# Investigations of anisotropic flow using multi-particle azimuthal correlations in pp, p-Pb, Xe-Xe, and Pb-Pb collisions at the LHC

Measurements of anisotropic flow coefficients ($v_n$) and their cross-correlations using two- and multi-particle cumulant methods are reported in collisions of pp at $\sqrt{s} = 13$ TeV, p-Pb at $\sqrt{s_{_{\rm NN}}} = 5.02$ TeV, Xe-Xe at $\sqrt{s_{_{\rm NN}}} = 5.44$ TeV, and Pb-Pb at $\sqrt{s_{_{\rm NN}}} = 5.02$ TeV recorded with the ALICE detector. These measurements are performed as a function of multiplicity in the mid-rapidity region $|\eta|<~0.8$ for the transverse momentum range $0.2 <~ p_{\rm T} <~ 3.0$ GeV/$c$. An ordering of the coefficients $v_2 > v_3 > v_4$ is found in pp and p-Pb collisions, similar to that seen in large collision systems, while a weak $v_2$ multiplicity dependence is observed relative to nucleus--nucleus collisions in the same multiplicity range. Using the novel subevent method, $v_{2}$ measured in pp and p-Pb collisions with four-particle cumulants is found to be compatible with that from six-particle cumulants. The symmetric cumulants $SC(m,n)$ calculated with the subevent method which evaluate the correlation strength between $v_n^2$ and $v_m^2$ are also presented. The presented data, which add further support to the existence of long-range multi-particle azimuthal correlations in high multiplicity pp and p-Pb collisions, can neither be described by PYTHIA8 nor by IP-Glasma+MUSIC+UrQMD model calculations, and hence provide new insights into the understanding of collective effects in small collision systems.

Accepted by: PRL
HEP Data
e-Print: arXiv:1903.01790 | PDF | inSPIRE
CERN-EP-2019-033

Figures

## Figure 1

 Multiplicity dependence of $v_n\{k\}$ for \pp, \pPb, \XeXe\ and \PbPb\ collisions. Statistical uncertainties are shown as vertical lines and systematic uncertainties as filled boxes (coloured online) Data are compared with PYTHIA 8~ simulations (solid lines) of pp collisions at $\sqrt{s} = 13$ TeV and IP-Glasma+MUSIC+UrQMD~ calculations of pp, \pPb, \PbPb\ collisions at $\snn = 5.02$ TeV and \XeXe\ collisions at $\snn = 5.44$ TeV (filled bands - coloured online) (a)~$v_2$, $v_3$ and $v_4$ measured using two-particle cumulants with a pseudorapidity gap greater than $1.4$ or $1.0$ units (b)~$v_2$ measured using multi-particle cumulants, with the 3-subevent method for the four-particle cumulant, and 2-subevent method for higher order cumulants in \PbPb\ collisions.

## Figure 2

 Multiplicity dependence of the symmetric cumulant (a) $SC(3,2)_{\rm{3-sub}}$ and (b) $SC(4,2)_{\rm{3-sub}}$ for \pp, \pPb, \XeXe\ and \PbPb\ collisions. Statistical uncertainties are shown as vertical lines and systematic uncertainties as filled boxes (coloured online). The measurements in large collision systems are compared with the IP-Glasma+MUSIC+UrQMD~ calculations and results in pp collisions are compared with the PYTHIA 8 model~.

## Figure 3

 Multiplicity dependence of (a) SC$(3,2)_{\rm{3-sub}} / \langle v_3^2\rangle\langle v_2^2\rangle$ and (b) SC$(4,2)_{\rm{3-sub}} / \langle v_4^2\rangle\langle v_2^2\rangle$ for \pp, \pPb, \XeXe\ and \PbPb\ collisions. Observables in the denominator are obtained from the two-particle cumulants with a pseudorapidity gap $|\Delta\eta| > 1.4$ for $v_2$ and $|\Delta\eta| > 1.0$ for higher harmonics. Statistical uncertainties are shown as vertical lines and systematic uncertainties as filled boxes (coloured online). The results are compared with PYTHIA 8~ and the IP-Glasma+MUSIC+UrQMD~ calculations.