Neutral Pion Production in Au+Au Collisions at $\sqrt{s_{NN}}$ = 200 GeV

The STAR collaboration Abelev, B.I. ; Aggarwal, M.M. ; Ahammed, Z. ; et al.
Phys.Rev.C 80 (2009) 044905, 2009.
Inspire Record 825863 DOI 10.17182/hepdata.96845

The results of mid-rapidity ($0 < y < 0.8$) neutral pion spectra over an extended transverse momentum range ($1 < p_T < 12$ GeV/$c$) in $\sqrt{s_{NN}}$ = 200 GeV Au+Au collisions, measured by the STAR experiment, are presented. The neutral pions are reconstructed from photons measured either by the STAR Barrel Electro-Magnetic Calorimeter (BEMC) or by the Time Projection Chamber (TPC) via tracking of conversion electron-positron pairs. Our measurements are compared to previously published $\pi^{\pm}$ and $\pi^0$ results. The nuclear modification factors $R_{\mathrm{CP}}$ and $R_{\mathrm{AA}}$ of $\pi^0$ are also presented as a function of $p_T$ . In the most central Au+Au collisions, the binary collision scaled $\pi^0$ yield at high $p_T$ is suppressed by a factor of about 5 compared to the expectation from the yield of p+p collisions. Such a large suppression is in agreement with previous observations for light quark mesons and is consistent with the scenario that partons suffer considerable energy loss in the dense medium formed in central nucleus-nucleus collisions at RHIC.

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The diphoton invariant mass distributions using the EMC-TPC method in 0-20% Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV.

The diphoton invariant mass distributions using the EMC-TPC method in 0-20% Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV.

The diphoton invariant mass distributions using the EMC-EMC method in 0-20% Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV.

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K/pi Fluctuations at Relativistic Energies

The STAR collaboration Abelev, B.I. ; Aggarwal, M.M. ; Ahammed, Z. ; et al.
Phys.Rev.Lett. 103 (2009) 092301, 2009.
Inspire Record 810902 DOI 10.17182/hepdata.98971

We report results for $K/\pi$ fluctuations from Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6, 62.4, 130, and 200 GeV using the STAR detector at the Relativistic Heavy Ion Collider. Our results for $K/\pi$ fluctuations in central collisions show little dependence on the incident energies studied and are on the same order as results observed by NA49 at the Super Proton Synchrotron in central Pb+Pb collisions at $\sqrt{s_{NN}}$ = 12.3 and 17.3 GeV. We also report results for the collision centrality dependence of $K/\pi$ fluctuations as well as results for $K^{+}/\pi^{+}$, $K^{-}/\pi^{-}$, $K^{+}/\pi^{-}$, and $K^{-}/\pi^{+}$ fluctuations. We observe that the $K/\pi$ fluctuations scale with the multiplicity density, $dN/d\eta$, rather than the number of participating nucleons.

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(Color online) The event-by-event $K/\pi$ ratio for 200 GeV Au+Au central collisions (0-5%) compared with the same quantity calculated from mixed events. The inset shows the ratio of the distribution from real events to that from mixed events. The errors shown are statistical.

(Color online) The event-by-event $K/\pi$ ratio for 200 GeV Au+Au central collisions (0-5%) compared with the same quantity calculated from mixed events. The inset shows the ratio of the distribution from real events to that from mixed events. The errors shown are statistical.

(Color online) Measured dynamical $K/\pi$ fluctuations in terms of σdyn for central collisions (0 - 5%) of 19.6, 62.4, 130, and 200 GeV Au+Au compared with the central collisions (0 - 3.5%) of Pb+Pb from NA49 [7] and the statistical hadronization (SH) model of Ref. [14]. The solid line represents the relationship of the incident energy dependence of $\sigma_{dyn}$ in central collisions to the collision centrality dependence of $\nu_{dyn,K\pi}$ at higher energies. Both statistical (vertical line with horizontal bar) and systematic (no vertical line) error bars are shown for the experimental data.

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Measurements of $\phi$ meson production in relativistic heavy-ion collisions at RHIC

The STAR collaboration Abelev, B.I. ; Aggarwal, M.M. ; Ahammed, Z. ; et al.
Phys.Rev.C 79 (2009) 064903, 2009.
Inspire Record 797805 DOI 10.17182/hepdata.99047

We present results for the measurement of $\phi$ meson production via its charged kaon decay channel $\phi \to K^+K^-$ in Au+Au collisions at $\sqrt{s_{_{NN}}}=62.4$, 130, 200 GeV, and in p+p and d+Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV from the STAR experiment at RHIC. The mid-rapidity ($|y|<0.5$) $\phi$ meson spectra in central Au+Au collisions are found to be well described by a single exponential distribution. On the other hand, the spectra from p+p, d+Au and peripheral Au+Au collisions show power-law tails at intermediate and high transverse momenta ($p_{T}$) and are described better by Levy distributions. The constant $\phi/K^-$ yield ratio vs. beam species, collision centrality and colliding energy is in contradiction with expectations from models having kaon coalescence as the dominant mechanism for $\phi$ production at RHIC. The $\Omega/\phi$ yield ratio as a function of $p_{T}$ is consistent with a model based on the recombination of thermal $s$ quarks up to $p_{T}\sim 4$ GeV/c, but disagrees at higher transverse momenta. The measured nuclear modification factor, $R_{dAu}$, for the $\phi$ meson increases above unity at intermediate $p_{T}$, similar to that for pions and protons, while $R_{AA}$ is suppressed due to jet quenching in central Au+Au collisions. Number of constituent quark scaling of both $R_{cp}$ and $v_{2}$ for the $\phi$ meson with respect to other hadrons in Au+Au collisions at $\sqrt{s_{_{NN}}}$=200 GeV at intermediate $p_{T}$ is observed. These observations support quark coalescence as being the dominant mechanism of hadronization in the intermediate $p_{T}$ region at RHIC.

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Background-subtracted invariant mass distributions at 0.4 < $p_{T}$ < 0.8 GeV/c in d + Au 200 GeV collisions (0–100%) with (solid points) and without (open points) the $\delta$-dipangle cut. The dashed curves show a Breit-Wigner (see the text for details) + linear background function fit to the case with the $\delta$-dip-angle cut.

Background-subtracted invariant mass distributions at 0.4 < $p_{T}$ < 0.8 GeV/c in d + Au 200 GeV collisions (0–100%) with (solid points) and without (open points) the $\delta$-dipangle cut. The dashed curves show a Breit-Wigner (see the text for details) + linear background function fit to the case with the $\delta$-dip-angle cut.

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.

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Global polarization of $\Xi$ and $\Omega$ hyperons in Au+Au collisions at $\sqrt{s_{_{NN}}}$ = 200 GeV

The STAR collaboration Adam, J. ; Adamczyk, L. ; Adams, J.R. ; et al.
Phys.Rev.Lett. 126 (2021) 162301, 2021.
Inspire Record 1838481 DOI 10.17182/hepdata.100234

Global polarization of $\Xi$ and $\Omega$ hyperons has been measured for the first time in Au+Au collisions at $\sqrt{s_{_{NN}}}$ = 200 GeV. The measurements of the $\Xi^-$ and $\bar{\Xi}^+$ hyperon polarization have been performed by two independent methods, via analysis of the angular distribution of the daughter particles in the parity violating weak decay $\Xi\rightarrow\Lambda+\pi$, as well as by measuring the polarization of the daughter $\Lambda$-hyperon, polarized via polarization transfer from its parent. The polarization, obtained by combining the results from the two methods and averaged over $\Xi^-$ and $\bar{\Xi}^+$, is measured to be $\langle P_\Xi \rangle = 0.47\pm0.10~({\rm stat.})\pm0.23~({\rm syst.})\,\%$ for the collision centrality 20%-80%. The $\langle P_\Xi \rangle$ is found to be slightly larger than the inclusive $\Lambda$ polarization and in reasonable agreement with a multi-phase transport model (AMPT). The $\langle P_\Xi \rangle$ is found to follow the centrality dependence of the vorticity predicted in the model, increasing toward more peripheral collisions. The global polarization of $\Omega$, $\langle P_\Omega \rangle = 1.11\pm0.87~({\rm stat.})\pm1.97~({\rm syst.})\,\%$ was obtained by measuring the polarization of daughter $\Lambda$ in the decay $\Omega \rightarrow \Lambda + K$, assuming the polarization transfer factor $C_{\Omega\Lambda}=1$.

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$\Xi$ and $\Omega$ global polarization in Au+Au collisions at 200 GeV. Decay parameter from PDG2020, $\alpha_{\Xi}$=-$\alpha_{\bar{\Xi}}$=-0.401, is used.

The energy dependence of $\Lambda$ and $\bar{\Lambda}$ global polarization. Note that the results from previous measurements are rescaled using updated decay parameters (PDG2020), $\alpha_{\Lambda}$=0.732 and $\alpha_{\bar{\Lambda}}$=-0.758. The original data can be found in <a href="https://www.hepdata.net/record/ins1510474">this page</a>.

Centrality dependence of $\Xi$ global poalrization in Au+Au collisions at 200 GeV. Decay parameter from PDG2020, $\alpha_{\Xi}$=-$\alpha_{\bar{\Xi}}$=-0.401, is used.

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Measurements of $D^{0}$ and $D^{*}$ Production in $p$ + $p$ Collisions at $\sqrt{s}$ = 200 GeV

The STAR collaboration Adamczyk, L. ; Agakishiev, G. ; Aggarwal, M.M. ; et al.
Phys.Rev.D 86 (2012) 072013, 2012.
Inspire Record 1111571 DOI 10.17182/hepdata.101344

We report measurements of charmed-hadron ($D^{0}$, $D^{*}$) production cross sections at mid-rapidity in $p$ + $p$ collisions at a center-of-mass energy of 200 GeV by the STAR experiment. Charmed hadrons were reconstructed via the hadronic decays $D^{0}\rightarrow K^{-}\pi^{+}$, $D^{*+}\rightarrow D^{0}\pi^{+}\rightarrow K^{-}\pi^{+}\pi^{+}$ and their charge conjugates, covering the $p_T$ range of 0.6$-$2.0 GeV/$c$ and 2.0$-$6.0 GeV/$c$ for $D^{0}$ and $D^{*+}$, respectively. From this analysis, the charm-pair production cross section at mid-rapidity is $d\sigma/dy|_{y=0}^{c\bar{c}}$ = 170 $\pm$ 45 (stat.) $^{+38}_{-59}$ (sys.) $\mu$b. The extracted charm-pair cross section is compared to perturbative QCD calculations. The transverse momentum differential cross section is found to be consistent with the upper bound of a Fixed-Order Next-to-Leading Logarithm calculation.

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$c\bar{c}$ production cross section as inferred from D$^0$ and D$^\star$ production in p+p collisions at $\sqrt{s} = 200$ GeV at $|\eta| < 1$ compared with FONLL calculations. The D$^0$ and D$^\star$ data points were divided by the charm quark fragmentation ratios 0.565 ($c \rightarrow$ D$^0$) and 0.224 ($c \rightarrow$ D$^{\star +}$) [34], respectively, to convert to the $c\bar{c}$ production cross section.


Transverse Single-Spin Asymmetry and Cross-Section for pi0 and eta Mesons at Large Feynman-x in Polarized p+p Collisions at sqrt(s)=200 GeV

The STAR collaboration Adamczyk, L. ; Agakishiev, G. ; Aggarwal, M.M. ; et al.
Phys.Rev.D 86 (2012) 051101, 2012.
Inspire Record 1116643 DOI 10.17182/hepdata.101343

Measurements of the differential cross-section and the transverse single-spin asymmetry, A_N, vs. x_F for pi0 and eta mesons are reported for 0.4 < x_F < 0.75 at an average pseudorapidity of 3.68. A data sample of approximately 6.3 pb^{-1} was analyzed, which was recorded during p+p collisions at sqrt{s} = 200 GeV by the STAR experiment at RHIC. The average transverse beam polarization was 56%. The cross-section for pi0 is consistent with a perturbative QCD prediction, and the eta/pi0 cross-section ratio agrees with previous mid-rapidity measurements. For 0.55 < x_F < 0.75, A_N for eta (0.210 +- 0.056) is 2.2 standard deviations larger than A_N for pi0 (0.081 +- 0.016).

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(c) $A_N$ vs. $M_{\gamma\gamma}$ for the above mass distribution. The error bars are statistical uncertainties only.

Differential production cross-sections for $\pi^0$ and $\eta$ at average pseudorapidity of 3.68. Also shown are the previously published STAR results for similar kinematics [21] and a NLO pQCD calculation of the π0 cross-section [32]. The error band represents the uncertainty in the calculation due to scale variations.

The $\eta$ to $\pi^0$ cross-section ratio is shown in the bottom panel. The error bars indicate the total statistical and systematic uncertainties.

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Cross sections and transverse single-spin asymmetries in forward neutral pion production from proton collisions at s**(1/2) = 200-GeV.

The STAR collaboration Adams, J. ; Adler, C. ; Aggarwal, M.M. ; et al.
Phys.Rev.Lett. 92 (2004) 171801, 2004.
Inspire Record 631869 DOI 10.17182/hepdata.101348

Measurements of the production of forward high-energy pi0 mesons from transversely polarized proton collisions at \sqrt{s}=200 GeV are reported. The cross section is generally consistent with next-to-leading order perturbative QCD calculations. The analyzing power is small at x_F below about 0.3, and becomes positive and large at higher x_F, similar to the trend in data at \sqrt{s}<=20 GeV. The analyzing power is in qualitative agreement with perturbative QCD model expectations. This is the first significant spin result seen for particles produced with p_T>1 GeV/c at a polarized proton collider.

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Inclusive $\pi^{0}$ production cross section versus leading $\pi^{0}$ energy ($E_{\pi}$). The average transverse momentum ($\langle p_{T}\rangle$) is correlated with $E_{\pi}$, as the PFPD was at a fixed pseudorapidity ($\eta$). The inner error bars are statistical, and are smaller than the symbols for most points. The outer error bars combine these with the $E_{\pi}$-dependent systematic errors. The curves are NLO pQCD calculations evaluated at $\eta=3.8$ [29-31].

Analyzing powers versus Feynman $x$ ($x_{F}$). The average transverse momentum ($\langle p_{T}\rangle$) is correlated with $x_{F}$. The solid points are for identified $\pi^{0}$ mesons. The open points are for the total energy ($E_{\scriptsize{\mbox{tot}}}$), shifted by $x_{F}+0.01$. The inner error bars are statistical, and the outer combine these with the point-to-point systematic errors. The curves are from pQCD models evaluated at $p_{T}=1.5$ GeV/c [14-17]. The $A_{N}$ values are proportional to $A^{\scriptsize{\mbox{CNI}}}_{N}$, assumed to be 0.013 at 100 GeV.


Three-particle coincidence of the long range pseudorapidity correlation in high energy nucleus-nucleus collisions

The STAR collaboration Abelev, B.I. ; Aggarwal, M.M. ; Ahammed, Z. ; et al.
Phys.Rev.Lett. 105 (2010) 022301, 2010.
Inspire Record 840812 DOI 10.17182/hepdata.102404

We report the first three-particle coincidence measurement in pseudorapidity ($\Delta\eta$) between a high transverse momentum ($p_{\perp}$) trigger particle and two lower $p_{\perp}$ associated particles within azimuth $\mid$$\Delta\phi$$\mid$$&lt;$0.7 in $\sqrt{{\it s}_{NN}}$ = 200 GeV $d$+Au and Au+Au collisions. Charge ordering properties are exploited to separate the jet-like component and the ridge (long-range $\Delta\eta$ correlation). The results indicate that the particles from the ridge are uncorrelated in $\Delta\eta$ not only with the trigger particle but also between themselves event-by-event. In addition, the production of the ridge appears to be uncorrelated to the presence of the narrow jet-like component.

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Correlated hadron distribution in ∆φ(|η|<1 with a high-p⊥trigger particle in 0-12% Au+Au collisions for 3<p(t)⊥<10 GeV/cand 1<p(a)⊥<3GeV/c. The ZYA1-normalized flow background is shown by the curve.

Correlated hadron distribution ∆η(|∆φ|<0.7) with a high-p⊥ trigger particle in 0-12% Au+Au collisions for 3<p(t)⊥<10 GeV/c and 1<p(a)⊥<3GeV/c. The ∆η distributions are background subtracted and corrected for ∆η acceptance and are for like and unlike-sign pairs separately. The curves in are Gaussian fits. Errors are statistical.

Background-subtracted charge-independent (AAT ) correlated hadron pair density in minimum bias d+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 0.033 for d+Au respectively.

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Version 2
Long range rapidity correlations and jet production in high energy nuclear collisions

The STAR collaboration Abelev, B.I. ; Aggarwal, M.M. ; Ahammed, Z. ; et al.
Phys.Rev.C 80 (2009) 064912, 2009.
Inspire Record 830070 DOI 10.17182/hepdata.101345

The STAR Collaboration at RHIC presents a systematic study of high transverse momentum charged di-hadron correlations at small azimuthal pair separation \dphino, in d+Au and central Au+Au collisions at $\rts = 200$ GeV. Significant correlated yield for pairs with large longitudinal separation \deta is observed in central Au+Au, in contrast to d+Au collisions. The associated yield distribution in \detano$\times$\dphi can be decomposed into a narrow jet-like peak at small angular separation which has a similar shape to that found in d+Au collisions, and a component which is narrow in \dphi and \textcolor{black}{depends only weakly on} $\deta$, the 'ridge'. Using two systematically independent analyses, \textcolor{black}{finite ridge yield} is found to persist for trigger $\pt > 6$ \GeVc, indicating that it is correlated with jet production. The transverse momentum spectrum of hadrons comprising the ridge is found to be similar to that of bulk particle production in the measured range ($2 < \pt < 4 \GeVc$).

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FIG. $2: \quad Y_{\text {slice }}(\Delta \eta ; \delta=0.3)$ (Eq. 5 ) for central Au+Au collisions, $2 \mathrm{GeV} / \mathrm{c}<p_{t}^{a s s o c}<p_{t}^{t r i g}$, and various $p_{t}^{t r i g}$ vs. $\Delta \eta$; the shaded bands represents the systematic uncertainties due to $v_{2}$ (not shown for $6<p_{t}^{\text {trig }}<10 \mathrm{GeV} / \mathrm{c}$ ). The solid and dashed lines represents a constant or linear fit to $1<|\Delta \eta|$ $<1.8$; only shown for $3<p_{t}^{t r i g}<4 \mathrm{GeV} / c$ (see text). Some data points are displaced horizontally for clarity.

FIG. 3. Left panel: width of Gaussian fit to jet-like peak for Eq. (6) $(\Delta \eta$ width, circles) and Eq. (7) $(\Delta \phi$ width, triangles) ; $ 2 \mathrm{GeV}/c<p_{t}^{\text{assoc}}<p_{t}^{\text {trig }}$, as a function of $p_{t}^{\text {trig }},$ for central $\mathrm{Au}+$ Au collisions (filled symbols) and $d+$ Au collisions (open symbols). Some data points are displaced horizontally for clarity. Right panel: the distributions of Eqs. (6) and (7) for $4<p_{t}^{\text {trig }}<5 \mathrm{GeV} / c$ and $2 \mathrm{GeV} / c<p_{t}^{\text {assoc }}<p_{t}^{\text {trig }}$.

FIG. 3. Left panel: width of Gaussian fit to jet-like peak for Eq. (6) $(\Delta \eta$ width, circles) and Eq. (7) $(\Delta \phi$ width, triangles) ; $ 2 \mathrm{GeV}/c<p_{t}^{\text{assoc}}<p_{t}^{\text {trig }}$, as a function of $p_{t}^{\text {trig }},$ for central $\mathrm{Au}+$ Au collisions (filled symbols) and $d+$ Au collisions (open symbols). Some data points are displaced horizontally for clarity. Right panel: the distributions of Eqs. (6) and (7) for $4<p_{t}^{\text {trig }}<5 \mathrm{GeV} / c$ and $2 \mathrm{GeV} / c<p_{t}^{\text {assoc }}<p_{t}^{\text {trig }}$.

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Energy and system size dependence of \phi meson production in Cu+Cu and Au+Au collisions

The STAR collaboration Abelev, B.I. ; Aggarwal, M.M. ; Ahammed, Z. ; et al.
Phys.Lett.B 673 (2009) 183-191, 2009.
Inspire Record 800796 DOI 10.17182/hepdata.101351

We study the beam-energy and system-size dependence of \phi meson production (using the hadronic decay mode \phi -- K+K-) by comparing the new results from Cu+Cu collisions and previously reported Au+Au collisions at \sqrt{s_NN} = 62.4 and 200 GeV measured in the STAR experiment at RHIC. Data presented are from mid-rapidity (|y|&lt;0.5) for 0.4 &lt; pT &lt; 5 GeV/c. At a given beam energy, the transverse momentum distributions for \phi mesons are observed to be similar in yield and shape for Cu+Cu and Au+Au colliding systems with similar average numbers of participating nucleons. The \phi meson yields in nucleus-nucleus collisions, normalised by the average number of participating nucleons, are found to be enhanced relative to those from p+p collisions with a different trend compared to strange baryons. The enhancement for \phi mesons is observed to be higher at \sqrt{s_NN} = 200 GeV compared to 62.4 GeV. These observations for the produced \phi(s\bar{s}) mesons clearly suggest that, at these collision energies, the source of enhancement of strange hadrons is related to the formation of a dense partonic medium in high energy nucleus-nucleus collisions and cannot be alone due to canonical suppression of their production in smaller systems.

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Midrapidity $(|y| < 0.5)$ transverse momentum spectra of $\phi$ mesons for various collision centrality classes for $Cu+Cu$ collisions at $\sqrt{s_{NN}}=62.4$ and 200 GeV. To study the system size dependence, comparison of $40-50\%$ $Au+Au$ spectra to $10-20\%$ $Cu+Cu$ spectra at 200 GeV, and $40-60\%$ $Au+Au$ spectra to $20-30\%$ $Cu+Cu$ spectra at 62.4 GeV are shown. These centralities for the two colliding systems have similar $\langle N_{\scriptsize{\mbox{part}}}\rangle$ values as outlined in Table 2. The errors represent the statistical and systematic errors added in quadrature. They are found to be within the symbol size. The spectra are fitted to a Levy function discussed in the text.

Midrapidity $(|y| < 0.5)$ transverse momentum spectra of $\phi$ mesons for various collision centrality classes for $Cu+Cu$ collisions at $\sqrt{s_{NN}}=62.4$ and 200 GeV. To study the system size dependence, comparison of $40-50\%$ $Au+Au$ spectra to $10-20\%$ $Cu+Cu$ spectra at 200 GeV, and $40-60\%$ $Au+Au$ spectra to $20-30\%$ $Cu+Cu$ spectra at 62.4 GeV are shown. These centralities for the two colliding systems have similar $\langle N_{\scriptsize{\mbox{part}}}\rangle$ values as outlined in Table 2. The errors represent the statistical and systematic errors added in quadrature. They are found to be within the symbol size. The spectra are fitted to a Levy function discussed in the text.

Upper panels. $N_{\scriptsize{\mbox{part}}}$ scaled ($R^{N_{\scriptsize{\mbox{part}}}}_{AA}$) nuclear modification factors as a function of $p_{T}$ of $\phi$ mesons for $0-10\%$ and $20-30\%$ $Cu+Cu$ and $Au+Au$ collisions at $\sqrt{s_{NN}}=200$ GeV. Lower panel. Same as above for $N_{\scriptsize{\mbox{bin}}}$ scaled ($R^{N_{\scriptsize{\mbox{bin}}}}_{AA}$) nuclear modification factor. The error bars represent the statistical and systematic errors added in quadrature. The shaded band in upper panel around 1 at $p_{T}=4.5-5.5$ GeV/$c$ in the right side reflects the uncertainty in $N_{\scriptsize{\mbox{part}}}$ and that on the lower panel for $N_{\scriptsize{\mbox{bin}}}$ calculation for central $Au+Au$ collisions. The respective uncertainties for central $Cu+Cu$ collisions are of similar order.

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