CMS-HIN-11-005 ; CERN-PH-EP-2013-196 | ||
Measurement of higher-order harmonic azimuthal anisotropy in PbPb collisions at $\sqrt{s_{\mathrm{NN}}} = $ 2.76 TeV | ||
CMS Collaboration | ||
31 October 2013 | ||
Phys. Rev. C 89 (2014) 044906 | ||
Abstract: Measurements are presented by the CMS Collaboration at the Large Hadron Collider (LHC) of the higher-order harmonic coefficients that describe the azimuthal anisotropy of charged particles emitted in $\sqrt{s_{\mathrm{NN}}} = $ 2.76 TeV PbPb collisions. Expressed in terms of the Fourier components of the azimuthal distribution, the n = 3-6 harmonic coefficients are presented for charged particles as a function of their transverse momentum (0.3 $ < p_{\mathrm{T}} < $ 8.0 GeV/$c$), collision centrality (0-70%), and pseudorapidity ($ | \eta | < $ 2.0 ). The data are analyzed using the event plane, multi-particle cumulant, and Lee-Yang zeros methods, which provide different sensitivities to initial state fluctuations. Taken together with earlier LHC measurements of elliptic flow ($n= $ 2), the results on higher-order harmonic coefficients develop a more complete picture of the collective motion in high-energy heavy-ion collisions and shed light on the properties of the produced medium. | ||
Links: e-print arXiv:1310.8651 [nucl-ex] (PDF) ; CDS record ; inSPIRE record ; Public twiki page ; CADI line (restricted) ; |
Figures | |
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Figure 1:
Event plane resolution correction factors $R_n$ corresponding to different event plane angles $\Psi _m$ used in the analysis, as discussed in the text, are shown as a function of centrality for event planes determined with HF$-$ (open symbols) and HF$+$ (filled symbols). The ${R}_2\{\Psi _2\}$ values are from Ref. [18] and are included for comparison purposes. Statistical uncertainties are smaller than the symbols. The heights of the open gray rectangles indicate the systematic uncertainties. |
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Figure 2:
Measurements of the azimuthal asymmetry coefficient $v_{3}$ from three different methods as a function of ${p_{\mathrm {T}}}$ for the indicated centrality bins, as specified in percent. The event plane (filled circles) and cumulant (filled stars) results are with $ {| \eta | } < $ 0.8 . The two particle correlation results (open circles) are from a previous CMS measurement [48]. Statistical (error bars) and systematic (light gray boxes) uncertainties are shown. |
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Figure 3:
Measurements of the azimuthal asymmetry coefficient $v_{4}$ from four different methods as a function of ${p_{\mathrm {T}}}$ for the indicated centrality bins, as specified in percent. The event plane (filled circles and filled diamonds), cumulant (filled stars), and Lee-Yang zeros (open stars) analyses are with $ {| \eta | } < $ 0.8 . The two particle correlation results (open circles) are from a previous CMS measurement [48]. Statistical (error bars) and systematic (light gray boxes) uncertainties are shown. |
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Figure 4:
Measurements of the azimuthal asymmetry coefficient $v_{5}$ from two different methods as a function of ${p_{\mathrm {T}}}$ for the indicated centrality bins, as specified in percent. The event plane analysis (filled circles) is with $ {| \eta | } < $ 0.8 . The two particle correlation results (open circles) are from a previous CMS measurement [48]. Statistical (error bars) and systematic (light gray boxes) uncertainties are shown. |
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Figure 5:
Measurements of the azimuthal asymmetry coefficient $v_{6}$ from the event plane (filled circles and filled diamonds) and Lee-Yang zeros (open stars) methods as a function of ${p_{\mathrm {T}}}$ for the indicated centrality bins, as specified in percent. The results are for $ {| \eta | } < $ 0.8 . Statistical (error bars) and systematic (light gray boxes) uncertainties are shown. |
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Figure 6:
Yield-weighted average azimuthal asymmetry coefficients $v_{n}$, for $n = $ 2-6, with 0.3 $ < {p_{\mathrm {T}}} < $ 3.0 GeV/$c$ are shown for three different methods as a function of centrality. The $v_2$ results are from Ref. [18] and included for completeness. Statistical (error bars) and systematic (light gray boxes) uncertainties are shown. The different results found for a given $v_{n}$ reflect the role of participant fluctuations and the variable sensitivity to them in each method, as discussed in the text. |
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Figure 7:
(a) Yield-weighted average azimuthal asymmetry coefficients $v_{n}$, for $n = $ 2 , 4 and 6, with 0.3 $ < {p_{\mathrm {T}}} <$ 3.0 GeV/$c$ and based on a second-order, $m= $ 2 , reference frame are shown for three different methods as a function of centrality. The $v_2$ results are from Ref. [18] and included for completeness. (b) Results for the event plane and cumulant analyses for distributions based on higher-order, $m> $ 2 , reference distributions. Statistical (error bars) and systematic (light gray boxes) uncertainties are shown. |
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Figure 8:
Yield-weighted average azimuthal asymmetry coefficients $v_{n}$, for $n = $ 2-4, with 0.3 $ < {p_{\mathrm {T}}} <$ 3.0 GeV/$c$ are shown as a function of pseudorapidity $\eta $ for the indicated centrality ranges, as specified in percent. Statistical (error bars) and systematic (light gray boxes) uncertainties are shown. The $v_2$ results are from Ref. [18] and included for completeness. |
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Figure 9:
Comparison of the $v_{3}$ results for PbPb collisions at $ {\sqrt {\smash [b]{s_{_\mathrm {NN}}}}} = $ 2.76 TeV of the ALICE, ATLAS, and CMS Collaborations for the indicated centrality ranges, as specified in percent. The PHENIX results for AuAu collisions at $ {\sqrt {s_{_\mathrm {NN}}}} = $ 200 GeV are also shown. Statistical (error bars) and systematic (light gray boxes) uncertainties are indicated. References and experimental conditions are given in Table {tbl:expsum}. The predictions of the IP-Glasma+MUSIC model [62] for PbPb collisions at $ {\sqrt {s_{_\mathrm {NN}}}} = $ 2.76 TeV are shown by the solid lines in the 0-5%, 10-20%, 20-30%, 30-40%, and 40-50% panels for 0 $ < {p_{\mathrm {T}}} <$ 2 GeV/$c$. |
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Figure 10:
Comparison of the $v_{4}$ results for PbPb collisions at $ {\sqrt {s_{_\mathrm {NN}}}} = $ 2.76 TeV of the ALICE, ATLAS, and CMS Collaborations for the indicated centrality ranges, as specified in percent. The PHENIX results for AuAu collisions at $ {\sqrt {s_{_\mathrm {NN}}}} = $ 200 GeV are also shown. Statistical (error bars) and systematic (light gray boxes) uncertainties are indicated. References and experimental conditions are given in Table {tbl:expsum}. The predictions of the IP-Glasma+MUSIC model [62] for PbPb collisions at $ {\sqrt {s_{_\mathrm {NN}}}} = $ 2.76 TeV are shown by the solid lines in the 0-5%, 10-20%, 20-30%, 30-40%, and 40-50% panels for 0 $ < {p_{\mathrm {T}}} < $ 2 GeV/$c$. |
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Figure 11:
Comparison of the $v_{5}$ results of the ALICE, ATLAS, and CMS Collaborations for the indicated centrality ranges, as specified in percent. Statistical (error bars) and systematic (light gray boxes) uncertainties are indicated. References and experimental conditions are given in Table {tbl:expsum}. The predictions of the IP-Glasma+MUSIC model [62] are shown by the solid lines in the 0-5%, 10-20%, 20-30%, 30-40%, and 40-50% panels for 0 $ < {p_{\mathrm {T}}} <$ 2 GeV/$c$. |
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Figure 12:
Comparison of the $v_{6}$ results of the ATLAS and CMS Collaborations for the indicated centrality ranges, as specified in percent. Statistical (error bars) and systematic (light gray boxes) uncertainties are indicated. References and experimental conditions are given in Table {tbl:expsum}. |
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Figure 13:
Yield-weighted average azimuthal asymmetry parameters $v_{n}$, for $n = $ 2 -6 with 0.3 $ < {p_{\mathrm {T}}} <$ 3.0 GeV/$c$, as a function of the corresponding Glauber model rms anisotropy parameters $\sqrt {<\epsilon _{n}^2>}$. The CMS $v_2$ results are from Ref. [18] and included for completeness. The $v_{4}\{\Psi _{2}\}$ and $v_{6}\{\Psi _{2}\}$ results are plotted against $\sqrt {<\epsilon _{4,2}^{2}>}$ and $\sqrt {<\epsilon _{6,2}^{2}>}$, respectively. Statistical (error bars) and systematic (light gray boxes) uncertainties are indicated. |
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Figure 14:
The azimuthal asymmetry parameter $v_n$, scaled by the corresponding Glauber model rms anisotropy parameter $\sqrt {\epsilon _n^2}$ for the indicated ${p_{\mathrm {T}}}$ and centrality ranges, as specified in percent, as a function of harmonic number $n$. Statistical (error bars) and systematic (light gray boxes) uncertainties are indicated. |
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Figure 15:
Estimate of the event-by-event $v_{n}$ fluctuations in $v_n$ for $n=$ 2 (filled circles) and 3 (filled stars) as discussed in the text. The results where the event plane $v_2$ values are adjusted to their corresponding rms values, as discussed in the text, are indicated by the filled boxes and labelled $n = 2 \mathrm {RMS}$. The results of event-by-event-fluctuation (E-by-E) analyses by the ATLAS Collaboration for the $n$ = 2 and 3 harmonics [69] are also shown. Statistical (error bars) and systematic (light gray boxes) uncertainties are indicated. The systematic uncertainties for the ATLAS results correspond to the mid-point of the uncertainty range indicated by the ATLAS Collaboration. |
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Figure 16:
The yield-weighted average values of the ratio $v_{4}/v_{2}^{2}$ as a function of centrality for 0.3 $ < {p_{\mathrm {T}}} <$ 3.0 GeV/$c$ (filled circles) and 1.2 $ < {p_{\mathrm {T}}} <$ 1.6 GeV/$c$ (open squares) are shown for PbPb collisions at $ {\sqrt {\smash [b]{s_{_\mathrm {NN}}}}} = $ 2.76 TeV. The PHENIX results (stars) for 1.2 $ < {p_{\mathrm {T}}} < $ 1.6 GeV/$c$ are also shown for AuAu collisions at $ {\sqrt {\smash [b]{s_{_\mathrm {NN}}}}} = $ 200 GeV [22]. The dotted line is based on the method presented in Ref. [34] that allows the expected $v_{4}/v_{2}^{2}$ ratio for an event plane analysis to be calculated based on the ideal hydrodynamics limit of 0.5 and the observed relative fluctuation ratio $\sigma /\delimiter "426830A v_n \delimiter "526930B $, as discussed in the text. Statistical (error bars) and systematic (light gray boxes) uncertainties are indicated. |
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Figure 17:
Measurements of $2 - v_{3}^{4}\{4\}/v_{3}^{4}\{\Psi _{3}\}$ versus centrality. The CGC and Glauber model calculations are from Ref. [61]. Statistical (error bars) and systematic (light gray boxes) uncertainties are indicated. |
Tables | |
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Table 1:
The average number of participating nucleons and participant eccentricities, weighted by $r^n$, calculated using the Glauber model in bins of centrality. Systematic uncertainties resulting from the uncertainties in the Glauber-model parameters are indicated. |
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Table 2:
Summary of experimental conditions for the data shown in this report. The Figure(s) column indicates the figures in this report where the data are shown. The ${p_{\mathrm {T}}}$ range for previously published data corresponds to that shown in the original report. |
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Table 3:
Systematic uncertainties in the $v_{3}\{\Psi _{3}\}$ values as a function of centrality in percent. Common uncertainties are shown at the top of the table, followed by those specific to the differential ( ${p_{\mathrm {T}}}$ dependent) and integral ($ {| \eta | }$ dependent) measurements. |
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Table 4:
Systematic uncertainties in the $v_{4}\{\Psi _{4}\}$ values as a function of centrality in percent. Common uncertainties are shown at the top of the table, followed by those specific to the differential ($ {p_{\mathrm {T}}} $ dependent) and integral ($ {| \eta | }$ dependent) measurements. |
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Table 5:
Systematic uncertainties in the $v_{4}\{\Psi _{2}\}$ values as a function of centrality in percent. Common uncertainties are shown at the top of the table, followed by those specific to the differential ($ {p_{\mathrm {T}}} $ dependent) and integral ($ {| \eta | }$ dependent) measurements. |
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Table 6:
Systematic uncertainties in the $v_{5}\{\Psi _{5}\}$ values as a function of centrality in percent. Common uncertainties are shown at the top of the table, followed by those specific to the differential ($ {p_{\mathrm {T}}} $ dependent) and integral ($ {| \eta | }$ dependent) measurements. |
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Table 7:
Systematic uncertainties in the $v_{6}\{\Psi _{6}\}$ values as a function of centrality in percent. Common uncertainties are shown at the top of the table, followed by those specific to the differential ($ {p_{\mathrm {T}}} $ dependent) and integral ($ {| \eta | }$ dependent) measurements. |
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Table 8:
Systematic uncertainties in the $v_{6}\{\Psi _{2}\}$ values as a function of centrality in percent. Common uncertainties are shown at the top of the table, followed by those specific to the differential ($ {p_{\mathrm {T}}} $ dependent) and integral ($ {| \eta | }$ dependent) measurements. |
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Table 9:
Systematic uncertainties in the $v_{3}\{4\}$ values as a function of centrality in percent. Common uncertainties are shown at the top of the table, followed by those specific to the differential ($ {p_{\mathrm {T}}} $ dependent) and integral ($ {| \eta | }$ dependent) measurements. |
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Table 10:
Systematic uncertainties in the $v_{4}\{5\}$ values as a function of centrality in percent. Common uncertainties are shown at the top of the table, followed by those specific to the differential ($ {p_{\mathrm {T}}} $ dependent) and integral ($ {| \eta | }$ dependent) measurements. |
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Table 11:
Systematic uncertainties in the $v_{4}\{\mathrm {LYZ}\}$ values as a function of centrality in percent. Common uncertainties are shown at the top of the table, followed by those specific to the differential ($ {p_{\mathrm {T}}} $ dependent) and integral ($ {| \eta | }$ dependent) measurements. |
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Table 12:
Systematic uncertainties in the $v_{6}\{\mathrm {LYZ}\}$ values as a function of centrality in percent. Common uncertainties are shown at the top of the table, followed by those specific to the differential ($ {p_{\mathrm {T}}} $ dependent) and integral ($ {| \eta | }$ dependent) measurements. |
Summary |
Results from the CMS Collaboration have been presented on higher-order harmonic anisotropies of charged particles for PbPb collisions at $\sqrt{s_{\mathrm{NN}}}= $ 2.76 TeV. The harmonic coefficients $v_{n}$ have been studied as a function of transverse momentum (0.3 $ Comparisons of the event plane results with those of the cumulant and Lee-Yang zeros analyses suggest a strong influence of initial state fluctuations on the azimuthal anisotropies. The weak centrality dependence found for the event plane results based on event planes of harmonic order greater than two is also consistent with the presence of a strong fluctuation component. The pseudorapidity dependence of the higher-order azimuthal anisotropy parameters based on the event plane method is similar to that observed for elliptic flow, with only a modest decrease from the mid-rapidity values out to the limits of the measurement at $\abs{\eta}= $ 2.0 . The mid-rapidity values are compared to those obtained by the ALICE [24,25] and ATLAS [26] Collaborations, and found to be in good agreement. A comparison is also done with lower-energy AuAu measurements by the PHENIX Collaboration at $\sqrt{s_{\mathrm{NN}}}= $ 200 GeV, with only small differences found with the much higher energy LHC data. The results obtained for $v_3$ are compared to predictions from both the CGC and Glauber models. Both of these initial state models are found to be consistent with the data. It is noted that a calculation that employs IP-Glasma-model initial conditions for the early time evolution, followed by a viscous hydrodynamic development of the plasma, is quite successful in reproducing the observed $v_{n}(p_{\mathrm{T}})$ results in the low-$p_{\mathrm{T}}$, flow-dominated region [62]. The measurements presented in this paper help to further establish the pattern of azimuthal particle emission at LHC energies. Recent theoretical investigations have significantly increased our understanding of the initial conditions and hydrodynamics that lead to the experimentally observed asymmetry patterns. However, further calculations are needed to fully explain the method dependent differences seen in the data for the anisotropy harmonics. These differences can be attributed to the role of fluctuations in the participant geometry. Understanding the role of these fluctuations is necessary in order to establish the initial state of the created medium, thereby allowing for an improved determination of its properties. The current results are directly applicable to the study of the initial spatial anisotropy, time development, and shear viscosity of the medium formed in ultra-relativistic heavy-ion collisions. |
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Compact Muon Solenoid LHC, CERN |