CMS-HIN-17-005 ; CERN-EP-2019-211 | ||
Mixed higher-order anisotropic flow and nonlinear response coefficients of charged particles in PbPb collisions at ${\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}} = $ 2.76 and 5.02 TeV | ||
CMS Collaboration | ||
19 October 2019 | ||
Eur. Phys. J. C 80 (2020) 534 | ||
Abstract: Anisotropies in the initial energy density distribution of the quark-gluon plasma created in high energy heavy ion collisions lead to anisotropies in the azimuthal distributions of the final-state particles known as collective flow. Fourier harmonic decomposition is used to quantify these anisotropies. The higher-order harmonics can be induced by the same order anisotropies (linear response) or by the combined influence of several lower order anisotropies (nonlinear response) in the initial state. The mixed higher-order anisotropic flow and nonlinear response coefficients of charged particles are measured as functions of transverse momentum and centrality in PbPb collisions at nucleon-nucleon center-of-mass energies ${\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}} = $ 2.76 and 5.02 TeV with the CMS detector. The results are compared with viscous hydrodynamic calculations using several different initial conditions, as well as microscopic transport model calculations. None of the models provides a simultaneous description of the mixed higher-order flow harmonics and nonlinear response coefficients. | ||
Links: e-print arXiv:1910.08789 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; |
Figures | |
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Figure 1:
Mixed higher-order flow harmonics, $v_4\{\Psi _{22}\}$, $v_5\{\Psi _{23}\}$, $v_6\{\Psi _{222}\}$, $v_6\{\Psi _{33}\}$, and $v_7\{\Psi _{223}\}$ from the scalar-product method at $ {\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}} = $ 2.76 and 5.02 TeV as a function of ${p_{\mathrm{T}}}$ in the 0-20% (upper row) and 20-60% (lower row) centrality ranges. Statistical (bars) and systematic (shaded boxes) uncertainties are shown. |
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Figure 2:
Comparison of mixed higher-order flow harmonics, $v_4\{\Psi _{22}\}$, $v_5\{\Psi _{23}\}$, $v_6\{\Psi _{222}\}$, $v_6\{\Psi _{33}\}$ and $v_7\{\Psi _{223}\}$ with the corresponding overall flow, $v_4\{\Psi _{4}\}$, $v_5\{\Psi _{5}\}$, $v_6\{\Psi _{6}\}$, $v_6\{\Psi _{6}\}$ and $v_7\{\Psi _{7}\}$, respectively, at $ {\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}} = $ 5.02 TeV as a function ${p_{\mathrm{T}}}$ in the 0-20% (upper row) and 20-60% (lower row) centrality ranges. Statistical (bars) and systematic (shaded boxes) uncertainties are shown. |
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Figure 3:
Nonlinear response coefficients, $\chi _{422}$, $\chi _{523}$, $\chi _{6222}$, $\chi _{633}$, and $\chi _{7223}$ from the scalar-product method at $ {\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}} = $ 2.76 and 5.02 TeV as a function of ${p_{\mathrm{T}}}$ in the 0-20% (upper row) and 20-60% (lower row) centrality ranges. Statistical (bars) and systematic (shaded boxes) uncertainties are shown. The results are compared with hydrodynamic predictions [24] at $ {\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}} = $ 2.76 TeV with $\eta /s = $ 0.08 and Glauber initial conditions in the 5-10% (blue lines) and 35-40% (dashed green lines) centrality ranges. |
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Figure 4:
Mixed higher-order flow harmonics, $v_4\{\Psi _{22}\}$, $v_5\{\Psi _{23}\}$, $v_6\{\Psi _{222}\}$, $v_6\{\Psi _{33}\}$, and $v_7\{\Psi _{223}\}$ from the scalar-product method at $ {\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}} = $ 2.76 and 5.02 TeV, as a function of centrality. Statistical (bars) and systematic (shaded boxes) uncertainties are shown. Hydrodynamic predictions [21] with $\eta /s = $ 0.08 (blue lines) at 2.76 TeV are shown in panel (b) and (e). |
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Figure 5:
Nonlinear response coefficients, $\chi _{422}$, $\chi _{523}$, $\chi _{6222}$, $\chi _{633}$, and $\chi _{7223}$ from the scalar-product method at $ {\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}} = $ 2.76 and 5.02 TeV, as a function of centrality. Statistical (bars) and systematic (shaded boxes) uncertainties are shown. The results are compared with predictions at $ {\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}} = $ 2.76 TeV from AMPT [42] as well as hydrodynamics with a deformed symmetric Gaussian density profile as the initial conditions using $\eta /s = $ 0.08 from Ref. [21], and from iEBE-VISHNU hydrodynamics with both Glauber and the KLN initial conditions using the same $\eta /s$ [22]. |
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Figure 6:
The same results as in Fig. 5 but compared with predictions from a hydrodynamics $+$ hadronic cascade hybrid approach with the IP-Glasma initial conditions using $\eta /s = 0.095$ [44] at $ {\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}} = $ 5.02 TeV and from iEBE-VISHNU hydrodynamics with the KLN initial conditions using $\eta /s = $ 0, 0.08 (the same curve as in Fig. 5) and 0.2 [22] at $ {\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}} = $ 2.76 TeV. |
Summary |
The mixed higher-order flow harmonics and nonlinear response coefficients of charged particles have been studied as functions of transverse momentum ${p_{\mathrm{T}}}$ and centrality inPbPbcollisions at ${\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}} = $ 2.76 and 5.02 TeV using the CMS detector. The measurements use the scalar-product method, covering a ${p_{\mathrm{T}}}$ range from 0.3 to 8.0 GeV/$c$, pseudorapidity $ |{\eta}| < $ 0.8, and a centrality range of 0-60%. The mixed higher-order flow harmonics, $v_4\{\Psi_{22}\}$, $v_5\{\Psi_{23}\}$, $v_6\{\Psi_{222}\}$, $v_6\{\Psi_{33}\}$, and $v_7\{\Psi_{223}\}$ all have a qualitatively similar ${p_{\mathrm{T}}}$ dependence, first increasing at low ${p_{\mathrm{T}}}$, reaching a maximum at about 3-4 GeV/$c$, and then decreasing at higher ${p_{\mathrm{T}}}$. As a comparison, the overall $v_n$ harmonics ($n = 4$-7) with respect to their own symmetry planes are measured in the same ${p_{\mathrm{T}}}$, $\eta$, and centrality ranges. The relative contribution of the nonlinear part for $v_5$ is larger than for other harmonics in the centrality range 20-60%. In addition, the nonlinear response coefficients of the odd harmonics are observed to be larger than those of even harmonics for ${p_{\mathrm{T}}}$ less than 3 GeV/$c$. At ${p_{\mathrm{T}}}$ less than 1 GeV/$c$, a viscous hydrodynamic calculation with Glauber initial conditions and shear viscosity to entropy density ratio $\eta/s = $ 0.08 predicts a much stronger ${p_{\mathrm{T}}}$ dependence for the nonlinear response coefficients. The coefficients, including the first-time measurement of $\chi_{7223}$, as a function of centrality, are compared with AMPT and hydrodynamic predictions using different $\eta/s$ and initial conditions. Compared to the data, none of the models provides a simultaneous description of the mixed higher-order flow harmonics and nonlinear response coefficients. Therefore, these results can constrain both initial conditions and transport properties of the produced medium. |
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Compact Muon Solenoid LHC, CERN |