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CMS-PAS-HIN-18-015
Measurement of correlated azimuthal anisotropy Fourier harmonics with subevent cumulants in pPb collisions at 8.16 TeV
Abstract: Event-by-event correlations of azimuthal anisotropy Fourier coefficients ($v_n$) in 8.16 TeV pPb data are extracted using a subevent four-particle cumulant technique with the CMS experiment at the LHC. Each combination of four particles is required to fall into two, three or four distinct subevents within the full pseudorapidity range from -2.4 to 2.4 using tracks with transverse momentum between 0.3 and 3.0 GeV/$c$. Using the subevent technique, $v_n$ correlations are measured as a function of particle multiplicity and compared to the standard method without using subevents. At high multiplicity, $v_2$ and $v_3$ anticorrelation exhibits a consistent behavior among the various methods. The $v_2$ and $v_4$ correlation strength is found to depend on the number of subevents used in the calculation. Toward the low-multiplicity region, data from different methods diverge because of different contributions of few-particle correlations. The results presented represent a key step in understanding the onset of collective behavior from low to high multiplicities in small systems.
Figures Summary Additional Figures References CMS Publications
Figures

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Figure 1:
$SC(2,3)$ and $SC(2,4)$ as a function of ${N_{\text{trk}}^{\text{offline}}}$ from 2-, 3- and 4-subevents method (blue, red and green full circles respectively). For comparison, published results from the Ref. [31] with no subevents (open black circles) are also shown. Shaded areas are the systematic uncertainties for these measurements.

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Figure 2:
Left: $SC(2,3)$ Relative difference from 2-, 3-subevents (red) and 2-, 4-subevents (green) as a function of $ {N_{\text{trk}}^{\text{offline}}} $. Right: $SC(2,4)$ Relative difference from 2-, 3-subevents (red) and 2-, 4-subevents (green) as a function of $ {N_{\text{trk}}^{\text{offline}}} $. Shaded areas are the systematic uncertainties for these measurements.
Summary
The first measurement of event-by-event correlations of different Fourier harmonic orders $SC(2,3)$ and $SC(2,4)$ with 2-, 3-, and 4-subevents in pPb collisions at ${\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV is presented using data collected by the CMS experiment at CERN. The pPb data analyzed with the subevent method are compared to previously published results using the calculation without subevents. In all cases, an anti-correlation is observed between $v_2$ and $v_3$, while $v_2$ and $v_4$ are positively correlated. For ${N_{\text{trk}}^{\text{offline}}} > $ 100, both, standard and $n$-subevent methods give similar results for $SC(2,3)$ suggesting that non-flow is not the dominant contribution in this region. The $SC(2,4)$ results show a different behavior in the same multiplicity region for different numbers of subevents, which emphasizes the sensitivity of cumulant calculations to other effects such as event-plane decorrelation. At multiplicities ${N_{\text{trk}}^{\text{offline}}} < $ 80, the subevent method suppresses the non-flow contribution and thus reveals the harmonic correlation from collectivity for ${N_{\text{trk}}^{\text{offline}}} > $ 50. The results presented in this note provide further strong evidence of collectivity observed in small systems down to multiplicities ${N_{\text{trk}}^{\text{offline}}} \sim $ 50, and will also impose more constraints on the theoretical interpretations. Future analysis with 4-subevents in pp and PbPb and comparison with present data from pPb collisions will further increase our understanding of how collective flow effects manifest themselves in small collision systems.
Additional Figures

png pdf
Additional Figure 1:
$SC(2,3)$ and $SC(2,4)$ as a function of $N_{\mathrm{trk}}^{\mathrm{offline}}$ from 2-, 3- and 4-subevents method (blue, red and green full circles respectively). For comparison, published results from the Ref. [1] with no subevents (open black circles) are also shown. Shaded areas are the systematic uncertainties for these measurements.
References
1 STAR Collaboration Distributions of charged hadrons associated with high transverse momentum particles in pp and Au + Au collisions at $ \sqrt{s_{\mathrm{NN}}}\ = $ 200 GeV PRL 95 (2005) 152301 nucl-ex/0501016
2 STAR Collaboration Long range rapidity correlations and jet production in high energy nuclear collisions PRC 80 (2009) 064912 0909.0191
3 PHOBOS Collaboration System size dependence of cluster properties from two- particle angular correlations in Cu+Cu and Au+Au collisions at $ \sqrt{s_{\mathrm{NN}}}\ = $ 200 GeV PRC 81 (2010) 024904 0812.1172
4 PHOBOS Collaboration High transverse momentum triggered correlations over a large pseudorapidity acceptance in Au+Au collisions at $ \sqrt{s_{\mathrm{NN}}}\ = $ 200 GeV PRL 104 (2010) 062301 0903.2811
5 STAR Collaboration Three-particle coincidence of the long range pseudorapidity correlation in high energy nucleus-nucleus collisions PRL 105 (2010) 022301 0912.3977
6 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
7 CMS Collaboration Centrality dependence of dihadron correlations and azimuthal anisotropy harmonics in PbPb collisions at $ \sqrt{s_{\mathrm{NN}}}\ = $ 2.76 TeV EPJC 72 (2012) 2012 CMS-HIN-11-006
1201.3158
8 ALICE Collaboration Harmonic decomposition of two-particle angular correlations in Pb-Pb collisions at $ \sqrt{s_{\mathrm{NN}}}\ = $ 2.76 TeV PLB 708 (2012) 249 1109.2501
9 ATLAS Collaboration Measurement of the azimuthal anisotropy for charged particle production in $ \sqrt{s_{\mathrm{NN}}}\ = $ 2.76 TeV lead-lead collisions with the ATLAS detector PRC 86 (2012) 014907 1203.3087
10 CMS Collaboration Studies of azimuthal dihadron correlations in ultra-central PbPb collisions at $ \sqrt{s_{\mathrm{NN}}}\ = $ 2.76 TeV JHEP 02 (2014) 088 CMS-HIN-12-011
1312.1845
11 J.-Y. Ollitrault Anisotropy as a signature of transverse collective flow PRD 46 (1992) 229
12 B. Alver and G. Roland Collision geometry fluctuations and triangular flow in heavy-ion collisions PRC 81 (2010) 054905 1003.0194
13 S. Voloshin and Y. Zhang Flow study in relativistic nuclear collisions by Fourier expansion of azimuthal particle distributions Z. Phys. C 70 (1996) 665 hep-ph/9407282
14 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) 034903 1504.01289
15 ALICE Collaboration Correlated event-by-event fluctuations of flow harmonics in Pb-Pb collisions at $ \sqrt{s_{_{\rm NN}}}= $ 2.76 TeV PRL 117 (2016) 182301 1604.07663
16 A. Bilandzic et al. Generic framework for anisotropic flow analyses with multiparticle azimuthal correlations PRC 89 (2014) 064904 1312.3572
17 B. H. Alver, C. Gombeaud, M. Luzum, and J.-Y. Ollitrault Triangular flow in hydrodynamics and transport theory PRC 82 (2010) 034913 1007.5469
18 B. Schenke, S. Jeon, and C. Gale Elliptic and triangular flow in event-by-event D=3+1 viscous hydrodynamics PRL 106 (2011) 042301 1009.3244
19 Z. Qiu, C. Shen, and U. Heinz Hydrodynamic elliptic and triangular flow in Pb-Pb collisions at $ \sqrt{s_{\mathrm{NN}}}\ = $ 2.76 TeV PLB 707 (2012) 151 1110.3033
20 G. Giacalone, L. Yan, J. Noronha-Hostler, and J.-Y. Ollitrault Symmetric cumulants and event-plane correlations in Pb + Pb collisions PRC 94 (2016) 014906 1605.08303
21 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
22 CMS Collaboration Measurement of long-range near-side two-particle angular correlations in pp collisions at $ \sqrt s = $ 13 TeV PRL 116 (2016) 172302 CMS-FSQ-15-002
1510.03068
23 ATLAS Collaboration Observation of Long-Range Elliptic Azimuthal Anisotropies in $ \sqrt{s}= $ 13 and 2.76 TeV pp Collisions with the ATLAS Detector PRL 116 (2016) 172301 1509.04776
24 ATLAS Collaboration Measurement of long-range pseudorapidity correlations and azimuthal harmonics in $ \sqrt{s_{NN}}= $ 5.02 TeV proton-lead collisions with the ATLAS detector PRC 90 (2014) 044906 1409.1792
25 CMS Collaboration Long-range two-particle correlations of strange hadrons with charged particles in pPb and PbPb collisions at LHC energies PLB 742 (2015) 200 CMS-HIN-14-002
1409.3392
26 LHCb Collaboration Measurements of long-range near-side angular correlations in $ \sqrt{s_{\text{NN}}}= $ 5 TeV proton-lead collisions in the forward region PLB 762 (2016) 473 1512.00439
27 STAR Collaboration Long-range pseudorapidity dihadron correlations in $ d $+Au collisions at $ \sqrt{s_{\rm NN}}= $ 200 GeV PLB 747 (2015) 265 1502.07652
28 CMS Collaboration Evidence for collective multi-particle correlations in pPb collisions PRL 115 (2015) 012301 CMS-HIN-14-006
1502.05382
29 CMS Collaboration Evidence for collectivity in pp collisions at the LHC PLB 765 (2017) 193 CMS-HIN-16-010
1606.06198
30 ATLAS Collaboration Measurement of multi-particle azimuthal correlations in $ pp $, $ p+ $Pb and low-multiplicity Pb$ + $Pb collisions with the ATLAS detector EPJC 77 (2017) 428 1705.04176
31 CMS Collaboration Observation of Correlated Azimuthal Anisotropy Fourier Harmonics in $ pp $ and $ p+Pb $ Collisions at the LHC PRL 120 (2018) 092301 CMS-HIN-16-022
1709.09189
32 P. Di Francesco, M. Guilbaud, M. Luzum, and J.-Y. Ollitrault Systematic procedure for analyzing cumulants at any order PRC 95 (2017) 044911 1612.05634
33 J. Jia, M. Zhou, and A. Trzupek Revealing long-range multiparticle collectivity in small collision systems via subevent cumulants PRC 96 (2017) 034906 1701.03830
34 ATLAS Collaboration Measurement of long-range multiparticle azimuthal correlations with the subevent cumulant method in $ pp $ and $ p + Pb $ collisions with the ATLAS detector at the CERN Large Hadron Collider PRC 97 (2018) 024904 1708.03559
35 P. Huo, K. Gajdosova, J. Jia, and Y. Zhou Importance of non-flow in mixed-harmonic multi-particle correlations in small collision systems PLB 777 (2018) 201--206 1710.07567
36 CMS Collaboration Description and performance of track and primary-vertex reconstruction with the CMS tracker JINST 9 (2014) P10009 CMS-TRK-11-001
1405.6569
37 CMS Collaboration The CMS experiment at the CERN LHC JINST 3 (2008) S08004 CMS-00-001
38 Geant4 Collaboration Geant4---a simulation toolkit Nucl. Instrum. and Meth. A 506 (2003) 250
39 CMS Collaboration Multiplicity and transverse momentum dependence of two- and four-particle correlations in pPb and PbPb collisions PLB 724 (2013) 213 CMS-HIN-13-002
1305.0609
40 CMS Collaboration Evidence for transverse momentum and pseudorapidity dependent event plane fluctuations in PbPb and pPb collisions PRC 92 (2015) 034911 CMS-HIN-14-012
1503.01692
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