CMS-PAS-HIN-16-018

CMS-PAS-HIN-16-018
Measurement of mixed higher order flow harmonics in PbPb collisions
CMS Collaboration
February 2017

Abstract: The mixed higher order flow harmonics and nonlinear response coefficients of charged particles are measured for the first time as a function of $p_{\rm{T}}$ and centrality in PbPb collisions at $\sqrt{s_{NN}} = $ 2.76 TeV and 5.02 TeV with the CMS detector. The results are obtained using the scalar product method, and cover a $p_{\rm{T}}$ range from 0.3 GeV/$c$ to 8.0 GeV/$c$, pseudorapidity $\|\eta\| < $ 2.4, and a centrality range of 0-60%. At 5.02 TeV, results for mixed harmonics are compared to the matching higher order flow harmonics from two-particle correlations, which measure $v_n$ values with respect to the $n$-th order event plane. It is observed that the nonlinear response coefficients of the odd harmonics are larger than the even harmonics ones. The results are compared with hydrodynamic predictions with different shear viscosity to entropy density ratios and different initial conditions.
Links: CDS record (PDF) ; inSPIRE record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: The mixed higher order flow harmonics, $v_4\{\Psi _{22}\}$, $v_5\{\Psi _{23}\}$, $v_6\{\Psi _{222}\}$, $v_6\{\Psi _{33}\}$ and $v_7\{\Psi _{223}\}$ from the scalar product method at 2.76 and 5.02 TeV as a function of $ {p_{\mathrm {T}}} $ with $\|\eta \|< $ 2.4 in the 0-20% (top row) and 20-60% (bottom row) centrality ranges. Statistical (error bars) and systematic (shaded boxes) uncertainties are shown.
png pdf	Figure 2: Comparison of mixed higher order flow harmonics and flow from two-particle correlations at 5.02 TeV as a function ${p_{\mathrm {T}}} $ with $\|\eta \|< $ 2.4 in the 0-20% (top row) and 20-60% (bottom row) centrality ranges. Statistical (error bars) and systematic (shaded boxes) uncertainties are shown.
png pdf	Figure 3: The nonlinear response coefficients, $\chi _{422}$, $\chi _{523}$, $\chi _{6222}$, $\chi _{633}$ and $\chi _{7223}$ from the scalar product method at 2.76 and 5.02 TeV as a function of $ {p_{\mathrm {T}}}$ with $\|\eta \|<$ 2.4 in the 0-20% (top row) and 20-60% (bottom row) centrality ranges. Statistical (error bars) and systematic (shaded boxes) uncertainties are shown.
png pdf	Figure 4: The mixed higher order flow harmonics, $v_4\{\Psi _{22}\}$, $v_5\{\Psi _{23}\}$, $v_6\{\Psi _{222}\}$, $v_6\{\Psi _{33}\}$ and $v_7\{\Psi _{223}\}$ from the scalar product method at 2.76 and 5.02 TeV as a function of centrality with $\|\eta \|<$ 2.4 in the 0.3 $ < {p_{\mathrm {T}}} < $ 3.0 GeV/$c$ range. Statistical (error bars) and systematic (shaded boxes) uncertainties are shown. The hydrodynamic predictions [12] with $\eta /s =$ 0.08 (magenta lines) are compared with data.
png pdf	Figure 5: The nonlinear response coefficients, $\chi _{422}$, $\chi _{523}$, $\chi _{6222}$, $\chi _{633}$ and $\chi _{7223}$ from the scalar product method at 2.76 and 5.02 TeV as a function of centrality with $\|\eta \|< $ 2.4 in the 0.3 $< {p_{\mathrm {T}}} < $ 3.0 GeV/c range. Statistical (error bars) and systematic (shaded boxes) uncertainties are shown. The results are compared with predictions from AMPT and hydrodynamics with a deformed symmetric Gaussian density profile as the initial condition using $\eta /s = $ 0.08 in Ref. [12], and from iEBE-VISHNU hydrodynamics with Glauber and KLN initial conditions using the same $\eta /s $ [14].
png pdf	Figure 6: The nonlinear response coefficients, $\chi _{422}$, $\chi _{523}$, $\chi _{6222}$, $\chi _{633}$ and $\chi _{7223}$ from the scalar product method at 2.76 and 5.02 TeV as a function of centrality with $\|\eta \|<$ 2.4 in the 0.3 $ < {p_{\mathrm {T}}} < $ 3.0 GeV/c range. Statistical (error bars) and systematic (shaded boxes) uncertainties are shown. The results are compared with predictions from AMPT in Ref. [12] and from iEBE-VISHNU hydrodynamics with KLN initial condition using $\eta /s = $ 0, 0.08 and 0.2 [14].

Tables
png pdf	Table 1: Summary of different sources of systematic uncertainties for each mixed higher order flow harmonic.

Summary

The mixed higher order flow harmonics and nonlinear response coefficients of charged particles has been studied for the first time as a function of $ p_{\mathrm{T}} $ and centrality in PbPb collisions at $\sqrt{s_{NN}} = $ 2.76 TeV and 5.02 TeV using the CMS detector. The measurements are done with the scalar product method, covering a $ p_{\mathrm{T}} $ range from 0.3 GeV/$c$ to 8.0 GeV/c, $|\eta|< $ 2.4 and centrality range of 0-60%. Additionally, as a comparison, $v_n$ harmonics ($n=$ 4, ... , 7) are measured with the two-particle correlation method over 0.3 $< p_{\mathrm{T}} < $ 8.0 GeV/$c$ and $|\eta| < $ 2.4 and within the same centrality range. The shape of the mixed higher order flow harmonics, $v_4\{\Psi_{22}\}$, $v_5\{\Psi_{23}\}$, $v_6\{\Psi_{222}\}$, $v_6\{\Psi_{33}\}$ and $v_7\{\Psi_{223}\}$, and nonlinear response coefficients, $\chi_{422}$, $\chi_{523}$, $\chi_{6222}$, $\chi_{633}$ and $\chi_{7223}$ as a function $p_{\mathrm{T}}$ are similar, first increases at low $p_{\mathrm{T}}$, reach maximum at about 3-4 GeV/$c$ then decreases at higher $p_{\mathrm{T}}$. The contribution of nonlinear part for $v_5$ and $v_7$ are larger than other harmonics in the centrality range 20-60%. It is clearly observed that the nonlinear response coefficients of the odd harmonics, $\chi_{523}$ and $\chi_{7223}$, are larger than the even harmonics. The data are compared with AMPT and hydrodynamic predictions with different shear viscosity to entropy density ratios and initial condition models. The predictions from AMPT are favored by the measurement. These results will provide constraints on the theoretical description of the medium close to the freeze-out temperature, which is poorly understood so far.

References
1	B. Alver and G. Roland	Collision geometry fluctuations and triangular flow in heavy-ion collisions	PRC 81 (2010) 054905, , [Erratum: Phys. Rev.C82,039903(2010)]	1003.0194
2	B. Alver et al.	Importance of correlations and fluctuations on the initial source eccentricity in high-energy nucleus-nucleus collisions	PRC 77 (2008) 014906	0711.3724
3	STAR Collaboration	Elliptic flow fluctuations in Au + Au collisions at s(NN)**(1/2) = 200-GeV	JPG 35 (2008) 104102	0808.0356
4	PHOBOS Collaboration	Non-flow correlations and elliptic flow fluctuations in gold-gold collisions at $ \sqrt{s_{NN}}=200 $ GeV	PRC 81 (2010) 034915	1002.0534
5	J.-Y. Ollitrault, A. M. Poskanzer, and S. A. Voloshin	Effect of flow fluctuations and nonflow on elliptic flow methods	PRC 80 (2009) 014904	0904.2315
6	Z. Qiu and U. W. Heinz	Event-by-event shape and flow fluctuations of relativistic heavy-ion collision fireballs	PRC 84 (2011) 024911	1104.0650
7	PHENIX Collaboration	Measurements of Higher-Order Flow Harmonics in Au+Au Collisions at $ \sqrt{s_{NN}} = 200 $ GeV	PRL 107 (2011) 252301	1105.3928
8	ATLAS Collaboration	Measurement of event-plane correlations in $ \sqrt{s_{NN}}=2.76 $ TeV lead-lead collisions with the ATLAS detector	PRC 90 (2014), no. 2, 024905	1403.0489
9	ATLAS Collaboration	Measurement of the correlation between flow harmonics of different order in lead-lead collisions at $ \sqrt{s_{NN}} $=2.76 TeV with the ATLAS detector	PRC 92 (2015), no. 3, 034903	1504.01289
10	U. Heinz, Z. Qiu, and C. Shen	Fluctuating flow angles and anisotropic flow measurements	PRC 87 (2013), no. 3, 034913	1302.3535
11	CMS Collaboration	Evidence for transverse momentum and pseudorapidity dependent event plane fluctuations in PbPb and pPb collisions	PRC 92 (2015), no. 3, 034911	CMS-HIN-14-012 1503.01692
12	L. Yan and J.-Y. Ollitrault	$ \nu_4, \nu_5, \nu_6, \nu_7 $: nonlinear hydrodynamic response versus LHC data	PLB 744 (2015) 82--87	1502.02502
13	R. Andrade et al.	On the necessity to include event-by-event fluctuations in experimental evaluation of elliptical flow	PRL 97 (2006) 202302	nucl-th/0608067
14	J. Qian, U. W. Heinz, and J. Liu	Mode-coupling effects in anisotropic flow in heavy-ion collisions	PRC 93 (2016), no. 6, 064901	1602.02813
15	D. Teaney and L. Yan	Non linearities in the harmonic spectrum of heavy ion collisions with ideal and viscous hydrodynamics	PRC 86 (2012) 044908	1206.1905
16	STAR Collaboration	Azimuthal anisotropy at RHIC: The First and fourth harmonics	PRL 92 (2004) 062301	nucl-ex/0310029
17	CMS Collaboration	Measurement of higher-order harmonic azimuthal anisotropy in PbPb collisions at $ \sqrt{s_{NN}} $ = 2.76 TeV	PRC 89 (2014), no. 4, 044906	CMS-HIN-11-005 1310.8651
18	M. Luzum and J.-Y. Ollitrault	Eliminating experimental bias in anisotropic-flow measurements of high-energy nuclear collisions	PRC 87 (2013), no. 4, 044907	1209.2323
19	CMS Collaboration	Centrality dependence of dihadron correlations and azimuthal anisotropy harmonics in PbPb collisions at $ \sqrt{s_{NN}} $= 2.76 TeV	EPJC 72 (2012) 10052	CMS-HIN-11-006 1201.3158
20	CMS Collaboration	Observation of Long-Range Near-Side Angular Correlations in Proton-Proton Collisions at the LHC	JHEP 09 (2010) 091	CMS-QCD-10-002 1009.4122
21	CMS Collaboration	Long-range and short-range dihadron angular correlations in central PbPb collisions at a nucleon-nucleon center of mass energy of 2.76 TeV	JHEP 07 (2011) 076	CMS-HIN-11-001 1105.2438
22	CMS Collaboration	Observation of long-range near-side angular correlations in proton-lead collisions at the LHC	PLB 718 (2013) 795	CMS-HIN-12-015 1210.5482
23	CMS Collaboration	The CMS Experiment at the CERN LHC	JINST 03 (2008) S08004	CMS-00-001
24	GEANT4 Collaboration	GEANT4: A Simulation toolkit	NIMA 506 (2003) 250--303
25	CMS Collaboration	Description and performance of track and primary-vertex reconstruction with the CMS tracker	JINST 9 (2014), no. 10, P10009	CMS-TRK-11-001 1405.6569
26	I. P. Lokhtin and A. M. Snigirev	A Model of jet quenching in ultrarelativistic heavy ion collisions and high-p(T) hadron spectra at RHIC	EPJC 45 (2006) 211--217	hep-ph/0506189
27	CMS Collaboration	Multiplicity and transverse momentum dependence of two- and four-particle correlations in pPb and PbPb collisions	PLB 724 (2013) 213--240	CMS-HIN-13-002 1305.0609