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CMS-HIN-18-015 ; CERN-EP-2019-031
Correlations of azimuthal anisotropy Fourier harmonics in pPb collisions at ${\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}} = $ 8.16 TeV
Phys. Rev. C 103 (2021) 014902
Abstract: Event-by-event correlations of azimuthal anisotropy Fourier coefficients ($v_n$) in 8.16 TeV pPb collision data, collected by the CMS experiment at the LHC, are extracted using a subevent four-particle cumulant technique. The pseudorapidity range of the CMS tracker from $ -2.4 $ to $ 2.4 $ is divided into either two, three, or four distinct subevent regions. Each combination of four particles constructed from tracks with transverse momentum between 0.3 and 3.0 GeV is then analyzed in terms of how the particles populate the subevents. Using the subevent technique, correlations between $v_n$ of different orders are measured as functions of particle multiplicity and compared to the standard cumulant method without subevents. At high multiplicity, the $v_2$ and $v_3$ coefficients exhibit an anticorrelation; this behavior is observed consistently using various methods. The $v_2$ and $v_4$ correlation strength is found to depend on the number of subevents used in the calculation. At low-multiplicities, the results from different methods diverge because of different contributions of few-particle correlations. These findings significantly lower the multiplicity range that was previously established for the onset of collective behavior in small systems.
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Figure 1:
The $\text {SC}(2,3)$ (left) and $\text {SC}(2,4)$ (right) distributions as functions of $ {N_\mathrm {trk}^\mathrm {offline}} $ from 2 subevents (full blue circles), 3 subevents (red squares), and 4 subevents (green crosses). For comparison, published results from Ref. [34] with no subevents (open black circles), are also shown. Bars represent statistical uncertainties while grey areas represent the systematic uncertainties.

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Figure 2:
The relative difference of $\text {SC}(2,3)$ (left) and $\text {SC}(2,4)$ (right) between 2 and 3 subevents (red squares) as well as between 2 and 4 subevents (green crosses) as a function of $ {N_\mathrm {trk}^\mathrm {offline}} $. Bars represent statistical uncertainties while shaded areas represent the systematic uncertainties.
The first measurement of event-by-event correlations of different Fourier harmonic orders in symmetric cumulants $\text{SC}(2,3)$ and $\text{SC}(2,4)$ with 2, 3, and 4 subevents in proton-lead (pPb) collisions at ${\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}} = $ 8.16 TeV is presented using data collected by the CMS experiment. The pPb data analyzed with the subevent method are compared to previously published results using the technique without subevents. In all cases, an anticorrelation is observed between the single-particle anisotropy harmonics $v_2$ and $v_3$, while $v_2$ and $v_4$ are positively correlated. For charged-particle multiplicity ${N_\mathrm{trk}^\mathrm{offline}} > $ 100, both standard and $n$-subevent methods give similar results for $\text{SC}(2,3)$, suggesting that nonflow effects have a small contribution in this region. The $\text{SC}(2,4)$ results show a different behavior in the same multiplicity region for different numbers of subevents. The contributions from other effects which might explain this difference for $\text{SC}(2,3)$ and $\text{SC}(2,4)$ remain to be studied. By suppressing the nonflow contribution, the subevent method reveals that harmonic correlations from collectivity extend below ${N_\mathrm{trk}^\mathrm{offline}} \sim $ 80, most clearly for $\text{SC}(2,3)$. The results presented in this paper show that the collectivity observed in small systems extends down to multiplicities ${N_\mathrm{trk}^\mathrm{offline}} \sim $ 50, and impose more constraints on theoretical interpretations of the origin of such observed collectivity.
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