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Response relation in Pb-Pb and p-Pb collisions at 5.02 TeV

We carry out simulations using a multi-phase transport (AMPT) model to describe the response relation between $v_2$ and $\varepsilon_2$ in Pb-Pb and p-Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV, respectively. To simulate such relation, two methods have been introduced in the calculation: one is the directed response (DR) method, which correlates the outgoing particles with the initial anisotropy directly, and the other one is the cumulants response (CR) method, which is constructed from a cumulants correlation between outgoing particles. Based on calculations of the DR and CR methods, the response relations as a function of the transverse momentum are both shown in Pb-Pb and p-Pb collisions. By comparing the DR and CR methods, we found that the linear response relations are almost identical in all the present collisions. Similar results of linear+cubic response relations are also shown in the higher multiplicity systems, and it has become a significant difference in the lower multiplicity systems, i.e., the peripheral Pb-Pb collisions and p-Pb collisions. Throughout the whole $p_{T}$-dependent simulations, the $κ_2$ in the linear response and in the linear+cubic response are almost identical, except for in the lower multiplicity systems by the DR method. If one implements a pseudorapidity gap by the CR calculation, the $p_{T}$-dependent and $η$-independent response relations are similarly shown in peripheral Pb-Pb systems and p-Pb systems, which may imply that a collective response exists in the most central p-Pb collisions. These collective behaviors are dominantly produced on the stage of the medium expansions.