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Flow Harmonics vn in pPb and PbPb Collisions
Available online at www.sciencedirect.com
Nuclear Physics A 956 (2016) 753–756 www.elsevier.com/locate/nuclphysa
Flow Harmonics vn in pPb and PbPb Collisions Quan Wang CERN Building 42-1-22, Geneva 23, Switzerland CH-1211
Abstract Previous CMS measurements have demonstrated the collective nature of multiparticle correlations in high-multiplicity pPb collisions at the LHC. This collectivity is consistent with a hydrodynamic flow origin. However, it can also be interpreted in terms of initial state effects arising from gluon saturation. The pseudorapidity dependence of the azimuthal Fourier coefficients (vn ) is expected to be sensitive to the underlying mechanism with, in the hydrodynamic picture, the longer lifetime of the fireball on the Pb-going side expected to lead to a larger flow signal than found on the p-going side. To investigate the detailed properties of the observed collectivity, differential vn values in transverse momentum (pT ) and pseudorapidity (η) are presented over the full range of the CMS tracker detector (−2.4 < η < 2.4) for pPb collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV. Results based on multiparticle analyses involving four or more particles are shown. An event plane analysis is presented where the influence of recently demonstrated event-plane decorrelation is considered. Comparisons are made with peripheral PbPb collisions measured at similar mid-rapidity particle multiplicities. The results will be discussed in the context of current models of the longitudinal dependence of the multiparticle correlations. Keywords: Flow, Multiparticle Cumulant, Event Plane, Lee-Yang Zeros
1. Introduction Recent studies of multiparticle correlations in proton on lead collisions have raised the prospect that a quark-gluon plasma droplet might be formed that exhibits fluid-like behavior [1, 2, 3, 4]. In AA collisions, the long-range two-particle correlations are attributed to the collective flow from a strongly interacting, expanding medium [5]. The detailed azimuthal angle distribution of emitted particles can be characterized by its Fourier components [6]. In particular, the second and third Fourier components, known as elliptic and triangular flow, respectively, most directly reflect the medium response to the initial collision geometry and to its fluctuations. To provide further constraints on the theoretical understanding of the particle production mechanism in different collision systems, this analysis presents results on the pseudorapidity η and pT dependence of flow harmonics vn from pPb and PbPb collisions using the 4-, 6- and 8-particle Q-cumulant method, the Lee-Yang Zeros (LYZ) method, and the event-plane method. Within the hydrodynamic picture, the longer lifetime of the medium for pseudorapidities on the Pb-going side in pPb collisions is expected to lead to larger values for the flow harmonics than found for the p-going side pseudorapidities [7]. The pPb system is √ studied at sNN = 5.02 TeV using high-statistics data obtained by the CMS experiment during the 2013 pPb run at the LHC. With a large data sample, the particle correlations have been studied in a regime of high http://dx.doi.org/10.1016/j.nuclphysa.2016.02.073 0375-9474/© 2016 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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multiplicity pPb collisions comparable to the particle multiplicity in mid-central (50–60% centrality) PbPb collisions. This allows for a direct comparison of pPb and PbPb systems over a broad range of high particle multiplicities, allowing for a better understanding of the multiparticle nature of the observed correlations. 2. Method The event-plane method takes advantage of the long-range behavior by establishing an event-plane angle in one range of pseudorapidity and then measuring the correlations of particles in a different range with respect to this reference angle [8]. It can be expressed in terms of Q-vectors [9] as ⎞ M M ⎛⎜
⎟⎟ ⎜ ⎜ n sin (nΨn ) = ⎜⎜⎝ wi cos (nφi ) , n cos (nΨn ) , Q n = Qnx , Qny = Q wi sin (nφi )⎟⎟⎟⎠ . Q (1) i=1
where wi is the weight to optimize the resolution. Then Q∗ Qn |QnA nA | vn {EP} ≡ . QnA Q∗nB QnA Q∗nC |QnA | |QnB | |QnA | |QnC | Q
nB
i=1
(2)
Q∗ nC
|QnB | |QnC | The Qn vectors associated with the event planes A, B, and C (i.e., QnA , QnB , and QnC ) are based on either transverse energy or transverse momenta measured in the respective detectors, with wi (QnA ) and wi (QnB ) taken as the transverse energy measured in calorimeters and wi (QnC ) set to the transverse momentum of the particles detected in the tracker region. It has recently been noted and now experimentally confirmed by CMS [10], that the event-plane angle should not be considered as a global observable. This angle can vary as a function of transverse momentum and pseudorapidity. The variation with pseudorapidity can have a significant effect on the harmonic coefficient values (vn ) deduced using the event-plane method. Further studies show that, taking the pseudorapidity range of event plane C same as the particle of interest (POI), i.e. ηC = ηPOI , can account for the decorrelation effect if it is a Gaussian spreading. With a “twist” type decorrelation, this technique can partially account for the effect. The multiparticle correlation is measured using the Q-cumulant method [11]. By correlating the mparticles (m=4, 6, 8) within the reference phase space of |η| < 2.4 and pT range of 0.3 < pT < 3.0 GeV/c, the reference flow v2 {m} can be obtained. With respect to the reference flow, the differential v2 {m}(pT , η) can then be derived by replacing one of the m-particle cumulants with a particle from a certain POI phase space in pT or η. A software library is developed to explicitly calculate such cumulants. The LYZ method allows a direct study of the large-order behavior by using the asymptotic form of the cumulant expansion to relate locations of the zeros of a generating function to the azimuthal correlations. This method has been employed in previous CMS PbPb and pPb analyses [12, 13, 4]. 3. Results The momentum dependent v2 (pT ) results for the pPb and PbPb reactions are shown in Fig. 1 for the different methods. The event-plane results, shown separately for the p-going and Pb-going event planes, are found to be significantly higher than the multiparticle cumulant (v2 {6} and v2 {8}) and Lee-Yang Zeros (v2 {LYZ}) results. The two-particle correlations (v2 {2}) and 4-particle cumulant (v2 {4}) from Ref. [14] are also shown. The greater values found for v2 {EP} and v2 {2} suggest a significant, and expected, contribution of fluctuations in the initial state geometry to these results. The effect of event-plane decorrelation with pseudorapidity can be seen in Fig. 2 by comparing the p v2 {EP}(pT ) results within a symmetric pseudorapidity in the center-of-mass frame (v2 correspond to 2.0 < Pb η < 2.4, i.e. 1.6 < ηCM < 2.0, v2 correspond to −1.6 < η < −1.2, i.e. −2.0 < ηCM < −1.6), based on the two analyses with ηC = 0 and ηC = ηPOI .
Q. Wang / Nuclear Physics A 956 (2016) 753–756 v2{6} |η|<2.4
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Fig. 2. Left: Comparison of v2 (pT ) distributions based on event planes constructed from hadronic forward detector located on the p p-going (v2 ) and Pb-going (v2Pb ) sides of the tracker region, with ηC = 0. Right: Same, but with ηC = ηPOI .
The yield-weighted average v2 values with 0.3 ≤ pT < 3.0 GeV/c as a function of pseudorapidity are shown for the different analysis methods in Fig. 3. The pseudorapidity dependence is almost flat for the event-plane calculations where ηC = ηPOI . This is in contrast to the event-plane results for ηC = 0 and for the higher order particle correlations analyses, where the v2 values at larger pseudorapities are significantly smaller. It is only for the event-plane analysis with ηC = ηPOI that a partial accounting for the event-plane decorrelation behavior is achieved. Both the cumulant and LYZ analyses employ integral reference flows based on the full range of the CMS tracker and thus are not able to account for decorrelation effects. The different system dependence of v2 and v3 is illustrated in Fig. 4 where the event-plane results with ηC = ηPOI are shown for both systems. The v3 values, believed to result from initial geometry fluctuations, are almost identical for the two systems. The v2 values are likely to still reflect the lenticular shape of the collision geometry in the PbPb system, leading to larger v2 coefficients than seen for the pPb system. 4. Conclusion √ The η and pT dependence of the “elliptic flow” v2 coefficient is presented for pPb collisions at sNN = √ 5.02 TeV and for peripheral PbPb collisions with sNN = 2.76 TeV based on event-plane, multiparticle cumulant, and Lee-Yang Zeros analyses. The data are obtained using the CMS detector with the pseudorapidity coverage determined by the range of the CMS tracker detector, with |η| < 2.4. The pseudorapidity dependence of the “triangular flow” v3 coefficient is also presented based on an event-plane analysis. The event-plane analysis is done in both ways, accounting and not accounting event-plane decorrelation effects. Excluding the pseudorapidity decorrelation effects, little difference is found in v2 (pT ) between −2.0 < ηCM < −1.6 and 1.6 < ηCM < 2.0 in the range of pT < 2 GeV/c. In pPb and PbPb collisions, the offline show similar behavior, with the PbPb system values yield weighted v2 results at comparable values of Ntrk consistently about 20% higher than found for pPb collisions. No significant difference is observed for the PbPb v3 values as compared to pPb collisions.
Q. Wang / Nuclear Physics A 956 (2016) 753–756
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Fig. 3. v2 corresponding to event-plane, cumulant, and LYZ methods as a function of η in PbPb (left) and pPb (right) collisions for offline ranges. The v {EP} results are based on the furthest HF event plane in pseudorapidity. The pseudorapidities are given selected Ntrk 2 in the laboratory frame.
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√ √ Fig. 4. Elliptic (n=2) and triangular flow (n=3) harmonics for pPb collisions at sNN = 5.02 TeV and PbPb at sNN = 2.76 TeV with ηC = ηPOI . The v2 {EP} results are based on the furthest HF event plane in pseudorapidity.
References [1] S. Chatrchyan, et al., Observation of long-range near-side angular correlations in proton-lead collisions at the LHC, Phys. Lett. B 718 (2013) 795. arXiv:1210.5482, doi:10.1016/j.physletb.2012.11.025. √ [2] B. Abelev, et al., Long-range angular correlations on the near and away side in pPb collisions at sNN = 5.02 TeV , Phys. Lett. B 719 (2013) 29. arXiv:1212.2001, doi:10.1016/j.physletb.2013.01.012. √ [3] G. Aad, et al., Observation of Associated Near-side and Away-side Long-range Correlations in sNN = 5.02 TeV Proton-lead Collisions with the ATLAS DetectorarXiv:1212.5198. [4] V. Khachatryan, et al., Evidence for collective multi-particle correlations in pPb collisionsarXiv:1502.05382. [5] J.-Y. Ollitrault, Anisotropy as a signature of transverse collective flow, Phys. Rev. D 46 (1992) 229. doi:10.1103/PhysRevD.46.229. [6] S. Voloshin, Y. Zhang, Flow study in relativistic nuclear collisions by Fourier expansion of azimuthal particle distributions, Z. Phys. C 70 (1996) 665. arXiv:hep-ph/9407282, doi:10.1007/s002880050141. [7] P. Bozek, A. Bzdak, G.-L. Ma, Rapidity dependence of elliptic and triangular flow in proton-nucleus collisions from collective dynamicsarXiv:1503.03655. [8] A. M. Poskanzer, S. Voloshin, Methods for analyzing anisotropic flow in relativistic nuclear collisions, Phys.Rev. C58 (1998) 1671–1678. arXiv:nucl-ex/9805001, doi:10.1103/PhysRevC.58.1671. [9] M. Luzum, J.-Y. Ollitrault, Eliminating experimental bias in anisotropic-flow measurements of high-energy nuclear collisions, Phys.Rev. C87 (4) (2013) 044907. arXiv:1209.2323, doi:10.1103/PhysRevC.87.044907. [10] V. Khachatryan, et al., Evidence for transverse momentum and pseudorapidity dependent event plane fluctuations in PbPb and pPb collisionsarXiv:1503.01692. [11] A. Bilandzic, R. Snellings, S. Voloshin, Flow analysis with cumulants: Direct calculations, Phys.Rev. C83 (2011) 044913. arXiv:1010.0233, doi:10.1103/PhysRevC.83.044913. [12] S. Chatrchyan, et al., Measurement of the elliptic anisotropy of charged particles produced in PbPb collisions at nucleon-nucleon center-of-mass energy = 2.76 TeV, Phys. Rev. C 87 (2013) 014902. arXiv:1204.1409, doi:10.1103/PhysRevC.87.014902. √ [13] S. Chatrchyan, et al., Measurement of higher-order harmonic azimuthal anisotropy in PbPb collisions at sNN = 2.76 TeV, Phys.Rev. C89 (4) (2014) 044906. arXiv:1310.8651, doi:10.1103/PhysRevC.89.044906. [14] S. Chatrchyan, et al., Multiplicity and transverse momentum dependence of two- and four-particle correlations in pPb and PbPb collisions, Phys.Lett. B724 (2013) 213–240. arXiv:1305.0609, doi:10.1016/j.physletb.2013.06.028.
Nuclear Physics A 956 (2016) 753–756 www.elsevier.com/locate/nuclphysa
Flow Harmonics vn in pPb and PbPb Collisions Quan Wang CERN Building 42-1-22, Geneva 23, Switzerland CH-1211
Abstract Previous CMS measurements have demonstrated the collective nature of multiparticle correlations in high-multiplicity pPb collisions at the LHC. This collectivity is consistent with a hydrodynamic flow origin. However, it can also be interpreted in terms of initial state effects arising from gluon saturation. The pseudorapidity dependence of the azimuthal Fourier coefficients (vn ) is expected to be sensitive to the underlying mechanism with, in the hydrodynamic picture, the longer lifetime of the fireball on the Pb-going side expected to lead to a larger flow signal than found on the p-going side. To investigate the detailed properties of the observed collectivity, differential vn values in transverse momentum (pT ) and pseudorapidity (η) are presented over the full range of the CMS tracker detector (−2.4 < η < 2.4) for pPb collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV. Results based on multiparticle analyses involving four or more particles are shown. An event plane analysis is presented where the influence of recently demonstrated event-plane decorrelation is considered. Comparisons are made with peripheral PbPb collisions measured at similar mid-rapidity particle multiplicities. The results will be discussed in the context of current models of the longitudinal dependence of the multiparticle correlations. Keywords: Flow, Multiparticle Cumulant, Event Plane, Lee-Yang Zeros
1. Introduction Recent studies of multiparticle correlations in proton on lead collisions have raised the prospect that a quark-gluon plasma droplet might be formed that exhibits fluid-like behavior [1, 2, 3, 4]. In AA collisions, the long-range two-particle correlations are attributed to the collective flow from a strongly interacting, expanding medium [5]. The detailed azimuthal angle distribution of emitted particles can be characterized by its Fourier components [6]. In particular, the second and third Fourier components, known as elliptic and triangular flow, respectively, most directly reflect the medium response to the initial collision geometry and to its fluctuations. To provide further constraints on the theoretical understanding of the particle production mechanism in different collision systems, this analysis presents results on the pseudorapidity η and pT dependence of flow harmonics vn from pPb and PbPb collisions using the 4-, 6- and 8-particle Q-cumulant method, the Lee-Yang Zeros (LYZ) method, and the event-plane method. Within the hydrodynamic picture, the longer lifetime of the medium for pseudorapidities on the Pb-going side in pPb collisions is expected to lead to larger values for the flow harmonics than found for the p-going side pseudorapidities [7]. The pPb system is √ studied at sNN = 5.02 TeV using high-statistics data obtained by the CMS experiment during the 2013 pPb run at the LHC. With a large data sample, the particle correlations have been studied in a regime of high http://dx.doi.org/10.1016/j.nuclphysa.2016.02.073 0375-9474/© 2016 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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multiplicity pPb collisions comparable to the particle multiplicity in mid-central (50–60% centrality) PbPb collisions. This allows for a direct comparison of pPb and PbPb systems over a broad range of high particle multiplicities, allowing for a better understanding of the multiparticle nature of the observed correlations. 2. Method The event-plane method takes advantage of the long-range behavior by establishing an event-plane angle in one range of pseudorapidity and then measuring the correlations of particles in a different range with respect to this reference angle [8]. It can be expressed in terms of Q-vectors [9] as ⎞ M M ⎛⎜
⎟⎟ ⎜ ⎜ n sin (nΨn ) = ⎜⎜⎝ wi cos (nφi ) , n cos (nΨn ) , Q n = Qnx , Qny = Q wi sin (nφi )⎟⎟⎟⎠ . Q (1) i=1
where wi is the weight to optimize the resolution. Then Q∗ Qn |QnA nA | vn {EP} ≡ . QnA Q∗nB QnA Q∗nC |QnA | |QnB | |QnA | |QnC | Q
nB
i=1
(2)
Q∗ nC
|QnB | |QnC | The Qn vectors associated with the event planes A, B, and C (i.e., QnA , QnB , and QnC ) are based on either transverse energy or transverse momenta measured in the respective detectors, with wi (QnA ) and wi (QnB ) taken as the transverse energy measured in calorimeters and wi (QnC ) set to the transverse momentum of the particles detected in the tracker region. It has recently been noted and now experimentally confirmed by CMS [10], that the event-plane angle should not be considered as a global observable. This angle can vary as a function of transverse momentum and pseudorapidity. The variation with pseudorapidity can have a significant effect on the harmonic coefficient values (vn ) deduced using the event-plane method. Further studies show that, taking the pseudorapidity range of event plane C same as the particle of interest (POI), i.e. ηC = ηPOI , can account for the decorrelation effect if it is a Gaussian spreading. With a “twist” type decorrelation, this technique can partially account for the effect. The multiparticle correlation is measured using the Q-cumulant method [11]. By correlating the mparticles (m=4, 6, 8) within the reference phase space of |η| < 2.4 and pT range of 0.3 < pT < 3.0 GeV/c, the reference flow v2 {m} can be obtained. With respect to the reference flow, the differential v2 {m}(pT , η) can then be derived by replacing one of the m-particle cumulants with a particle from a certain POI phase space in pT or η. A software library is developed to explicitly calculate such cumulants. The LYZ method allows a direct study of the large-order behavior by using the asymptotic form of the cumulant expansion to relate locations of the zeros of a generating function to the azimuthal correlations. This method has been employed in previous CMS PbPb and pPb analyses [12, 13, 4]. 3. Results The momentum dependent v2 (pT ) results for the pPb and PbPb reactions are shown in Fig. 1 for the different methods. The event-plane results, shown separately for the p-going and Pb-going event planes, are found to be significantly higher than the multiparticle cumulant (v2 {6} and v2 {8}) and Lee-Yang Zeros (v2 {LYZ}) results. The two-particle correlations (v2 {2}) and 4-particle cumulant (v2 {4}) from Ref. [14] are also shown. The greater values found for v2 {EP} and v2 {2} suggest a significant, and expected, contribution of fluctuations in the initial state geometry to these results. The effect of event-plane decorrelation with pseudorapidity can be seen in Fig. 2 by comparing the p v2 {EP}(pT ) results within a symmetric pseudorapidity in the center-of-mass frame (v2 correspond to 2.0 < Pb η < 2.4, i.e. 1.6 < ηCM < 2.0, v2 correspond to −1.6 < η < −1.2, i.e. −2.0 < ηCM < −1.6), based on the two analyses with ηC = 0 and ηC = ηPOI .
Q. Wang / Nuclear Physics A 956 (2016) 753–756 v2{6} |η|<2.4
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Fig. 2. Left: Comparison of v2 (pT ) distributions based on event planes constructed from hadronic forward detector located on the p p-going (v2 ) and Pb-going (v2Pb ) sides of the tracker region, with ηC = 0. Right: Same, but with ηC = ηPOI .
The yield-weighted average v2 values with 0.3 ≤ pT < 3.0 GeV/c as a function of pseudorapidity are shown for the different analysis methods in Fig. 3. The pseudorapidity dependence is almost flat for the event-plane calculations where ηC = ηPOI . This is in contrast to the event-plane results for ηC = 0 and for the higher order particle correlations analyses, where the v2 values at larger pseudorapities are significantly smaller. It is only for the event-plane analysis with ηC = ηPOI that a partial accounting for the event-plane decorrelation behavior is achieved. Both the cumulant and LYZ analyses employ integral reference flows based on the full range of the CMS tracker and thus are not able to account for decorrelation effects. The different system dependence of v2 and v3 is illustrated in Fig. 4 where the event-plane results with ηC = ηPOI are shown for both systems. The v3 values, believed to result from initial geometry fluctuations, are almost identical for the two systems. The v2 values are likely to still reflect the lenticular shape of the collision geometry in the PbPb system, leading to larger v2 coefficients than seen for the pPb system. 4. Conclusion √ The η and pT dependence of the “elliptic flow” v2 coefficient is presented for pPb collisions at sNN = √ 5.02 TeV and for peripheral PbPb collisions with sNN = 2.76 TeV based on event-plane, multiparticle cumulant, and Lee-Yang Zeros analyses. The data are obtained using the CMS detector with the pseudorapidity coverage determined by the range of the CMS tracker detector, with |η| < 2.4. The pseudorapidity dependence of the “triangular flow” v3 coefficient is also presented based on an event-plane analysis. The event-plane analysis is done in both ways, accounting and not accounting event-plane decorrelation effects. Excluding the pseudorapidity decorrelation effects, little difference is found in v2 (pT ) between −2.0 < ηCM < −1.6 and 1.6 < ηCM < 2.0 in the range of pT < 2 GeV/c. In pPb and PbPb collisions, the offline show similar behavior, with the PbPb system values yield weighted v2 results at comparable values of Ntrk consistently about 20% higher than found for pPb collisions. No significant difference is observed for the PbPb v3 values as compared to pPb collisions.
Q. Wang / Nuclear Physics A 956 (2016) 753–756
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√ √ Fig. 4. Elliptic (n=2) and triangular flow (n=3) harmonics for pPb collisions at sNN = 5.02 TeV and PbPb at sNN = 2.76 TeV with ηC = ηPOI . The v2 {EP} results are based on the furthest HF event plane in pseudorapidity.
References [1] S. Chatrchyan, et al., Observation of long-range near-side angular correlations in proton-lead collisions at the LHC, Phys. Lett. B 718 (2013) 795. arXiv:1210.5482, doi:10.1016/j.physletb.2012.11.025. √ [2] B. Abelev, et al., Long-range angular correlations on the near and away side in pPb collisions at sNN = 5.02 TeV , Phys. Lett. B 719 (2013) 29. arXiv:1212.2001, doi:10.1016/j.physletb.2013.01.012. √ [3] G. Aad, et al., Observation of Associated Near-side and Away-side Long-range Correlations in sNN = 5.02 TeV Proton-lead Collisions with the ATLAS DetectorarXiv:1212.5198. [4] V. Khachatryan, et al., Evidence for collective multi-particle correlations in pPb collisionsarXiv:1502.05382. [5] J.-Y. Ollitrault, Anisotropy as a signature of transverse collective flow, Phys. Rev. D 46 (1992) 229. doi:10.1103/PhysRevD.46.229. [6] S. Voloshin, Y. Zhang, Flow study in relativistic nuclear collisions by Fourier expansion of azimuthal particle distributions, Z. Phys. C 70 (1996) 665. arXiv:hep-ph/9407282, doi:10.1007/s002880050141. [7] P. Bozek, A. Bzdak, G.-L. Ma, Rapidity dependence of elliptic and triangular flow in proton-nucleus collisions from collective dynamicsarXiv:1503.03655. [8] A. M. Poskanzer, S. Voloshin, Methods for analyzing anisotropic flow in relativistic nuclear collisions, Phys.Rev. C58 (1998) 1671–1678. arXiv:nucl-ex/9805001, doi:10.1103/PhysRevC.58.1671. [9] M. Luzum, J.-Y. Ollitrault, Eliminating experimental bias in anisotropic-flow measurements of high-energy nuclear collisions, Phys.Rev. C87 (4) (2013) 044907. arXiv:1209.2323, doi:10.1103/PhysRevC.87.044907. [10] V. Khachatryan, et al., Evidence for transverse momentum and pseudorapidity dependent event plane fluctuations in PbPb and pPb collisionsarXiv:1503.01692. [11] A. Bilandzic, R. Snellings, S. Voloshin, Flow analysis with cumulants: Direct calculations, Phys.Rev. C83 (2011) 044913. arXiv:1010.0233, doi:10.1103/PhysRevC.83.044913. [12] S. Chatrchyan, et al., Measurement of the elliptic anisotropy of charged particles produced in PbPb collisions at nucleon-nucleon center-of-mass energy = 2.76 TeV, Phys. Rev. C 87 (2013) 014902. arXiv:1204.1409, doi:10.1103/PhysRevC.87.014902. √ [13] S. Chatrchyan, et al., Measurement of higher-order harmonic azimuthal anisotropy in PbPb collisions at sNN = 2.76 TeV, Phys.Rev. C89 (4) (2014) 044906. arXiv:1310.8651, doi:10.1103/PhysRevC.89.044906. [14] S. Chatrchyan, et al., Multiplicity and transverse momentum dependence of two- and four-particle correlations in pPb and PbPb collisions, Phys.Lett. B724 (2013) 213–240. arXiv:1305.0609, doi:10.1016/j.physletb.2013.06.028.