\Lambda$ at 200 GeV.

The $K^{*0}$ $R_{CP}$ as a function of $p_T$ in Au+Au collisions at 62.4 and 200 GeV compared to the $R_{CP}$ of $K^0_S$ and $\Lambda$ at 200 GeV.

The $K^{*0}$ ~$R_{CP}$~ as a function of $p_T$ in Au+Au collisions at 62.4 and 200 GeV compared to the $R_{CP}$ of $K^0_S$ and $\Lambda$ at 200 GeV.

Background-subtracted charge-independent (AAT ) correlated hadron pair density in 40-80% Au+Au collisions for 3<p(t)⊥<10 GeV/cand 1<p(a)⊥<3 GeV/c. The results are for near-side correlated hadrons within |∆φ1,2|<0.7, and corrected for the 3-particle ∆η-∆η acceptance. Statistical errors at (∆η1,∆η2)∼(0,0)are approximately 0.058 for Au+Au respectively..

Background-subtracted charge-independent (AAT ) correlated hadron pair density in 0-12% Au+Au collisions for 3<p(t)⊥<10 GeV/cand 1<p(a)⊥<3 GeV/c. The results are for near-side correlated hadrons within |∆φ1,2|<0.7, and corrected for the 3-particle ∆η-∆η acceptance. Statistical errors at (∆η1,∆η2)∼(0,0)are approximately 0.084 for Au+Au respectively..

The average correlated hadron pair density per trigger particle as a function of R for all charges in minimum 0-12% Au+Au collision. The average〈ˆP〉for AAT as a function of R = $\sqrt{∆η21+ ∆η22}$. The average density is peaked at R∼0 and decreases with R for all systems. In 0-12% Au+Au collisions, the average denstiy drops more slowly andbecomes approximately constant aboveR>1, indicatingthe presence of the ridge.

The average correlated hadron pair density per trigger particle as a function of R for all charges in minimum 40-80% Au+Au collision. The average〈ˆP〉for AAT as a function of R = $\sqrt{∆η21+ ∆η22}$. The average density is peaked at R∼0 and decreases with R for all systems. For 40-80% Au+Au collisions the average density at R>1 is consistent with zero, indicating no ridge contribution

The average correlated hadron pair density per trigger particle as a function of R for all charges in minimum d+Au collision. The average〈ˆP〉for AAT as a function of R = $\sqrt{∆η21+ ∆η22}$. The average density is peaked at R∼0 and decreases with R for all systems. For d+Au collisions the average density at R>1 is consistent with zero, indicating no ridge contribution

Radial dependence of average 3-particle correlation pair density for 0-12% Au+Au (like-sign triplets) data. The results are shown in Fig. 3(b) Indeed, no jet-like component is apparent in A^±A^±T^±.The A^±A^±T^∓ result contains both jet-like and ridge components.

Radial dependence of average 3-particle correlation pair density for 40-80% Au+Au (like-sign triplets) data. The contribution from other charge combinations, namely A^±A^∓ T^±, are simply the difference between AAT in Fig.3(a) and (A^±A^±T^± + A^±A^± T^∓) in Fig. 3(b). We found this to be equal to twice the A^±A^± T^∓contribution within errors.

Radial dependence of average 3-particle correlation pair density for d+Au (AAT) data. We expect the ridge contributions in the correlated pair density to be the same in all charge combinations. We verified this for large ∆η correlatedpair densities within our current statistics, as can be seen from Fig. 3(b). Therefore the total ridge particle pair density (ˆPrr) can be obtained as four times A^±A^±T^±. The remaining jet-like signal, the sum of jet-like correlated particle pairs (ˆPjj) and cross pairs of a jet-like and a ridge particle (ˆPjr), can then be obtained by subtracting the total ridge from AAT.

for same-sign associated particles (A^\pm A^\pm T^\pm and A^\pm A^\pm T^\mp) in 0-12% Au+Au collisions Systematic uncertainties are shown in the shaded boxes due to background normalization and in the solid curves due to flow.

The R dependence of the average〈ˆPrr〉and〈ˆPjj〉+〈ˆPjr〉in 0-12% Au+Au collisions.The ridge pair density is consistent with a constant 60.14±0.02 (χ2/ndf=5.8/7). Gaussian fits indicate a best fit value σ = 2.1 (χ2/ndf=4.8/6, solid curve) and σ >1.4 (dashed curve) with 84% confidence level. On the otherhand, the jet-like component is narrow with a Gaussianσ=0.34+0.13−0.09(χ2/ndf=0.8/6, dominated by statistical errors), comparing well to those from the correlated single hadron density.

The average correlated hadron pair density per trigger particle in 0-12% Au+Au collisions for the jet-like andridge components as a function of R. The solid curves are Gaussian fits. The dashed curve is a Gaussian fit with a fixed σ=1.4 to the ridge data. The systematic uncertainities on the ridge data are shown in shaded boxes due to background normalization and in open boxes due to flow.

The R dependence of the average in 0-12% Au+Au collisions.for the ridge as a function of ξ within R<1.4. The solid curves are Gaussian fits. To investigate possible structures in the ridge, we show in Fig. 4(b) the average ridge particle pair density as a function of ξ = arctan(∆η2/∆η1) within R<1.4. The data are consistent with a uniform distribution in ξ(χ2/ndf=1.7/7). This suggests that the ridge particles are uncorrelated in ∆η not only with the trigger particle but also between themselves. In other words,the ridge appears to be uniform in ∆η event-by-event.

Upper panels: same-event (full points) and mixed-event (solid line) $K^{+}K^{-}$ invariant mass distributions at 0.6 < $p_{T}$ < 1.4 GeV/c in p + p 200 GeV collisions (a), 0.8 < $p_{T}$ < 1.2 GeV/c in Au + Au 62.4 GeV collisions (60–80%) (c), and 0.8 < $p_{T}$ < 1.2 GeV/c in Au + Au 200 GeV collisions (0–10%) (e). Lower panels: the corresponding $\phi$ meson mass peaks after subtracting the background. Dashed curves show a Breit-Wigner + linear background function fit in (b), (d). In (f), both linear and quadratic backgrounds are shown as dashed and dot-dashed lines, respectively.

Upper panels: same-event (full points) and mixed-event (solid line) $K^{+}K^{-}$ invariant mass distributions at 0.6 < $p_{T}$ < 1.4 GeV/c in p + p 200 GeV collisions (a), 0.8 < $p_{T}$ < 1.2 GeV/c in Au + Au 62.4 GeV collisions (60–80%) (c), and 0.8 < $p_{T}$ < 1.2 GeV/c in Au + Au 200 GeV collisions (0–10%) (e). Lower panels: the corresponding $\phi$ meson mass peaks after subtracting the background. Dashed curves show a Breit-Wigner + linear background function fit in (b), (d). In (f), both linear and quadratic backgrounds are shown as dashed and dot-dashed lines, respectively.

Upper panels: same-event (full points) and mixed-event (solid line) $K^{+}K^{-}$ invariant mass distributions at 0.6 < $p_{T}$ < 1.4 GeV/c in p + p 200 GeV collisions (a), 0.8 < $p_{T}$ < 1.2 GeV/c in Au + Au 62.4 GeV collisions (60–80%) (c), and 0.8 < $p_{T}$ < 1.2 GeV/c in Au + Au 200 GeV collisions (0–10%) (e). Lower panels: the corresponding $\phi$ meson mass peaks after subtracting the background. Dashed curves show a Breit-Wigner + linear background function fit in (b), (d). In (f), both linear and quadratic backgrounds are shown as dashed and dot-dashed lines, respectively.

Reconstruction efficiency including acceptance of $\phi$ meson as a function of $p_{T}$ in several centrality bins of Au + Au, d + Au, and p + p 200 GeV collisions.

Reconstruction efficiency including acceptance of $\phi$ meson as a function of $p_{T}$ in several centrality bins of Au + Au, d + Au, and p + p 200 GeV collisions.

Reconstruction efficiency including acceptance of $\phi$ meson as a function of $p_{T}$ in several centrality bins of Au + Au, d + Au, and p + p 200 GeV collisions.

Event plane $\Phi_{2}$ resolution as a function of centrality in Au + Au 200 GeV collisions, where the vertical axis starts from 0.3 for clarity.

$\phi−\Phi_{2}$ distribution for $\phi$ meson at 1.5 < $p_{T}$ < 2.0 GeV/c in Au + Au collisions (0–80$\%$) at 200 GeV. The line is the fitting result. Error bars are statistical only.

<cos2($\phi_{K^{+}K^{-}}$-$\Phi_{2}$)> (full red points) and <sin2($\phi_{K^{+}K^{-}}$-$\Phi_{2}$)> (open blue points) as a function of $m_{inv}$ of $K^{+}K^{-}$ pairs at 0.5 < $p_{T}$ < 1.0 GeV/c in Au + Au 200 GeV collisions (0–80\%), where the solid curve is the result of fitting by Eq. (10). The arrow shows the position of the $\phi$ invariant mass peak. The dashed line shows the zero horizontal line.

Masses and widths (FWHMs) of $\phi$ as a function of $p_{T}$ in p + p 200 GeV (NSD), d + Au 200 GeV (0–20$\%$), Au + Au 62.4 GeV (0–20$\%$), and Au + Au 200 GeV (0–5$\%$) collisions, with the corresponding $PDG$ values.

Masses and widths (FWHMs) of $\phi$ as a function of $p_{T}$ in p + p 200 GeV (NSD), d + Au 200 GeV (0–20$\%$), Au + Au 62.4 GeV (0–20$\%$), and Au + Au 200 GeV (0–5$\%$) collisions, with the corresponding $PDG$ values.

Masses and widths (FWHMs) of $\phi$ as a function of $p_{T}$ in p + p 200 GeV (NSD), d + Au 200 GeV (0–20$\%$), Au + Au 62.4 GeV (0–20$\%$), and Au + Au 200 GeV (0–5$\%$) collisions, with the corresponding $PDG$ values.

Masses and widths (FWHMs) of $\phi$ as a function of $p_{T}$ in p + p 200 GeV (NSD), d + Au 200 GeV (0–20$\%$), Au + Au 62.4 GeV (0–20$\%$), and Au + Au 200 GeV (0–5$\%$) collisions, with the corresponding $PDG$ values.

Masses and widths (FWHMs) of $\phi$ as a function of $p_{T}$ in p + p 200 GeV (NSD), d + Au 200 GeV (0–20$\%$), Au + Au 62.4 GeV (0–20$\%$), and Au + Au 200 GeV (0–5$\%$) collisions, with the corresponding $PDG$ values.

Masses and widths (FWHMs) of $\phi$ as a function of $p_{T}$ in p + p 200 GeV (NSD), d + Au 200 GeV (0–20$\%$), Au + Au 62.4 GeV (0–20$\%$), and Au + Au 200 GeV (0–5$\%$) collisions, with the corresponding $PDG$ values.

Masses and widths (FWHMs) of $\phi$ as a function of $p_{T}$ in p + p 200 GeV (NSD), d + Au 200 GeV (0–20$\%$), Au + Au 62.4 GeV (0–20$\%$), and Au + Au 200 GeV (0–5$\%$) collisions, with the corresponding $PDG$ values.

Masses and widths (FWHMs) of $\phi$ as a function of $p_{T}$ in p + p 200 GeV (NSD), d + Au 200 GeV (0–20$\%$), Au + Au 62.4 GeV (0–20$\%$), and Au + Au 200 GeV (0–5$\%$) collisions, with the corresponding $PDG$ values.

Masses and widths (FWHMs) of $\phi$ as a function of $p_{T}$ in p + p 200 GeV (NSD), d + Au 200 GeV (0–20$\%$), Au + Au 62.4 GeV (0–20$\%$), and Au + Au 200 GeV (0–5$\%$) collisions, with the corresponding $PDG$ values.

Masses and widths (FWHMs) of $\phi$ as a function of $p_{T}$ in p + p 200 GeV (NSD), d + Au 200 GeV (0–20$\%$), Au + Au 62.4 GeV (0–20$\%$), and Au + Au 200 GeV (0–5$\%$) collisions, with the corresponding $PDG$ values.

Masses and widths (FWHMs) of $\phi$ as a function of $p_{T}$ in p + p 200 GeV (NSD), d + Au 200 GeV (0–20$\%$), Au + Au 62.4 GeV (0–20$\%$), and Au + Au 200 GeV (0–5$\%$) collisions, with the corresponding $PDG$ values.

Masses and widths (FWHMs) of $\phi$ as a function of $p_{T}$ in p + p 200 GeV (NSD), d + Au 200 GeV (0–20$\%$), Au + Au 62.4 GeV (0–20$\%$), and Au + Au 200 GeV (0–5$\%$) collisions, with the corresponding $PDG$ values.

Masses and widths (FWHMs) of $\phi$ as a function of $p_{T}$ in p + p 200 GeV (NSD), d + Au 200 GeV (0–20$\%$), Au + Au 62.4 GeV (0–20$\%$), and Au + Au 200 GeV (0–5$\%$) collisions, with the corresponding $PDG$ values.

Invariant mass distributions of $\phi$ meson at 0.6 < $p_{T}$ < 1.0 GeV/c in p + p 200 GeV (NSD) and Au + Au 200 GeV (0–5$\%$) collisions. Solid symbols: experimental data. Open symbols: MC simulation. Curves are the results of a Breit-Wigner function fit. Note: Two sets of MC data are shown for Au + Au 200 GeV, and see text for details.

Invariant mass distributions of $\phi$ meson at 0.6 < $p_{T}$ < 1.0 GeV/c in p + p 200 GeV (NSD) and Au + Au 200 GeV (0–5$\%$) collisions. Solid symbols: experimental data. Open symbols: MC simulation. Curves are the results of a Breit-Wigner function fit. Note: Two sets of MC data are shown for Au + Au 200 GeV, and see text for details.

Invariant mass distributions of $\phi$ meson at 0.6 < $p_{T}$ < 1.0 GeV/c in p + p 200 GeV (NSD) and Au + Au 200 GeV (0–5$\%$) collisions. Solid symbols: experimental data. Open symbols: MC simulation. Curves are the results of a Breit-Wigner function fit. Note: Two sets of MC data are shown for Au + Au 200 GeV, and see text for details.

Invariant mass distributions of $\phi$ meson at 0.6 < $p_{T}$ < 1.0 GeV/c in p + p 200 GeV (NSD) and Au + Au 200 GeV (0–5$\%$) collisions. Solid symbols: experimental data. Open symbols: MC simulation. Curves are the results of a Breit-Wigner function fit. Note: Two sets of MC data are shown for Au + Au 200 GeV, and see text for details.

Invariant mass distributions of $\phi$ meson at 0.6 < $p_{T}$ < 1.0 GeV/c in p + p 200 GeV (NSD) and Au + Au 200 GeV (0–5$\%$) collisions. Solid symbols: experimental data. Open symbols: MC simulation. Curves are the results of a Breit-Wigner function fit. Note: Two sets of MC data are shown for Au + Au 200 GeV, and see text for details.

$\phi$ meson transverse mass distributions for different collision systems and different energies. For clarity, distributions for some centrality bins have been scaled by factors indicated in the figure. Curves represent the exponential (solid) and Levy (dashed) function fits to the distributions. Error bars are statistical only. Note that a scale factor of 1.09 is applied to the $\phi$ meson spectra for Au + Au collisions at 200 GeV in Ref. [50] to correct for the kaon identification efficiency effect missed previously.

$\phi$ meson transverse mass distributions for different collision systems and different energies. For clarity, distributions for some centrality bins have been scaled by factors indicated in the figure. Curves represent the exponential (solid) and Levy (dashed) function fits to the distributions. Error bars are statistical only. Note that a scale factor of 1.09 is applied to the $\phi$ meson spectra for Au + Au collisions at 200 GeV in Ref. [50] to correct for the kaon identification efficiency effect missed previously.

$\phi$ meson transverse mass distributions for different collision systems and different energies. For clarity, distributions for some centrality bins have been scaled by factors indicated in the figure. Curves represent the exponential (solid) and Levy (dashed) function fits to the distributions. Error bars are statistical only. Note that a scale factor of 1.09 is applied to the $\phi$ meson spectra for Au + Au collisions at 200 GeV in Ref. [50] to correct for the kaon identification efficiency effect missed previously.

$\phi$ meson transverse mass distributions for different collision systems and different energies. For clarity, distributions for some centrality bins have been scaled by factors indicated in the figure. Curves represent the exponential (solid) and Levy (dashed) function fits to the distributions. Error bars are statistical only. Note that a scale factor of 1.09 is applied to the $\phi$ meson spectra for Au + Au collisions at 200 GeV in Ref. [50] to correct for the kaon identification efficiency effect missed previously.

$\phi$ meson transverse mass distributions for different collision systems and different energies. For clarity, distributions for some centrality bins have been scaled by factors indicated in the figure. Curves represent the exponential (solid) and Levy (dashed) function fits to the distributions. Error bars are statistical only. Note that a scale factor of 1.09 is applied to the $\phi$ meson spectra for Au + Au collisions at 200 GeV in Ref. [50] to correct for the kaon identification efficiency effect missed previously.

$\phi$ meson transverse mass distributions for different collision systems and different energies. For clarity, distributions for some centrality bins have been scaled by factors indicated in the figure. Curves represent the exponential (solid) and Levy (dashed) function fits to the distributions. Error bars are statistical only. Note that a scale factor of 1.09 is applied to the $\phi$ meson spectra for Au + Au collisions at 200 GeV in Ref. [50] to correct for the kaon identification efficiency effect missed previously.

$\phi$ meson transverse mass distributions for different collision systems and different energies. For clarity, distributions for some centrality bins have been scaled by factors indicated in the figure. Curves represent the exponential (solid) and Levy (dashed) function fits to the distributions. Error bars are statistical only. Note that a scale factor of 1.09 is applied to the $\phi$ meson spectra for Au + Au collisions at 200 GeV in Ref. [50] to correct for the kaon identification efficiency effect missed previously.

Comparison of transverse momentum spectra shape among different 200 GeV collision systems: Au + Au (0–5$\%$), d + Au (0–20$\%$), and p + p (inelastic). The spectra are normalized by $N_{bin}$ (top panel) and $N_{part}/2$ (bottom panel).

Comparison of transverse momentum spectra shape among different 200 GeV collision systems: Au + Au (0–5$\%$), d + Au (0–20$\%$), and p + p (inelastic). The spectra are normalized by $N_{bin}$ (top panel) and $N_{part}/2$ (bottom panel).

Comparison of transverse momentum spectra shape among different 200 GeV collision systems: Au + Au (0–5$\%$), d + Au (0–20$\%$), and p + p (inelastic). The spectra are normalized by $N_{bin}$ (top panel) and $N_{part}/2$ (bottom panel).

Comparison of transverse momentum spectra shape among different 200 GeV collision systems: Au + Au (0–5$\%$), d + Au (0–20$\%$), and p + p (inelastic). The spectra are normalized by $N_{bin}$ (top panel) and $N_{part}/2$ (bottom panel).

Comparison of transverse momentum spectra shape among different 200 GeV collision systems: Au + Au (0–5$\%$), d + Au (0–20$\%$), and p + p (inelastic). The spectra are normalized by $N_{bin}$ (top panel) and $N_{part}/2$ (bottom panel).

Comparison of transverse momentum spectra shape among different 200 GeV collision systems: Au + Au (0–5$\%$), d + Au (0–20$\%$), and p + p (inelastic). The spectra are normalized by $N_{bin}$ (top panel) and $N_{part}/2$ (bottom panel).

$N_{part}$ dependence of $(dN/dy)/0.5N_{part}$ in five different collision systems: Au + Au 62.4, 130, 200 GeV; p + p 200 GeV (inelastic); and d + Au 200 GeV. Statistical and systematic errors are included.

$N_{part}$ dependence of $(dN/dy)/0.5N_{part}$ in five different collision systems: Au + Au 62.4, 130, 200 GeV; p + p 200 GeV (inelastic); and d + Au 200 GeV. Statistical and systematic errors are included.

$N_{part}$ dependence of $(dN/dy)/0.5N_{part}$ in five different collision systems: Au + Au 62.4, 130, 200 GeV; p + p 200 GeV (inelastic); and d + Au 200 GeV. Statistical and systematic errors are included.

$N_{part}$ dependence of $(dN/dy)/0.5N_{part}$ in five different collision systems: Au + Au 62.4, 130, 200 GeV; p + p 200 GeV (inelastic); and d + Au 200 GeV. Statistical and systematic errors are included.

$N_{part}$ dependence of $(dN/dy)/0.5N_{part}$ in five different collision systems: Au + Au 62.4, 130, 200 GeV; p + p 200 GeV (inelastic); and d + Au 200 GeV. Statistical and systematic errors are included.

Top panel: $N_{part}$ dependence of $<p_{T}>_{\phi}$ in different collision systems. Bottom panel: Hadron mass dependence of $<p_{T}>$ in central Au + Au collisions at 62.4 and 200 GeV. The band and curve show two hydrodynamic model calculations for central Au + Au collisions at 200 GeV. Note: Hadron masses for the Au + Au 62.4 GeV data are shifted slightly in the $x$-axis direction for clarity, and systematic errors are included for $\phi$.

Top panel: $N_{part}$ dependence of $<p_{T}>_{\phi}$ in different collision systems. Bottom panel: Hadron mass dependence of $<p_{T}>$ in central Au + Au collisions at 62.4 and 200 GeV. The band and curve show two hydrodynamic model calculations for central Au + Au collisions at 200 GeV. Note: Hadron masses for the Au + Au 62.4 GeV data are shifted slightly in the $x$-axis direction for clarity, and systematic errors are included for $\phi$.

Top panel: $N_{part}$ dependence of $<p_{T}>_{\phi}$ in different collision systems. Bottom panel: Hadron mass dependence of $<p_{T}>$ in central Au + Au collisions at 62.4 and 200 GeV. The band and curve show two hydrodynamic model calculations for central Au + Au collisions at 200 GeV. Note: Hadron masses for the Au + Au 62.4 GeV data are shifted slightly in the $x$-axis direction for clarity, and systematic errors are included for $\phi$.

Top panel: $N_{part}$ dependence of $<p_{T}>_{\phi}$ in different collision systems. Bottom panel: Hadron mass dependence of $<p_{T}>$ in central Au + Au collisions at 62.4 and 200 GeV. The band and curve show two hydrodynamic model calculations for central Au + Au collisions at 200 GeV. Note: Hadron masses for the Au + Au 62.4 GeV data are shifted slightly in the $x$-axis direction for clarity, and systematic errors are included for $\phi$.

Top panel: $N_{part}$ dependence of $<p_{T}>_{\phi}$ in different collision systems. Bottom panel: Hadron mass dependence of $<p_{T}>$ in central Au + Au collisions at 62.4 and 200 GeV. The band and curve show two hydrodynamic model calculations for central Au + Au collisions at 200 GeV. Note: Hadron masses for the Au + Au 62.4 GeV data are shifted slightly in the $x$-axis direction for clarity, and systematic errors are included for $\phi$.

Top panel: $N_{part}$ dependence of $<p_{T}>_{\phi}$ in different collision systems. Bottom panel: Hadron mass dependence of $<p_{T}>$ in central Au + Au collisions at 62.4 and 200 GeV. The band and curve show two hydrodynamic model calculations for central Au + Au collisions at 200 GeV. Note: Hadron masses for the Au + Au 62.4 GeV data are shifted slightly in the $x$-axis direction for clarity, and systematic errors are included for $\phi$.

Top panel: Energy dependence of the ratio $\phi/\pi^{-}$ in A + A (full points) and p + p (open points) collisions. Stars are data from the STARexperiment at RHIC.Bottom panel: $N_{part}$ dependence of ratio $\phi/\pi^{-}$ in different collision systems. Systematic errors are included for the STAR data points.

Top panel: Energy dependence of the ratio $\phi/\pi^{-}$ in A + A (full points) and p + p (open points) collisions. Stars are data from the STARexperiment at RHIC.Bottom panel: $N_{part}$ dependence of ratio $\phi/\pi^{-}$ in different collision systems. Systematic errors are included for the STAR data points.

Top panel: Energy dependence of the ratio $\phi/\pi^{-}$ in A + A (full points) and p + p (open points) collisions. Stars are data from the STARexperiment at RHIC.Bottom panel: $N_{part}$ dependence of ratio $\phi/\pi^{-}$ in different collision systems. Systematic errors are included for the STAR data points.

Top panel: Energy dependence of the ratio $\phi/\pi^{-}$ in A + A (full points) and p + p (open points) collisions. Stars are data from the STARexperiment at RHIC.Bottom panel: $N_{part}$ dependence of ratio $\phi/\pi^{-}$ in different collision systems. Systematic errors are included for the STAR data points.

Top panel: Energy dependence of the ratio $\phi/\pi^{-}$ in A + A (full points) and p + p (open points) collisions. Stars are data from the STARexperiment at RHIC.Bottom panel: $N_{part}$ dependence of ratio $\phi/\pi^{-}$ in different collision systems. Systematic errors are included for the STAR data points.

Top panel: Energy dependence of the ratio $\phi/\pi^{-}$ in A + A (full points) and p + p (open points) collisions. Stars are data from the STARexperiment at RHIC.Bottom panel: $N_{part}$ dependence of ratio $\phi/\pi^{-}$ in different collision systems. Systematic errors are included for the STAR data points.

Top panel: Energy dependence of the ratio $\phi/\pi^{-}$ in A + A (full points) and p + p (open points) collisions. Stars are data from the STARexperiment at RHIC.Bottom panel: $N_{part}$ dependence of ratio $\phi/\pi^{-}$ in different collision systems. Systematic errors are included for the STAR data points.

Top panel: Energy dependence of ratio $\phi/K^{-}$ in $A + A$ and elementary ($e + e$ and $p + p$) collisions. Stars are data from STAR experiments at RHIC. Bottom panel: $N_{part}$ dependence of ratio $\phi/K^{-}$ in different collision systems. The dashed line shows results from $UrQMD$ model calculations. Systematic errors are included for the STAR data points.

Top panel: Energy dependence of ratio $\phi/K^{-}$ in $A + A$ and elementary ($e + e$ and $p + p$) collisions. Stars are data from STAR experiments at RHIC. Bottom panel: $N_{part}$ dependence of ratio $\phi/K^{-}$ in different collision systems. The dashed line shows results from $UrQMD$ model calculations. Systematic errors are included for the STAR data points.

Top panel: Energy dependence of ratio $\phi/K^{-}$ in $A + A$ and elementary ($e + e$ and $p + p$) collisions. Stars are data from STAR experiments at RHIC. Bottom panel: $N_{part}$ dependence of ratio $\phi/K^{-}$ in different collision systems. The dashed line shows results from $UrQMD$ model calculations. Systematic errors are included for the STAR data points.

Top panel: Energy dependence of ratio $\phi/K^{-}$ in $A + A$ and elementary ($e + e$ and $p + p$) collisions. Stars are data from STAR experiments at RHIC. Bottom panel: $N_{part}$ dependence of ratio $\phi/K^{-}$ in different collision systems. The dashed line shows results from $UrQMD$ model calculations. Systematic errors are included for the STAR data points.

Top panel: Energy dependence of ratio $\phi/K^{-}$ in $A + A$ and elementary ($e + e$ and $p + p$) collisions. Stars are data from STAR experiments at RHIC. Bottom panel: $N_{part}$ dependence of ratio $\phi/K^{-}$ in different collision systems. The dashed line shows results from $UrQMD$ model calculations. Systematic errors are included for the STAR data points.

Top panel: Energy dependence of ratio $\phi/K^{-}$ in $A + A$ and elementary ($e + e$ and $p + p$) collisions. Stars are data from STAR experiments at RHIC. Bottom panel: $N_{part}$ dependence of ratio $\phi/K^{-}$ in different collision systems. The dashed line shows results from $UrQMD$ model calculations. Systematic errors are included for the STAR data points.

Top panel: Energy dependence of ratio $\phi/K^{-}$ in $A + A$ and elementary ($e + e$ and $p + p$) collisions. Stars are data from STAR experiments at RHIC. Bottom panel: $N_{part}$ dependence of ratio $\phi/K^{-}$ in different collision systems. The dashed line shows results from $UrQMD$ model calculations. Systematic errors are included for the STAR data points.

Top panel: Energy dependence of ratio $\phi/K^{-}$ in $A + A$ and elementary ($e + e$ and $p + p$) collisions. Stars are data from STAR experiments at RHIC. Bottom panel: $N_{part}$ dependence of ratio $\phi/K^{-}$ in different collision systems. The dashed line shows results from $UrQMD$ model calculations. Systematic errors are included for the STAR data points.

The $\Omega/\phi$ ratio vs $p_{T}$ for three centrality bins in $\sqrt{s_{NN}} = 200 GeV$ Au + Au collisions, where the data points for 40–60$\%$ are shifted slightly for clarity. As shown in the legend, the lines represent results from Hwa and Yang [96], Ko et al. [97], and, for SCF, Refs. [98,99].

The $\Omega/\phi$ ratio vs $p_{T}$ for three centrality bins in $\sqrt{s_{NN}} = 200 GeV$ Au + Au collisions, where the data points for 40–60$\%$ are shifted slightly for clarity. As shown in the legend, the lines represent results from Hwa and Yang [96], Ko et al. [97], and, for SCF, Refs. [98,99].

$p_{T}$ dependence of the nuclear modification factor $R_{cp}$ in Au + Au 200 GeV collisions. The top and bottom panels present $R_{cp}$ from midperipheral and most-peripheral collisions, respectively. See legend for symbol and line designations. The rectangular bands showthe uncertainties of binary and participant scalings. Statistical and systematic errors are included.

$p_{T}$ dependence of the nuclear modification factor $R_{cp}$ in Au + Au 200 GeV collisions. The top and bottom panels present $R_{cp}$ from midperipheral and most-peripheral collisions, respectively. See legend for symbol and line designations. The rectangular bands showthe uncertainties of binary and participant scalings. Statistical and systematic errors are included.

$p_{T}$ dependence of the nuclear modification factor $R_{cp}$ in Au + Au 62.4 and 200 GeV and d + Au 200 GeV collisions, where rectangular bands represent the uncertainties of binary and participant scalings (see legend). Statistical and systematic errors are included.

$p_{T}$ dependence of the nuclear modification factor $R_{cp}$ in Au + Au 62.4 and 200 GeV and d + Au 200 GeV collisions, where rectangular bands represent the uncertainties of binary and participant scalings (see legend). Statistical and systematic errors are included.

$p_{T}$ dependence of the nuclear modification factor $R_{cp}$ in Au + Au 62.4 and 200 GeV and d + Au 200 GeV collisions, where rectangular bands represent the uncertainties of binary and participant scalings (see legend). Statistical and systematic errors are included.

$p_{T}$ dependence of the nuclear modification factor $R_{AB}$ for $\phi$ in Au + Au 200 GeV and d + Au 200 GeV collisions. For comparison, data points for $\pi^{+}+\pi^{-}$ in d + Au 200 GeV and $p+\bar{p}$ in d + Au 200 GeV are also shown (see legend). Rectangular bands show the uncertainties of binary (solid line) and participant (dot-dash line) scalings. Systematic errors are included for $\phi$, $\pi^{+}+\pi^{-}$, and $p+\bar{p}$.

$p_{T}$ dependence of the nuclear modification factor $R_{AB}$ for $\phi$ in Au + Au 200 GeV and d + Au 200 GeV collisions. For comparison, data points for $\pi^{+}+\pi^{-}$ in d + Au 200 GeV and $p+\bar{p}$ in d + Au 200 GeV are also shown (see legend). Rectangular bands show the uncertainties of binary (solid line) and participant (dot-dash line) scalings. Systematic errors are included for $\phi$, $\pi^{+}+\pi^{-}$, and $p+\bar{p}$.

$p_{T}$ dependence of the elliptic flow $v_{2}$ of $\phi$, $\Lambda$, and $K_{s}^{0}$ in Au + Au collisions (0–80$\%$) at 200 GeV. Data points for $\phi$ are from the reaction plane method (full up-triangles) and invariant mass method (full circles), where data points from the reaction plane method are shifted slightly along the $x$ axis for clarity. Vertical error bars represent statistical errors, while the square bands represent systematic uncertainties. The magenta curved band represents the $v_{2}$ of $\phi$ meson from the AMPT model with a string melting mechanism [116]. The dash and dot curves represent parametrizations inspired by number-of-quark scaling ideas from Ref. [117] for NQ = 2 and NQ = 3, respectively.

Elliptic flow $v_{2}$ as a function of $p_{T}$ , $v_{2}$($p_{T}$), for the $\phi$ meson from different centralities. The vertical error bars represent the statistical errors, while the square bands represent the systematic uncertainties. For clarity, data points of 10–40$\%$ are shifted in the $p_{T}$ direction slightly.

Elliptic flow $v_{2}$ as a function of $p_{T}$ , $v_{2}$($p_{T}$), for the $\phi$ meson from different centralities. The vertical error bars represent the statistical errors, while the square bands represent the systematic uncertainties. For clarity, data points of 10–40$\%$ are shifted in the $p_{T}$ direction slightly.

Efficiency corrected two-particle azimuthal distributions for minimum bias and central d+Au collisions, and for p+p collisions. Curves are fits using Eq. 3, with parameters given in Table I. Trigger particles are selected with 4 GeV/c < $p_{T}$ (trig) < 6 GeV/c, while associated particles are selected within 2 GeV/c < $p_{T}$ < $p_{T}$ (trig), with |$\eta$| < 0.7 for both sets. Only statistical errors are listed. Normalization uncertainties are less than 5%.

Comparison of two-particle azimuthal distributions for central d+Au collisions to those seen in p+p and central Au+Au collisions. The respective pedestals have been subtracted. Trigger particles are selected with 4 GeV/c < $p_{T}$ (trig) < 6 GeV/c, while associated particles are selected within 2 GeV/c < $p_{T}$ < $p_{T}$ (trig), with |$\eta$| < 0.7 for both sets. Only statistical errors are listed. Normalization uncertainties are less than 5%.