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Mapping Nuclear Deformation with Differential Radial Flow in Heavy-Ion Collisions

Jie Zhu, Xiang-Yu Wu, Guang-You Qin

Abstract

In relativistic heavy-ion collisions, the radial flow of the fireball, usually characterized by transverse momentum spectra of final-state particles, encodes essential information about the hot and dense nuclear matter created in the collisions. However, the response of radial flow, including its $p_T$-differential structure $v_0(p_T)$ and longitudinal fluctuations $v_0(η)$, to intrinsic nuclear deformation remains unexplored. Using realistic $(3+1)$-dimensional viscous hydrodynamic calculations with Trento-3D initial conditions, we investigate how nuclear deformation affects the differential radial flow. We observe a clear, positive correlation between quadrupole deformation $β_2$ and radial flow: both magnitudes of $v_0$ and $v_0(p_T)$ are enhanced in central collisions when $β_2$ is increased. In contrast, the Pearson coefficient $ρ(n(p_T), [p_T])$ exhibits a universal step-like behavior across all collision systems and centralities. Further analysis of longitudinal decorrelation of radial flow reveals a rich structure: in central collisions, large $β_2$ tends to suppress the decorrelation, whereas hexadecapole deformation $β_4$ tends to enhance it. Such decorrelation effect increases toward peripheral collisions. Our results demonstrate that precise measurements of radial flow, spanning transverse momentum and longitudinal dependences, can provide powerful, complementary constraints on nuclear deformation in high-energy nucleus-nucleus collisions.

Mapping Nuclear Deformation with Differential Radial Flow in Heavy-Ion Collisions

Abstract

In relativistic heavy-ion collisions, the radial flow of the fireball, usually characterized by transverse momentum spectra of final-state particles, encodes essential information about the hot and dense nuclear matter created in the collisions. However, the response of radial flow, including its -differential structure and longitudinal fluctuations , to intrinsic nuclear deformation remains unexplored. Using realistic -dimensional viscous hydrodynamic calculations with Trento-3D initial conditions, we investigate how nuclear deformation affects the differential radial flow. We observe a clear, positive correlation between quadrupole deformation and radial flow: both magnitudes of and are enhanced in central collisions when is increased. In contrast, the Pearson coefficient exhibits a universal step-like behavior across all collision systems and centralities. Further analysis of longitudinal decorrelation of radial flow reveals a rich structure: in central collisions, large tends to suppress the decorrelation, whereas hexadecapole deformation tends to enhance it. Such decorrelation effect increases toward peripheral collisions. Our results demonstrate that precise measurements of radial flow, spanning transverse momentum and longitudinal dependences, can provide powerful, complementary constraints on nuclear deformation in high-energy nucleus-nucleus collisions.
Paper Structure (14 sections, 15 equations, 11 figures)

This paper contains 14 sections, 15 equations, 11 figures.

Table of Contents

  1. Introduction
  2. The multi-stage hybrid framework
  3. TRENTo-3D
  4. CLVisc
  5. Results and discussions
  6. Calibration
  7. Radial flow observables
  8. Integrated radial flow observable $v_0$
  9. $p_T$-differential radial flow observable $v_0(p_T)$
  10. $\eta$-differential radial flow observable $v_0(\eta)$ and longitudinal decorrelation $r_0(\eta)$
  11. Summary and outlook
  12. ACKNOWLEDGMENTS
  13. The sensitivity of $P([p_T])$ to system size and nuclear shape
  14. Scaled differential radial flow $v_0(p_T)/v_0$

Figures (11)

  • Figure 1: Comparison of the numerical results for the pseudorapidity dependence of charged hadrons production in various centrality classes of Au+Au and U+U collisions at $\sqrt{s_{NN}}=$200 GeV with experimental measurements from PHOBOS PHOBOS:2010eyu and PHENIX PHENIX:2015tbb.
  • Figure 2: Comparison of numerical simulations for the $p_T$ spectra (upper) and the mean $p_T$ (lower) in various centrality classes of Au+Au and U+U collisions at $\sqrt{s_{NN}}$=200 GeV with experimental measurements from PHENIX PHENIX:2003iij and STAR STAR:2008medSTAR:2022nvh.
  • Figure 3: Centrality dependence of the integrated radial flow ($v_0$), the fluctuation and the mean value of $[p_T]$ in Au+Au and U+U collisions, and their ratios between U+U and Au+Au collisions. Different deformation shapes of uranium are also explored. The experimental data are from STAR:2024wgy.
  • Figure 4: Transverse momentum dependence of radial flow in Au+Au and U+U collisions for several deformation parameters in three centrality bins: 0-10%, 20-30% and 40-50%.
  • Figure 5: Pearson correlation coefficient between $n(p_T)$ and the mean $p_T$ in five centrality classes for different collision systems and deformation parameters.
  • ...and 6 more figures