Elliptic flow of identified hadrons in Au+Au collisions at $\sqrt{{s}_{\mathit{NN}}}=7.7$--62.4 GeV

Elliptic flow of identified hadrons in Au+Au collisions at $\sqrt{s_{NN}} = 7.7$ –62.4 GeV

L. Adamczyk et al. (STAR Collaboration)

Phys. Rev. C 88, 014902 – Published 3 July 2013

Abstract

Measurements of the elliptic flow, $v_{2}$ , of identified hadrons ( $π^{\pm}$ , $K^{\pm}$ , $K_{s}^{0}$ , $p$ , $\bar{p}$ , $ϕ$ , $Λ$ , $\bar{Λ}$ , $Ξ^{-}$ , ${\bar{Ξ}}^{+}$ , $Ω^{-}$ , ${\bar{Ω}}^{+}$ ) in $Au + Au$ collisions at $\sqrt{s_{NN}} = 7.7$ , 11.5, 19.6, 27, 39, and 62.4 GeV are presented. The measurements were done at midrapidity using the time-projection chamber and the time-of-flight detectors of the Solenoidal Tracker at RHIC experiment during the beam-energy scan program at Relativistic Heavy Ion Collider. A significant difference in the $v_{2}$ values for particles and the corresponding antiparticles was observed at all transverse momenta for the first time. The difference increases with decreasing center-of-mass energy, $\sqrt{s_{NN}}$ (or increasing baryon chemical potential, $μ_{B}$ ), and is larger for the baryons as compared to the mesons. This implies that particles and antiparticles are no longer consistent with the universal number-of-constituent quark (NCQ) scaling of $v_{2}$ that was observed at $\sqrt{s_{NN}} = 200$ GeV. However, for the selected group of particles ( $π^{+}$ , $K^{+}$ , $K_{s}^{0}$ , $p$ , $Λ$ , $Ξ^{-}$ , $Ω^{-}$ ) NCQ scaling at $(m_{T} - m_{0}) / n_{q} > 0.4$ GeV/ $c^{2}$ is not violated within $\pm 10 %$ . The $v_{2}$ values for $ϕ$ mesons at 7.7 and 11.5 GeV are approximately two standard deviations from the trend defined by the other hadrons at the highest measured $p_{T}$ values.

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Received 10 January 2013

DOI:https://doi.org/10.1103/PhysRevC.88.014902

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Vol. 88, Iss. 1 — July 2013

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Figure 1
The uncorrected multiplicity, $N_{ch}^{raw}$ , distribution of reconstructed charged particles per unit pseudorapidity interval at midrapidity for the six different center-of-mass energies. The solid black points depict the measured data and a Glauber Monte Carlo simulation is overlayed as the solid curve. Three different centrality classes are indicated by the different shaded regions.
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Figure 2
The mean specific energy loss, $〈 d E / d x 〉$ , of reconstructed tracks within a pseudorapidity range of $| η | < 1$ in the TPC (a) and the mass squared, $m^{2}$ , as a function of momentum (b). The Bichsel functions [31] used to determine the $n σ_{particle}$ values [cf. Eq. (1)] are shown in (a) as the dashed curves. The horizontal dashed lines in (b) correspond to the nominal particle masses of $π$ , $K$ , and $p$ .
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Figure 3
The mass-squared, $m^{2}$ , distributions for reconstructed positive- ( $q > 0$ ) and negative- ( $q < 0$ ) charged particles from $0 %$ – $80 %$ central $Au + Au$ collisions at a beam energy of 19.6 GeV. Three different momentum ranges are shown.
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Figure 4
(a) The mass-squared, $m^{2}$ , versus $n σ_{π}$ and (b) $x, y (n σ_{π}, m^{2})$ [see Eqs. (2) to (6)] distributions for $2.2 < p_{T} < 2.4$ $GeV / c$ from $0 %$ – $80 %$ central $Au + Au$ collisions at 27 GeV. The black dashed contour lines in (b) depict the result of a simultaneous fit with three $2 \times 2$ D Gaussians (one $2 \times 2$ D Gaussian per particle). The diagonal dashed line depicts a cut to remove the remaining proton contamination (see text). (c) The projected distribution to the $x (n σ_{π}, m^{2})$ axis. The red solid curve shows the projection of the $2 \times 2$ D Gaussian fits. (d) The same as (c), but after the $2 \times 2$ D Gaussian of the protons was removed. The red solid line shows the sum of the two 1D Gaussian fits. The fit range is indicated by the two vertical dashed lines.
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Figure 5
Examples of the invariant mass distributions at $\sqrt{s_{NN}} = 62.4$ GeV for $ϕ$ , $K_{s}^{0}$ , $Λ$ , $\bar{Λ}$ , $Ξ^{-}$ , ${\bar{Ξ}}^{+}$ , $Ω^{-}$ , and ${\bar{Ω}}^{+}$ . The combinatorial background is described by the mixed-event technique, which is shown as a gray shaded histogram.
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Figure 6
The EP resolution for the six different center-of-mass energies for the full TPC EP (circles) and the $η$ -sub EP (stars), as a function of the centrality for two different and independent flattening methods.
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Figure 7
Two examples of the $v_{2}$ signal extraction for $ϕ$ mesons at 39 GeV in the transverse momentum range of $0.8 < p_{T} < 1.0$ $GeV / c$ . The EP method (a) and the invariant mass method (b) give almost identical results. (a) The $ϕ - Ψ_{2}$ data points are reflected at $π / 2$ . A fit with Eq. (13) to the data obtained by integrating the fit is shown as a solid black line. The red dashed line shows the fit result to the data obtained by counting the particles in each bin. (b) The solid black curve is the fit from Eq. (15). The dashed red curve is the signal part of that equation and the dashed blue curve is the background part.
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Figure 8
The elliptic flow, $v_{2}$ , as a function of the transverse momentum, $p_{T}$ , from $0 %$ – $80 %$ central $Au + Au$ collisions for various particle species and energies. Only the statistical error bars are shown. Systematic errors are much smaller than the statistical errors. The black dashed line is a fit to the 39-GeV data points with Eq. (17).
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Figure 9
The ratio of the elliptic flow, $v_{2} (p_{T})$ , relative to the 39-GeV fit functions for $0 %$ – $80 %$ central $Au + Au$ collisions for various particle species and energies. The error bars are statistical only. Systematic errors are much smaller than the statistical errors. The fit and the $v_{2} (p_{T})$ data points are shown in Fig. 8.
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Figure 10
The elliptic flow, $v_{2} (p_{T})$ , in $0 %$ – $80 %$ central $Au + Au$ collisions for selected particles (a) and antiparticles (b) (see text), plotted only for the transverse momentum range of $0.2 < p_{T} < 1.6$ $GeV / c$ to emphasize the mass ordering at low $p_{T}$ . Only statistical error bars are shown. Systematic errors are much smaller than the statistical errors. The fit functions to guide the eye correspond to Eq. (17).
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Figure 11
The elliptic flow, $v_{2}$ , of charged pions (a) and kaons (b) as a function of the transverse momentum, $p_{T}$ , for $0 %$ – $80 %$ central $Au + Au$ collisions. The point-by-point systematic uncertainties are shown by the shaded areas attached to the data points; otherwise they are smaller than the symbol size. The global systematic uncertainties are very small and shown as shaded horizontal bars. The bottom row of each panel shows the difference between a particle and corresponding antiparticle $v_{2} (p_{T})$ and a fit with a horizontal line. The red shaded area around each fit depicts the combined statistical and systematic fit errors. Different $Δ v_{2}$ ranges were used for the top and bottom panels.
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Figure 12
The elliptic flow, $v_{2}$ , of $p$ , $\bar{p}$ (a) and $Λ$ , $\bar{Λ}$ (b) as a function of the transverse momentum, $p_{T}$ , for $0 %$ – $80 %$ central $Au + Au$ collisions. The point-by-point systematic uncertainties are shown by the shaded areas attached to the data points; otherwise they are smaller than the symbol size. The global systematic uncertainties are shown as the shaded horizontal bar. The lower row of each panel depicts the difference between a particle and corresponding antiparticle $v_{2} (p_{T})$ with a fit with a horizontal line. The red shaded area around each fit shows the combined statistical and systematic fit errors.
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Figure 13
The elliptic flow, $v_{2}$ , of $Ξ^{-}$ , ${\bar{Ξ}}^{+}$ (a) and $Ω^{-}$ , ${\bar{Ω}}^{+}$ (b) as a function of the transverse momentum, $p_{T}$ , for $0 %$ – $80 %$ central $Au + Au$ collisions. The point-by-point systematic uncertainties are shown by the shaded areas attached to the data points, while the global systematic uncertainties are shown as the shaded horizontal bar. Shown in the bottom row of each panel is the difference between a particle and corresponding antiparticle $v_{2} (p_{T})$ with a fit with a horizontal line. The red shaded area around each fit shows the combined statistical and systematic fit errors.
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Figure 14
The elliptic flow, $v_{2}$ , of $ϕ$ mesons as a function of the transverse momentum, $p_{T}$ , for $0 %$ – $80 %$ central $Au + Au$ collisions. The point-by-point systematic uncertainties are shown by the shaded areas attached to the data points, while the global systematic uncertainties are shown as the shaded horizontal bar.
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Figure 15
The elliptic flow, $v_{2}$ , of $p$ and $\bar{p}$ as a function of the transverse momentum, $p_{T}$ , for $0 %$ – $10 %$ central $Au + Au$ collisions. The point-by-point systematic uncertainties are shown by the shaded areas attached to the data points, while the global systematic uncertainties are shown as the shaded horizontal bar. Shown in the lower row of each panel is the difference between a particle and the corresponding antiparticle $v_{2} (p_{T})$ which are fit with a horizontal line. The red shaded area around each fit shows the combined statistical and systematic fit error.
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Figure 16
The elliptic flow, $v_{2}$ , of $p$ and $\bar{p}$ as a function of transverse momentum, $p_{T}$ , for $10 %$ – $40 %$ central $Au + Au$ collisions. The point-by-point systematic uncertainties are shown by the shaded areas attached to the data points, while the global systematic uncertainties are shown as the shaded horizontal bar. Shown in the bottom row of each panel is the difference between a particle and the corresponding antiparticle $v_{2} (p_{T})$ , which are fit with a horizontal line. The red shaded area around each fit shows the combined statistical and systematic fit error.
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Figure 17
Elliptic flow, $v_{2}$ , of $p$ and $\bar{p}$ as a function of transverse momentum $p_{T}$ for $40 %$ – $80 %$ centrality $Au + Au$ collisions. The point-by-point systematic uncertainties are shown by the shaded areas attached to the data points, while the global systematic uncertainties are shown as the shaded horizontal bar. Shown in the bottom row of each panel is the difference between a particle and the corresponding antiparticle $v_{2} (p_{T})$ which are fit with a horizontal line. The red shaded area around each fit shows the combined statistical and systematic fit error.
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Figure 18
The elliptic flow, $v_{2}$ , of $0 %$ – $80 %$ central $Au + Au$ collisions as a function of the reduced transverse mass, $m_{T} - m_{0}$ , for selected particles (a) and antiparticles (b). Only statistical error bars are shown. A significant splitting between the baryons (gray) and mesons (red) is observed at the higher energies. The splitting becomes smaller at 7.7 GeV. At lower energies, the baryons and mesons are consistent with each other within the measured $p_{T}$ range for the particles shown in (b).
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Figure 19
The NCQ-scaled elliptic flow, $v_{2} / n_{q}$ versus $(m_{T} - m_{0}) / n_{q}$ , for $0 %$ – $80 %$ central $Au + Au$ collisions for selected particles (a) and corresponding antiparticles (b). Only statistical error bars are shown. The dashed lines show the results of simultaneous fits with Eq. (17) to all particles except the pions.
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Figure 20
The NCQ-scaled elliptic flow, $v_{2} / n_{q}$ versus $(m_{T} - m_{0}) / n_{q}$ , ratio to the fit function (see text) for $0 %$ – $80 %$ central $Au + Au$ collisions for selected particles (a) and corresponding antiparticles (b). Only statistical error bars are shown. Most of the data points at the larger $(m_{T} - m_{0}) / n_{q}$ values are within a $\pm$ $10 %$ interval around unity, which is shown by the red dashed lines to guide the eye. Some data points for $ϕ$ and ${\bar{Ξ}}^{+}$ are outside of the plot axis range.
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Figure 21
The difference in the $v_{2}$ values between a particle $X$ and its corresponding antiparticle ( $\bar{X}$ ) (see legend) as a function of $\sqrt{s_{NN}}$ (a) and $μ_{B}$ (b) for $0 %$ – $80 %$ central $Au + Au$ collisions. The dashed lines in plot (a) are fits using Eq. (18), and lines through the origin are shown for plot (b). The values of $μ_{B}$ are from the parametrization of Ref. [51] (see text for details).
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Figure 22
The elliptic flow, $v_{2}$ , of $π^{\pm}$ , $K^{\pm}$ , $p$ , and $\bar{p}$ as a function of the transverse momentum, $p_{T}$ , for $0 %$ – $80 %$ central $Au + Au$ collisions at $\sqrt{s_{NN}} = 7.7$ , 11.5, and 39 GeV. Only statistical error bars are shown. The symbols depict the data while the lines show the model results from AMPT with default settings (blue), AMPT with the string melting (SM) option and a hadronic cross section of 3 mb (red) and from UrQMD (black). The solid and dashed lines represent positively and negatively charged particles, respectively. Shaded areas show the statistical errors for the model calculations.
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Figure 23
The proton and antiproton elliptic flow for $0 %$ – $80 %$ central $Au + Au$ collisions at $\sqrt{s_{NN}} = 19.6$ GeV, where “( $+$ , $-$ ) EP” refers to the EP reconstructed using all of the charged particles and “( $-$ ) EP” refers to the EP reconstructed using only the negatively charged particles. The error bars are statistical only.
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Figure 24
The NCQ-scaled elliptic flow, $v_{2} / n_{q}$ versus $p_{T} / n_{q}$ , for $0 %$ – $80 %$ central $Au + Au$ collisions for selected particles (a) and corresponding antiparticles (b). Only statistical error bars are shown. The dashed lines show the results of simultaneous fits with Eq. (17) to all particles except the pions.
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Figure 25
The NCQ-scaled elliptic flow, $v_{2} (p_{T}) / n_{q}$ , ratio to a fit function (see text) for $0 %$ – $80 %$ central $Au + Au$ collisions for selected particles (a) and corresponding antiparticles (b). Only statistical error bars are shown. Most of the data points at the larger $p_{T} / n_{q}$ values are consistent with unity to $\pm$ $10 %$ , which is shown as the shaded areas to guide the eye. Some of the data points for $ϕ$ and ${\bar{Ξ}}^{+}$ are outside of the plot range.
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Physical Review C

covering nuclear physics

Elliptic flow of identified hadrons in Au+Au collisions at $\sqrt{s_{NN}} = 7.7$ –62.4 GeV

L. Adamczyk et al. (STAR Collaboration)

Phys. Rev. C 88, 014902 – Published 3 July 2013

Abstract

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Physical Review C

covering nuclear physics

Elliptic flow of identified hadrons in Au+Au collisions at sNN=7.7–62.4 GeV

L. Adamczyk et al. (STAR Collaboration)

Phys. Rev. C 88, 014902 – Published 3 July 2013

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Elliptic flow of identified hadrons in Au+Au collisions at $\sqrt{s_{NN}} = 7.7$ –62.4 GeV