Multiparticle azimuthal cumulants in $p+\mathrm{Pb}$ collisions from a multiphase transport model

A new subevent cumulant method was recently developed, which can significantly reduce the nonflow contributions in long-range correlations for small systems compared to the standard cumulant method. In this work, we study multiparticle cumulants in $p+\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV with a multiphase transport model (AMPT), including two- and four-particle cumulants ($c_2\left\{2\right\}$ and $c_2\left\{4\right\}$) and symmetric cumulants [SC(2, 3) and SC(2, 4)]. Our numerical results show that $v_2\left\{2\right\}$ is consistent with the experimental data, while the magnitude of $c_2\left\{4\right\}$ is smaller than the experimental data, which may indicate that either the collectivity is underestimated or some dynamical fluctuations are absent in the AMPT model. For the symmetric cumulants, we find that the results from the standard cumulant method are consistent with the experimental data, but those from the subevent cumulant method show different behaviors. The results indicate that the measurements from the standard cumulant method are contaminated by nonflow effects, especially when the number of produced particles is small. The subevent cumulant method is a better tool to explore the $real$ collectivity in small systems.

Figure 1

$v_2\left\{2\right\}$ as a function of the number of charge particles $\langle N_{\mathrm{ch}}\rangle$ in $p+\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV, where filled squares represent the AMPT results using the subevent method, while open squares and filled circles represent the two-particle correlation results (with $\left|\mathrm{\Delta }\eta \right|>2$) from the published AMPT results [32] and CMS data [52], respectively.

Figure 2

$c_2\left\{4\right\}$ as a function of the number of charge particles $\langle N_{\mathrm{ch}}\rangle$ in $p+\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV, where open squares, open circles, and filled squares represent the AMPT results using the standard cumulant, two-subevent, and three-subevent methods, respectively. Filled circles represent the ATLAS data using the three-subevent cumulant method [21].

Figure 3

AMPT results on $c_2\left\{2\right\}$ with the three-subevent method as a function of the number of charge particles $\langle N_{\mathrm{ch}}\rangle$ for four evolution stages, i.e., initial stage (open squares), after parton cascade (open circles), after coalescence (filled squares), and after hadronic recatterings (filled circles), in $p+\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV.

Figure 4

Same as Fig. 3, but for $c_2\left\{4\right\}$ with the three-subevent method.

Figure 5

SC(2, 3) as a function of the number of charge particles $\langle N_{\mathrm{ch}}\rangle$ from AMPT calculations using the standard cumulant (open squares), two-subevent (open circles), and three-subevent (filled squares) methods, in comparison with the experimental data with the standard cumulant method (filled circles) [24], in $p+\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV.

Figure 6

Same as Fig. 5, but for SC(2, 4).