Elliptic and Triangular Flow in $p$-Pb and Peripheral Pb-Pb Collisions from Parton Scatterings

Using a multiphase transport model (AMPT) we calculate the elliptic $v_2$ and triangular $v_3$ Fourier coefficients of the two-particle azimuthal correlation function in proton-nucleus ($p$-Pb) and peripheral nucleus-nucleus (Pb-Pb) collisions. Our results for $v_3$ are in a good agreement with the CMS data collected at the Large Hadron Collider. The $v_2$ coefficient is very well described in $p$-Pb collisions and is underestimated for higher transverse momenta in Pb-Pb interactions. The characteristic mass ordering of $v_2$ in $p$-Pb is reproduced, whereas for $v_3$, this effect is not observed. We further predict the pseudorapidity dependence of $v_2$ and $v_3$ in $p$-Pb and observe that both are increasing when going from a proton side to a Pb-nucleus side. Predictions for the higher-order Fourier coefficients, $v_4$ and $v_5$, in $p$-Pb are also presented.

Figure 1

The transverse momentum dependence of the elliptic $v_2$ and triangular $v_3$ flow coefficients in $p$-Pb (upper panel) and Pb-Pb collisions (lower panel) as obtained in the AMPT model (open symbols) with the string melting mechanism. Different centrality classes are defined by the number of produced charged particles $N_{\text{track}}$ measured in $|\eta |<2.4$ and $p_T>0.4\mathrm{GeV}/c$. The CMS data are denoted by the full points.

Figure 2

The CMS data (full points) vs the AMPT model (open symbols) with the string melting mechanism for the integrated elliptic $v_2$ and triangular $v_3$ flow coefficients in $p$-Pb (left) and Pb-Pb (right) collisions as a function of the number of produced charged particles $N_{\text{track}}$ measured in $|\eta |<2.4$ and $p_T>0.4\mathrm{GeV}/c$.

Figure 3

The elliptic and triangular flow coefficients in $p$-Pb ($120<N_{\text{track}}<260$) as a function of the transverse momentum for pions, kaons, and protons as obtained in the AMPT model with the string melting mechanism.

Figure 4

Two narrow bins in pseudorapidity with $\mathrm{\Sigma }\eta ={\eta }_1+{\eta }_2\sim 0$. We shift both bins simultaneously to study the dependence of $C(\mathrm{\Delta }\varphi )$ on $\mathrm{\Sigma }\eta$ at a given $\mathrm{\Delta }\eta ={\eta }_2-{\eta }_1$.

Figure 5

The second and the third Fourier coefficients, as a function of the pseudorapidity sum $\mathrm{\Sigma }\eta ={\eta }_1+{\eta }_2$ at a given pseudorapidity separation $\mathrm{\Delta }\eta \sim 4$. Increasing $\mathrm{\Sigma }\eta$ corresponds to shifting towards a Pb-nucleus fragmentation region.

Figure 6

The AMPT results for the two-particle azimuthal correlation function Fourier coefficients as a function of the transverse momentum in $p$-Pb collisions.