- Email: [email protected]
Studies of higher-order flow harmonics in PbPb collisions at 2.76 TeV with CMS
Available online at www.sciencedirect.com
Nuclear Physics A 904–905 (2013) 519c–522c www.elsevier.com/locate/nuclphysa
Studies of higher-order flow harmonics in PbPb collisions at 2.76 TeV with CMS Shengquan Tuo (for the CMS Collaboration)1 Vanderbilt University, Nashville, TN, USA
Abstract High-order Fourier harmonics (vn , n > 2) in the azimuthal distributions of charged particles √ produced in PbPb collisions at a nucleon-nucleon center-of-mass energy sNN = 2.76 TeV are presented. The vn coefficients are studied using the event-plane method and a Fourier decomposition analysis of the two particle correlations in various collision centrality, pT and η ranges. A unique measurement of vn in the ultra-central collisions (UCC) is performed using the longrange component of the two particle correlations. These data provide strong constraints on the theoretical models of the initial condition in heavy ion collisions and the transport properties of the produced medium. 1. Introduction Sizable azimuthal anisotropies are a very important feature of the hot and dense medium produced in heavy ion collisions. Azimuthal anisotropies in the final state particle distributions are usually characterized by a series of Fourier coefficients vn = cos[n(φ − Ψn )], where φ is the azimuthal angle of the particle, Ψn is the nth order symmetry plane in the initial state. The significant magnitude of v2 , which is comparable to ideal hydrodynamic calculations, has contributed to the suggestion that a strongly coupled quark-gluon plasma (sQGP) has been produced at RHIC. In the past two years, high-order flow harmonics have been measured in experiments [1, 2] and calculated in various models [3]. The vn are understood to originate in the fluctuations (producing higher-order spatial symmetry) in the initial state nucleons, and the following transport or hydrodynamics expansion2 . Therefore they are sensitive to both the initial conditions and the transport properties of the medium, such as the shear viscosity to entropy density ratio, η/s. The high-order vn coefficients have been extensively studied at CMS [5] over a wide kinematic range and acceptance with various methods [1, 6, 7, 8]. In this paper, new results for v3 and v4 with pT from 0.3 to 8.0 GeV/c, |η| < 1.0 and 1.0 < |η| < 2.0, centrality in 0 − 60% from event-plane method are presented. The factorization of the Fourier coefficients (VnΔ ) from two particle correlations into a product of the single-particle vn is studied for n = 2, 3 and 4 in three centrality ranges, 0 − 5%, 15 − 20% and 35 − 40%. The vn in the ultra-central collisions (UCC, 0 − 0.2% here) are extracted as a function of pT from 0.3 to 8 GeV/c for n = 2, 3, 4, 5 and 6. The pT integrated vn for 0.3 < pT <3 GeV/c are also derived up to n = 7. The results are compared to hydrodynamic calculations with different initial conditions and η/s. 1A
list of members of the CMS Collaboration and acknowledgements can be found at the end of this issue. also exist in hydrodynamics. Non-linearities of the harmonic spectra [4] give rise to vn as well. © CERN for the benefit of the CMS Collaboration.
2 Fluctuations
0375-9474/ © 2013 CERN Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nuclphysa.2013.02.067
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S. Tuo / Nuclear Physics A 904–905 (2013) 519c–522c
2. Results for v3 and v4 from event-plane method The data used in this analysis are from the 2011 run of the LHC. The event-plane angles are reconstructed using the forward hadronic calorimeters (HF). Tracks with negative (positive) η are correlated with event-plane angles from the positive (negative) side of HF. CMS Preliminary 0-10% Lint = 150 μ b-1 PbPb sNN = 2.76 TeV
10-20%
20-30%
40-50%
50-60%
v4
0.10
0.05
|η|<1 1<|η|<2 30-40%
v4
0.10
0.05
2
4
p (GeV/c)
6
T
2
4
p (GeV/c) T
6
2
4
pT (GeV/c)
6
Figure 1: The measurement of v4 , as a function of the charged particle transverse momentum with |η| < 1 (solid markers) and 1 < |η| < 2 (open markers) for six centrality ranges. Error bars denote the statistical uncertainties.
Fig. 1 shows v4 as a function of pT in the pseudorapidity ranges |η| < 1 and 1 < |η| < 2 with centrality ranging from 0 − 10% to 50 − 60%. The pT -dependence of v4 shows a trend of first rapid rise, reaching a maximum at pT ≈ 3 GeV/c and then a decrease. We can see that v4 has a weak dependence on both centrality and |η|. This is also true for v3 [9] . This behavior is expected for anisotropies that are mainly driven by initial-state fluctuations [2]. 3. Factorization of Fourier coefficients Data from the 2010 run of LHC are used in this analysis [7]. The Fourier coefficientsVnΔ are extracted by fitting the Δφ distribution of the two particle correlations for particles that are separated in pseudorapidity (|Δη| > 2). In the low-pT regime, hadron production is mainly from the bulk medium, so the Fourier coefficients can be factorized into the product of collective flow assoc assoc ) = vn (ptrig ). components of the trigger and the associated particle: VnΔ (ptrig T , pT T ) × vn (pT low range from 1 to 1.5 GeV/c, the value of v (p ) is calculated as the square root of For the plow n T T trig trig trig low low low low VnΔ (pT , pT ). The values of vn (pT ) are then derived as vn (pT ) = VnΔ (pT , pT )/vn (pT ) . assoc assoc Fig. 2 shows the ratio of VnΔ (ptrig ) to vn (ptrig ). The ratio should be apT , pT T ) × vn (pT trig proximately unity, if factorization is also valid for higher momenta pT and passoc particles. For T up to the long-range correlation region (2 < |Δη| < 4), the factorization works for V3 with passoc T 3 - 3.5 GeV/c and ptrig up to approximately 8 GeV/c for all the three centrality ranges. T 4. Results for v n in the ultra-central collisions The UCC PbPb collisions have been collected using a unique trigger deployed in CMS during the 2011 run. Detailed studies on centrality selections and pileup rejections have been performed [10]. The vn coefficients are extracted from the long-range two particle correlations. Fig. 3 shows v2 − v6 as a function of pT from 0.3 - 8 GeV/c in the 0 − 0.2% central collisions. The plow T is chosen to be 1 - 3 GeV/c. The vn at higher pT are extracted assuming that factorization of the Fourier coefficients holds. Different vn harmonics exhibit different pT dependence. At higher pT (pT > 1 GeV/c), v2 is smaller than higher-order harmonics, even smaller than v5 for pT > 3 GeV/c. This behavior of the
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S. Tuo / Nuclear Physics A 904–905 (2013) 519c–522c
V3Δ v3×v3
n=3 1.5
CMS Lint = 3.9 μ b-1
1.0
assoc
1.5 < p
V3Δ v3×v3
T
1.0
assoc
2.0 < p
V3Δ v3×v3
35-40%
< 2.0 GeV/c
< 2.5 GeV/c
1.5 1.0
assoc
2.5 < p
T
V3Δ v3×v3
15-20%
1.5
T
< 3.0 GeV/c
1.5 1.0
assoc
3.0 < p
T
V3Δ v3×v3
PbPb sNN = 2.76 TeV
2 < |Δη| < 4 0-5% 0 < |Δη| < 1
< 3.5 GeV/c
1.5 1.0
assoc
4.0 < p
T
2
4
< 5.0 GeV/c
6
ptrig (GeV/c)
8
T
2
4
6
ptrig (GeV/c)
8
T
trig
2
4
6
ptrig (GeV/c)
8
T
trig
Figure 2: The ratios of V3Δ (pT , passoc ) to the product of v3 (pT ) and v3 (passoc ) for n = 3 in the short-range (0 < |Δη| < T T 1, open circles) and long-range (2 < |Δη| < 4, closed circles) regions, where v3 (pT ) is evaluated in a fixed plow T bin of 1 1.5 GeV/c, for five intervals of passoc and centralities of 0 − 5%, 15 − 20% and 35 − 40%. The error bars correspond to T statistical uncertainties only.
n=2
PbPb
vn{2part,|Δη|>2}
n=3 n=4
CMS Preliminary sNN = 2.76 TeV 0-0.2% centrality
n=5 n=6
0.05
0.00 0
2
4
6
p (GeV/c) T
Figure 3: The v2 − v6 values as a function of pT in 0 − 0.2% central PbPb collisions. Error bars denote the statistical uncertainties, while the shaded bands correspond to the systematic uncertainties.
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S. Tuo / Nuclear Physics A 904–905 (2013) 519c–522c
pT dependence can be compared to hydrodynamics calculations and provide strong constraints on theoretical models [10] . CMS Preliminary
vn{2part,|Δη|>2}
VISH2+1 Hydro Glauber, η/s=0.08 MC-KLN, η/s=0.2
0.02
0.01
CMS Preliminary PbPb sNN = 2.76 TeV 0-0.2% centrality
0.03
vn{2part,|Δη|>2}
PbPb sNN = 2.76 TeV 0-0.2% centrality
0.03
Glauber, η/s=0 Glauber, η/s=0.08 Glauber, η/s=0.20
0.02
0.01
0.00
0.00 2
4
n
6
0.3 < pT < 3 GeV/c
2
4
n
6
Figure 4: Comparison of pT -integrated (0.3 - 3.0 GeV/c) vn data with VISH2+1D hydrodynamic (left) and viscous hydrodynamic calculations (right) from [11] and [12] for different η/s values, in 0 − 0.2% central collisions. Error bars denote the statistical uncertainties of the data, while the shaded bands correspond to the systematic uncertainties.
Fig. 4 shows the comparison of pT -integrated vn from data and hydrodynamic calculations. The theory reproduces the main trends in the data, but more theoretical studies are needed to extract η/s. 5. Summary New measurements of vn from event-plane and two particle correlation methods, and for ultra-central collisions, have been performed in CMS. The v3 and v4 coefficients do not depend strongly on centrality and pseudorapidity. The Fourier coefficients from two particle correlations up to 3 - 3.5 GeV/c, and ptrig approximately factorize for V3Δ with passoc T T up to 8 GeV/c for central and mid-central collisions. The vn harmonics in UCC are sizable at mid-pT (2.0 - 6.0 GeV/c). These data provide constraints for theoretical models of the hydrodynamic evolution of heavy ion collisions. References [1] CMS Collaboration, CMS-PAS-HIN-11-005, http://cdsweb.cern.ch/record/1361385 [2] ALICE Collaboration, Phys. Rev. Lett. 107, 032301 (2011) [arXiv:1105.3865]; ATLAS Collaboration, Phys. Rev. C 86, 014907 (2012) [arXiv:1203.3087]; Paul Sorensen (for the STAR Collaboration) 2011 J. Phys. G: Nucl. Part. Phys. 38 124029 [arXiv:1110.0737]; PHENIX Collaboration, arXiv:1105.3928 Submitted to Phys. Rev. Lett.; [3] B. Alver and G. Roland, Phys. Rev. C 81 (2010) 054905; B. Alver et al. Phys. Rev. C 82, 034913 (2010) [arXiv:1007.5469]; C. Gale et al. [arXiv:1209.6330]; Z. Qiu et al. Physics Letters B 707, 151 (2012) [arXiv:1110.3033]; F. Gardim et al. arXiv:1203.2882v1; T. Hirano et al. arXiv:1204.5814v1; H. Petersen et al. Phys. Rev. C 82, 041901(R) (2010) [arXiv:1008.0625]; J. Xu et al. Phys. Rev. C 84, 044907 (2011) [arXiv:1108.0717] V. Konchakovski et al. Phys. Rev. C 85, 044922 (2012) [arXiv:1201.3320v2] [4] D. Teaney, L. Yan, arXiv:1206.1905 [5] S.Chatrchyan et al. [CMS Collaboration], JINST3, S08004 (2008). [6] S. Chatrchyan et al. [CMS Collaboration], arXiv:1204.1409, submitted to Phys. Rev. C [7] S. Chatrchyan et al. [CMS Collaboration], Eur. Phys. J. C 72 (2012) 2012 [arXiv:1201.3158] [8] S. Chatrchyan et al. [CMS Collaboration], Phys. Rev. Lett. 109, 022301 (2012) [arXiv:1204.1850] [9] CMS Collaboration, CMS-PAS-HIN-12-010, http://cdsweb.cern.ch/record/1472744 [10] CMS Collaboration, CMS-PAS-HIN-12-011, http://cdsweb.cern.ch/record/1472724 [11] M. Luzum and J. Ollitrault. Private communication. [12] C. Shen, Z. Qiu, and U. Heinz. Private communication.
Nuclear Physics A 904–905 (2013) 519c–522c www.elsevier.com/locate/nuclphysa
Studies of higher-order flow harmonics in PbPb collisions at 2.76 TeV with CMS Shengquan Tuo (for the CMS Collaboration)1 Vanderbilt University, Nashville, TN, USA
Abstract High-order Fourier harmonics (vn , n > 2) in the azimuthal distributions of charged particles √ produced in PbPb collisions at a nucleon-nucleon center-of-mass energy sNN = 2.76 TeV are presented. The vn coefficients are studied using the event-plane method and a Fourier decomposition analysis of the two particle correlations in various collision centrality, pT and η ranges. A unique measurement of vn in the ultra-central collisions (UCC) is performed using the longrange component of the two particle correlations. These data provide strong constraints on the theoretical models of the initial condition in heavy ion collisions and the transport properties of the produced medium. 1. Introduction Sizable azimuthal anisotropies are a very important feature of the hot and dense medium produced in heavy ion collisions. Azimuthal anisotropies in the final state particle distributions are usually characterized by a series of Fourier coefficients vn = cos[n(φ − Ψn )], where φ is the azimuthal angle of the particle, Ψn is the nth order symmetry plane in the initial state. The significant magnitude of v2 , which is comparable to ideal hydrodynamic calculations, has contributed to the suggestion that a strongly coupled quark-gluon plasma (sQGP) has been produced at RHIC. In the past two years, high-order flow harmonics have been measured in experiments [1, 2] and calculated in various models [3]. The vn are understood to originate in the fluctuations (producing higher-order spatial symmetry) in the initial state nucleons, and the following transport or hydrodynamics expansion2 . Therefore they are sensitive to both the initial conditions and the transport properties of the medium, such as the shear viscosity to entropy density ratio, η/s. The high-order vn coefficients have been extensively studied at CMS [5] over a wide kinematic range and acceptance with various methods [1, 6, 7, 8]. In this paper, new results for v3 and v4 with pT from 0.3 to 8.0 GeV/c, |η| < 1.0 and 1.0 < |η| < 2.0, centrality in 0 − 60% from event-plane method are presented. The factorization of the Fourier coefficients (VnΔ ) from two particle correlations into a product of the single-particle vn is studied for n = 2, 3 and 4 in three centrality ranges, 0 − 5%, 15 − 20% and 35 − 40%. The vn in the ultra-central collisions (UCC, 0 − 0.2% here) are extracted as a function of pT from 0.3 to 8 GeV/c for n = 2, 3, 4, 5 and 6. The pT integrated vn for 0.3 < pT <3 GeV/c are also derived up to n = 7. The results are compared to hydrodynamic calculations with different initial conditions and η/s. 1A
list of members of the CMS Collaboration and acknowledgements can be found at the end of this issue. also exist in hydrodynamics. Non-linearities of the harmonic spectra [4] give rise to vn as well. © CERN for the benefit of the CMS Collaboration.
2 Fluctuations
0375-9474/ © 2013 CERN Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nuclphysa.2013.02.067
520c
S. Tuo / Nuclear Physics A 904–905 (2013) 519c–522c
2. Results for v3 and v4 from event-plane method The data used in this analysis are from the 2011 run of the LHC. The event-plane angles are reconstructed using the forward hadronic calorimeters (HF). Tracks with negative (positive) η are correlated with event-plane angles from the positive (negative) side of HF. CMS Preliminary 0-10% Lint = 150 μ b-1 PbPb sNN = 2.76 TeV
10-20%
20-30%
40-50%
50-60%
v4
0.10
0.05
|η|<1 1<|η|<2 30-40%
v4
0.10
0.05
2
4
p (GeV/c)
6
T
2
4
p (GeV/c) T
6
2
4
pT (GeV/c)
6
Figure 1: The measurement of v4 , as a function of the charged particle transverse momentum with |η| < 1 (solid markers) and 1 < |η| < 2 (open markers) for six centrality ranges. Error bars denote the statistical uncertainties.
Fig. 1 shows v4 as a function of pT in the pseudorapidity ranges |η| < 1 and 1 < |η| < 2 with centrality ranging from 0 − 10% to 50 − 60%. The pT -dependence of v4 shows a trend of first rapid rise, reaching a maximum at pT ≈ 3 GeV/c and then a decrease. We can see that v4 has a weak dependence on both centrality and |η|. This is also true for v3 [9] . This behavior is expected for anisotropies that are mainly driven by initial-state fluctuations [2]. 3. Factorization of Fourier coefficients Data from the 2010 run of LHC are used in this analysis [7]. The Fourier coefficientsVnΔ are extracted by fitting the Δφ distribution of the two particle correlations for particles that are separated in pseudorapidity (|Δη| > 2). In the low-pT regime, hadron production is mainly from the bulk medium, so the Fourier coefficients can be factorized into the product of collective flow assoc assoc ) = vn (ptrig ). components of the trigger and the associated particle: VnΔ (ptrig T , pT T ) × vn (pT low range from 1 to 1.5 GeV/c, the value of v (p ) is calculated as the square root of For the plow n T T trig trig trig low low low low VnΔ (pT , pT ). The values of vn (pT ) are then derived as vn (pT ) = VnΔ (pT , pT )/vn (pT ) . assoc assoc Fig. 2 shows the ratio of VnΔ (ptrig ) to vn (ptrig ). The ratio should be apT , pT T ) × vn (pT trig proximately unity, if factorization is also valid for higher momenta pT and passoc particles. For T up to the long-range correlation region (2 < |Δη| < 4), the factorization works for V3 with passoc T 3 - 3.5 GeV/c and ptrig up to approximately 8 GeV/c for all the three centrality ranges. T 4. Results for v n in the ultra-central collisions The UCC PbPb collisions have been collected using a unique trigger deployed in CMS during the 2011 run. Detailed studies on centrality selections and pileup rejections have been performed [10]. The vn coefficients are extracted from the long-range two particle correlations. Fig. 3 shows v2 − v6 as a function of pT from 0.3 - 8 GeV/c in the 0 − 0.2% central collisions. The plow T is chosen to be 1 - 3 GeV/c. The vn at higher pT are extracted assuming that factorization of the Fourier coefficients holds. Different vn harmonics exhibit different pT dependence. At higher pT (pT > 1 GeV/c), v2 is smaller than higher-order harmonics, even smaller than v5 for pT > 3 GeV/c. This behavior of the
521c
S. Tuo / Nuclear Physics A 904–905 (2013) 519c–522c
V3Δ v3×v3
n=3 1.5
CMS Lint = 3.9 μ b-1
1.0
assoc
1.5 < p
V3Δ v3×v3
T
1.0
assoc
2.0 < p
V3Δ v3×v3
35-40%
< 2.0 GeV/c
< 2.5 GeV/c
1.5 1.0
assoc
2.5 < p
T
V3Δ v3×v3
15-20%
1.5
T
< 3.0 GeV/c
1.5 1.0
assoc
3.0 < p
T
V3Δ v3×v3
PbPb sNN = 2.76 TeV
2 < |Δη| < 4 0-5% 0 < |Δη| < 1
< 3.5 GeV/c
1.5 1.0
assoc
4.0 < p
T
2
4
< 5.0 GeV/c
6
ptrig (GeV/c)
8
T
2
4
6
ptrig (GeV/c)
8
T
trig
2
4
6
ptrig (GeV/c)
8
T
trig
Figure 2: The ratios of V3Δ (pT , passoc ) to the product of v3 (pT ) and v3 (passoc ) for n = 3 in the short-range (0 < |Δη| < T T 1, open circles) and long-range (2 < |Δη| < 4, closed circles) regions, where v3 (pT ) is evaluated in a fixed plow T bin of 1 1.5 GeV/c, for five intervals of passoc and centralities of 0 − 5%, 15 − 20% and 35 − 40%. The error bars correspond to T statistical uncertainties only.
n=2
PbPb
vn{2part,|Δη|>2}
n=3 n=4
CMS Preliminary sNN = 2.76 TeV 0-0.2% centrality
n=5 n=6
0.05
0.00 0
2
4
6
p (GeV/c) T
Figure 3: The v2 − v6 values as a function of pT in 0 − 0.2% central PbPb collisions. Error bars denote the statistical uncertainties, while the shaded bands correspond to the systematic uncertainties.
522c
S. Tuo / Nuclear Physics A 904–905 (2013) 519c–522c
pT dependence can be compared to hydrodynamics calculations and provide strong constraints on theoretical models [10] . CMS Preliminary
vn{2part,|Δη|>2}
VISH2+1 Hydro Glauber, η/s=0.08 MC-KLN, η/s=0.2
0.02
0.01
CMS Preliminary PbPb sNN = 2.76 TeV 0-0.2% centrality
0.03
vn{2part,|Δη|>2}
PbPb sNN = 2.76 TeV 0-0.2% centrality
0.03
Glauber, η/s=0 Glauber, η/s=0.08 Glauber, η/s=0.20
0.02
0.01
0.00
0.00 2
4
n
6
0.3 < pT < 3 GeV/c
2
4
n
6
Figure 4: Comparison of pT -integrated (0.3 - 3.0 GeV/c) vn data with VISH2+1D hydrodynamic (left) and viscous hydrodynamic calculations (right) from [11] and [12] for different η/s values, in 0 − 0.2% central collisions. Error bars denote the statistical uncertainties of the data, while the shaded bands correspond to the systematic uncertainties.
Fig. 4 shows the comparison of pT -integrated vn from data and hydrodynamic calculations. The theory reproduces the main trends in the data, but more theoretical studies are needed to extract η/s. 5. Summary New measurements of vn from event-plane and two particle correlation methods, and for ultra-central collisions, have been performed in CMS. The v3 and v4 coefficients do not depend strongly on centrality and pseudorapidity. The Fourier coefficients from two particle correlations up to 3 - 3.5 GeV/c, and ptrig approximately factorize for V3Δ with passoc T T up to 8 GeV/c for central and mid-central collisions. The vn harmonics in UCC are sizable at mid-pT (2.0 - 6.0 GeV/c). These data provide constraints for theoretical models of the hydrodynamic evolution of heavy ion collisions. References [1] CMS Collaboration, CMS-PAS-HIN-11-005, http://cdsweb.cern.ch/record/1361385 [2] ALICE Collaboration, Phys. Rev. Lett. 107, 032301 (2011) [arXiv:1105.3865]; ATLAS Collaboration, Phys. Rev. C 86, 014907 (2012) [arXiv:1203.3087]; Paul Sorensen (for the STAR Collaboration) 2011 J. Phys. G: Nucl. Part. Phys. 38 124029 [arXiv:1110.0737]; PHENIX Collaboration, arXiv:1105.3928 Submitted to Phys. Rev. Lett.; [3] B. Alver and G. Roland, Phys. Rev. C 81 (2010) 054905; B. Alver et al. Phys. Rev. C 82, 034913 (2010) [arXiv:1007.5469]; C. Gale et al. [arXiv:1209.6330]; Z. Qiu et al. Physics Letters B 707, 151 (2012) [arXiv:1110.3033]; F. Gardim et al. arXiv:1203.2882v1; T. Hirano et al. arXiv:1204.5814v1; H. Petersen et al. Phys. Rev. C 82, 041901(R) (2010) [arXiv:1008.0625]; J. Xu et al. Phys. Rev. C 84, 044907 (2011) [arXiv:1108.0717] V. Konchakovski et al. Phys. Rev. C 85, 044922 (2012) [arXiv:1201.3320v2] [4] D. Teaney, L. Yan, arXiv:1206.1905 [5] S.Chatrchyan et al. [CMS Collaboration], JINST3, S08004 (2008). [6] S. Chatrchyan et al. [CMS Collaboration], arXiv:1204.1409, submitted to Phys. Rev. C [7] S. Chatrchyan et al. [CMS Collaboration], Eur. Phys. J. C 72 (2012) 2012 [arXiv:1201.3158] [8] S. Chatrchyan et al. [CMS Collaboration], Phys. Rev. Lett. 109, 022301 (2012) [arXiv:1204.1850] [9] CMS Collaboration, CMS-PAS-HIN-12-010, http://cdsweb.cern.ch/record/1472744 [10] CMS Collaboration, CMS-PAS-HIN-12-011, http://cdsweb.cern.ch/record/1472724 [11] M. Luzum and J. Ollitrault. Private communication. [12] C. Shen, Z. Qiu, and U. Heinz. Private communication.