Probing Nuclear Geometry through Multi-Particle Azimuthal Correlations and Rapidity-Even Dipolar Flow in ${}^{16}$O+${}^{16}$O Collisions

We study symmetric and asymmetric cumulants as well as rapidity-even dipolar flow in ${}^{16}$O+${}^{16}$O collisions at $\sqrt{s_{NN}} = 200$~GeV to explore $α$-clustering phenomena in light nuclei within the viscous relativistic hydrodynamics framework. Signatures of $α$-clustering manifest in the anisotropic flow coefficients and their correlations – particularly in observables involving elliptic-triangular flow correlations. We show that final-state symmetric and asymmetric cumulants – especially $\mathrm{NSC}(2,3)$ and $\mathrm{NAC}_{2,1}(2,3)$ – are sensitive to the initial nuclear geometry. Additionally, we observe a significant difference in rapidity-even dipolar flow, $v_1^{\text{even}}$, between $α$-clustered and Woods–Saxon configurations in high-multiplicity events. These findings underscore the pivotal role of nuclear structure in heavy-ion collision dynamics and provide observables for distinguishing nuclear geometries, particularly in ultra-central collisions.

💡 Research Summary

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This paper investigates how α‑clustering in light nuclei influences the final‑state observables of relativistic heavy‑ion collisions, focusing on ${}^{16}$O+${}^{16}$O collisions at $\sqrt{s_{NN}}=200$ GeV. The authors generate two families of initial nuclear configurations: a conventional Woods‑Saxon distribution described by a three‑parameter Fermi (3pF) function, and a tetrahedral α‑cluster model in which four α particles sit at the vertices of a regular tetrahedron. Three values of the cluster radius $r_{\alpha}$ (2.0 fm, 1.6 fm, 1.2 fm) are used to vary the compactness of the clusters while keeping the overall root‑mean‑square radius fixed at 2.73 fm. Initial entropy density profiles are produced with the TRENTo model, employing parameters ($p$, $k$, $w_c$, $d_{\rm min}$) tuned to reproduce Au+Au multiplicities at the same beam energy. Hydrodynamic evolution starts at $\tau_0=0.4$ fm/$c$ using the MUSIC code with a constant shear viscosity $\eta/s=0.08$ and a temperature‑dependent bulk viscosity $\zeta/s$ parameterized to match lattice QCD constraints. The equation of state is the NEoS‑B model, which smoothly interpolates between lattice results at high temperature and a hadron resonance gas at low temperature.

The study focuses on multi‑particle flow cumulants, which are more robust against non‑flow effects than single‑particle $v_n$ coefficients. The symmetric cumulant $\mathrm{SC}(m,n)$ measures the covariance of $v_m^2$ and $v_n^2$, and is normalized to $\mathrm{NSC}(m,n)=\mathrm{SC}(m,n)/\langle v_m^2\rangle\langle v_n^2\rangle$ to remove trivial magnitude dependence. The asymmetric cumulant $\mathrm{AC}{2,1}(m,n)$ captures genuine three‑particle correlations of the form $(v_m^2)v_n$, and its normalized version $\mathrm{NAC}{2,1}(m,n)$ is defined analogously. The authors compute $\mathrm{NSC}(2,3)$ and $\mathrm{NAC}_{2,1}(2,3)$ for both nuclear configurations across several centrality classes (0–0.1 %, 0–1 %, 0–5 %, 20–30 %, 40–50 %).

Results show a pronounced sensitivity to the initial geometry. For the ultra‑central (0–0.1 %) class, the α‑clustered nuclei yield a strongly negative $\mathrm{NSC}(2,3)\approx -0.12$, indicating an anti‑correlation between elliptic ($v_2$) and triangular ($v_3$) flow, whereas the Woods‑Saxon case gives a milder negative value around $-0.04$. The asymmetric cumulant $\mathrm{NAC}_{2,1}(2,3)$ follows the same trend, with absolute values roughly two to three times larger for the clustered configuration. The magnitude of these differences diminishes for more peripheral centralities, confirming that the most central collisions preserve the imprint of the initial spatial anisotropy.

In addition to higher‑order cumulants, the paper examines the rapidity‑even directed flow $v_1^{\rm even}$, extracted via the event‑plane method with a $p_T$‑dependent weight that enforces zero net transverse momentum. Because $v_1^{\rm even}$ is driven primarily by fluctuations of the dipole asymmetry $\varepsilon_1$ and is relatively insensitive to shear viscosity, it serves as a clean probe of the initial dipole geometry. The simulations reveal that in high‑multiplicity events the clustered nuclei produce a measurable positive $v_1^{\rm even}\sim 3\times10^{-3}$ for low $p_T$ particles, while the Woods‑Saxon nuclei yield values consistent with zero. This difference directly reflects the larger initial dipole deformation generated by the tetrahedral arrangement of α clusters.

The authors argue that the combination of $\mathrm{NSC}(2,3)$, $\mathrm{NAC}_{2,1}(2,3)$, and $v_1^{\rm even}$ provides a powerful, experimentally accessible set of observables to discriminate between clustered and smooth nuclear density profiles. Their findings suggest that future RHIC and LHC runs with light‑ion beams (e.g., ${}^{16}$O, ${}^{12}$C) could employ these multi‑particle correlations to test the existence of α‑clustering in nuclei at high energies. The work thus bridges low‑energy nuclear structure physics with relativistic heavy‑ion phenomenology, highlighting how subtle features of the initial state survive the hydrodynamic evolution and manifest in final‑state flow patterns.