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Energy Dependence of Elliptic Flow Ratio $v_{2}^{\text{PP}}$/$v_{2}^{\text{RP}}$ in Heavy-ion Collisions Using the AMPT Model

Shaowei Lan, Qiuhua Liu, Yong Li, Shusu Shi

TL;DR

The paper investigates how initial-state geometry fluctuations are transformed into final-state momentum anisotropy in Au+Au collisions over the BES-I energy range using the AMPT model with string melting. By computing $v_2$ relative to the participant plane ($v_2^{\text{PP}}$) and the reaction plane ($v_2^{\text{RP}}$) and examining their ratio $v_2^{\text{PP}}/v_2^{\text{RP}}$ across energies, centralities, and hadronic cascade times, the study isolates the role of the partonic vs hadronic phases. The main findings are that the ratio is largely insensitive to hadronic rescattering, increases with beam energy, and saturates above $\sqrt{s_{NN}} \approx 62.4$ GeV, with a pronounced centrality dependence that peaks in central events and dips in mid-central events. These results imply that sufficient partonic interactions are required to convert initial geometric fluctuations into final momentum anisotropy, providing a sensitive probe of the early-time partonic dynamics and the relative importance of the partonic vs hadronic phases in heavy-ion collisions.

Abstract

We present a systematic study of the elliptic flow $v_2$ relative to the participant plane (PP) and reaction plane (RP) in Au+Au collisions at $\sqrt{s_{NN}} = 7.7$-200 GeV using the AMPT model with the string melting version. The ratio $v_{2}^{\text{PP}}$/$v_{2}^{\text{RP}}$ is investigated under different hadronic cascade times (0.6 fm/$c$, 10 fm/$c$, and the maximum evolution time) and across various collision centralities. The results show that, at a fixed collision energy, the ratio exhibits negligible sensitivity to the duration of the hadronic rescattering stage, indicating that hadronic interactions have little effect on the relative difference generated by initial-state fluctuations. However, a strong energy dependence is observed, the ratio increases with beam energy and saturates above $\sqrt{s_{NN}} \approx 62.4$ GeV, a trend that persists across all centralities. These findings highlight the dominant role of the partonic phase in converting initial-state geometry fluctuations into final-state momentum anisotropy. Conversely, at lower energies, the reduced partonic interaction strength limits this conversion efficiency, weakening the system's ability to preserve the initial geometric information. Our results suggest that the conversion of initial geometric fluctuations into final momentum anisotropy requires sufficient partonic interactions.

Energy Dependence of Elliptic Flow Ratio $v_{2}^{\text{PP}}$/$v_{2}^{\text{RP}}$ in Heavy-ion Collisions Using the AMPT Model

TL;DR

The paper investigates how initial-state geometry fluctuations are transformed into final-state momentum anisotropy in Au+Au collisions over the BES-I energy range using the AMPT model with string melting. By computing relative to the participant plane () and the reaction plane () and examining their ratio across energies, centralities, and hadronic cascade times, the study isolates the role of the partonic vs hadronic phases. The main findings are that the ratio is largely insensitive to hadronic rescattering, increases with beam energy, and saturates above GeV, with a pronounced centrality dependence that peaks in central events and dips in mid-central events. These results imply that sufficient partonic interactions are required to convert initial geometric fluctuations into final momentum anisotropy, providing a sensitive probe of the early-time partonic dynamics and the relative importance of the partonic vs hadronic phases in heavy-ion collisions.

Abstract

We present a systematic study of the elliptic flow relative to the participant plane (PP) and reaction plane (RP) in Au+Au collisions at -200 GeV using the AMPT model with the string melting version. The ratio / is investigated under different hadronic cascade times (0.6 fm/, 10 fm/, and the maximum evolution time) and across various collision centralities. The results show that, at a fixed collision energy, the ratio exhibits negligible sensitivity to the duration of the hadronic rescattering stage, indicating that hadronic interactions have little effect on the relative difference generated by initial-state fluctuations. However, a strong energy dependence is observed, the ratio increases with beam energy and saturates above GeV, a trend that persists across all centralities. These findings highlight the dominant role of the partonic phase in converting initial-state geometry fluctuations into final-state momentum anisotropy. Conversely, at lower energies, the reduced partonic interaction strength limits this conversion efficiency, weakening the system's ability to preserve the initial geometric information. Our results suggest that the conversion of initial geometric fluctuations into final momentum anisotropy requires sufficient partonic interactions.

Paper Structure

This paper contains 4 sections, 5 equations, 5 figures.

Table of Contents

  1. Introduction
  2. The AMPT model
  3. Results and discussions
  4. Summary

Figures (5)

  • Figure 1: The top panels show $v_2$ of charged hadrons as a function of $p_T$ for Au+Au 20-30% collisions at $\sqrt{s_{NN}} = 7.7,19.6, 39, 62.4,$ and 200 GeV from AMPT model at midrapidity ($|\eta|<$1). The results are shown with a parton-parton cross section of 3 mb and a hadronic cascade time evolved up to the maximum evolution time. The open circles and open squares represent the results of $v_{2}^{\text{PP}}$ and $v_{2}^{\text{RP}}$, respectively. The bottom panels show the ratio of $v_{2}^{\text{PP}}$/$v_{2}^{\text{RP}}$ as a function of $p_T$ for all centralities.
  • Figure 2: The ratio of elliptic flow coefficients $v_{2}^{\text{PP}}$/$v_{2}^{\text{RP}}$ and corresponding eccentricity ratio $\epsilon_{2}{\text{(PP)}} / \epsilon{\text{(RP)}}$ of charged hadrons as a function of collision centrality for Au+Au collisions at $\sqrt{s_{NN}} = 7.7,19.6, 39, 62.4,$ and 200 GeV from the AMPT model at midrapidity ($|\eta|<$1). The results are shown for a parton-parton cross section of 3 mb and a hadronic cascade time evolved up to the maximum evolution time. The black open circles represent the $v_{2}^{\text{PP}}$/$v_{2}^{\text{RP}}$ ratios, while the red open squares denote the $\epsilon_{2}{\text{(PP)}} / \epsilon{\text{(RP)}}$ ratios.
  • Figure 3: The top panels show $v_2$ of charged hadrons as a function of $p_T$ for Au+Au 20-30% collisions at $\sqrt{s_{NN}} = 39$ GeV from AMPT model at midrapidity ($|\eta|<$1). The results are shown for a parton-parton cross section of 3 mb and three different values of hadronic cascade time periods. The open circles and open squares represent the results of $v_{2}^{\text{PP}}$ and $v_{2}^{\text{RP}}$, respectively. The bottom panels show the ratio of $v_{2}^{\text{PP}}$/$v_{2}^{\text{RP}}$ as a function of $p_T$ for the three different values of hadronic cascade time. The red line represents the constant fit to the ratios.
  • Figure 4: The ratio of $v_{2}^{\text{PP}}$/$v_{2}^{\text{RP}}$ of charged hadrons as a function of collision energy for Au+Au 20-30% collisions from AMPT model. The results are shown for a parton-parton cross section of 3 mb and three different value of hadronic cascade time of 0.6 fm/$c$, 10 fm/$c$, and 30 fm/$c$, respectively.
  • Figure 5: The ratio of $v_{2}^{\text{PP}}$/$v_{2}^{\text{RP}}$ of charged hadrons as a function of collision energy for Au+Au collisions at 0-10%, 10-40% and 40-80% from AMPT model. The results are shown for a parton-parton cross section of 3 mb and a hadronic cascade time of 30 fm/$c$.