Investigations of Anisotropic Flow Using Multiparticle Azimuthal Correlations in $pp$, $p\text{−}\mathrm{Pb}$, Xe-Xe, and Pb-Pb Collisions at the LHC

Measurements of anisotropic flow coefficients ($v_n$) and their cross-correlations using two- and multiparticle cumulant methods are reported in collisions of $pp$ at $\sqrt{s}=13\mathrm{TeV}$, $p\text{−}\mathrm{Pb}$ at a center-of-mass energy per nucleon pair $\sqrt{s_{\mathrm{NN}}}=5.02\mathrm{TeV}$, Xe-Xe at $\sqrt{s_{\mathrm{NN}}}=5.44\mathrm{TeV}$, and Pb-Pb at $\sqrt{s_{\mathrm{NN}}}=5.02\mathrm{TeV}$ recorded with the ALICE detector. The multiplicity dependence of $v_n$ is studied in a very wide range from 20 to 3000 particles produced in the midrapidity region $|\eta |<0.8$ for the transverse momentum range $0.2<p_T<3.0\mathrm{GeV}/c$. An ordering of the coefficients $v_2>v_3>v_4$ is found in $pp$ and $p\text{−}\mathrm{Pb}$ 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 a novel subevent method, $v_2$ measured with four-particle cumulants is found to be compatible with that from six-particle cumulants in $pp$ and $p\text{−}\mathrm{Pb}$ collisions. The magnitude of the correlation between $v_n^2$ and $v_m^2$, evaluated with the symmetric cumulants $\mathrm{SC}(m,n)$ is observed to be positive at all multiplicities for $v_2$ and $v_4$, while for $v_2$ and $v_3$ it is negative and changes sign for multiplicities below 100, which may indicate a different $v_n$ fluctuation pattern in this multiplicity range. The observed long-range multiparticle azimuthal correlations in high multiplicity $pp$ and $p\text{−}\mathrm{Pb}$ collisions can neither be described by pythia 8 nor by impact-parameter-Glasma, music, and ultrarelativistic quantum molecular dynamics model calculations, and hence, provide new insights into the understanding of collective effects in small collision systems.

Figure 1

Multiplicity dependence of $v_n\{k\}$ for $pp$, $p\text{−}\mathrm{Pb}$, Xe-Xe, and Pb-Pb collisions. Statistical uncertainties are shown as vertical lines and systematic uncertainties as filled boxes. Data are compared with pythia 8.210 Monash 2013 [53] simulations (solid lines) of $pp$ collisions at $\sqrt{s}=13\mathrm{TeV}$ and impact-parameter-Glasma, music, and ultrarelativistic quantum molecular dynamics (IP-Glasma+music+UrQMD) [31, 54] calculations of $pp$, $p\text{−}\mathrm{Pb}$, Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02\mathrm{TeV}$, and Xe-Xe collisions at $\sqrt{s_{\mathrm{NN}}}=5.44\mathrm{TeV}$ (filled bands). The width of the band represents the statistical uncertainty of the model. (a), (b), and (c): $v_2$, $v_3$, and $v_4$ measured using two-particle cumulants with a pseudorapidity separation $|\mathrm{\Delta }\eta |>1.4$, 1.0 and 1.0, respectively. (d) $v_2$ measured using multiparticle cumulants, with the three-subevent method for the four-particle cumulant, and two-subevent method for higher order cumulants in Pb-Pb collisions.

Figure 2

Multiplicity dependence of the (a) and (c) symmetric cumulant $\mathrm{SC}(m,n{)}_{3-\mathrm{sub}}$ and (b) and (d) normalized ratio $\mathrm{SC}(m,n{)}_{3-\mathrm{sub}}/⟨v_m^2⟩⟨v_n^2⟩$ for $pp$, $p\text{−}\mathrm{Pb}$, Xe-Xe and Pb-Pb collisions. Observables in the denominator are obtained from the $v_2\{2,|\mathrm{\Delta }\eta |>1.4\}$ and $v_n\{2,|\mathrm{\Delta }\eta |>1.0\}$ for higher harmonics. Statistical uncertainties are shown as vertical lines and systematic uncertainties as filled boxes. The measurements in large collision systems are compared with the IP-Glasma+music+UrQMD [31, 54] calculations and results in $pp$ collisions are compared with the pythia 8 model [53].