[Paper Review] Ultracentral Collisions of Small and Deformed Systems at RHIC: ${U} {U}$, ${d} {Au}$, ${}^{9}{Be} {Au}$, ${}^{9}{Be} {}^{9}{Be}$, ${}^{3}{He} {}^{3}{He}$, and ${}^{3}{He} {Au}$ Collisions

Jacquelyn Noronha-Hostler, Noah Paladino+3 more|arXiv (Cornell University)|May 30, 2019

High-Energy Particle Collisions ResearchPhysics and Astronomy84 references3 citations

TL;DR

This paper investigates ultracentral collisions of small and deformed nuclei—such as $^{238}$U, $^9$Be, and $^3$He—using hydrodynamic and color glass condensate (CGC) models to distinguish between collective flow driven by initial geometry versus gluon correlations. It finds that nuclear deformation induces a distinct multiplicity dependence in elliptic and triangular flow harmonics, with $v_2\{2\}$ increasing with multiplicity in CGC scenarios for deformed systems, providing a key discriminator between hydrodynamic and CGC models in ultracentral collisions.

ABSTRACT

In this paper, we study a range of collision systems involving deformed ions and compare the elliptic and triangular flow harmonics produced in a hydrodynamics scenario versus a color glass condensate (CGC) scenario. For the hydrodynamics scenario, we generate initial conditions using TRENTO and work within a linear response approximation to obtain the final flow harmonics. For the CGC scenario, we use the explicit calculation of two-gluon correlations taken in the high-$p_T$ ``(semi)dilute-(semi)dilute'' regime to express the flow harmonics in terms of the density profile of the collision. We consider ultracentral collisions of deformed ions as a testbed for these comparisons because the difference between tip-on-tip and side-on-side collisions modifies the multiplicity dependence in both scenarios, even at zero impact parameter. We find significant qualitative differences in the multiplicity dependence obtained in the initial conditions+hydrodynamics scenario and the CGC scenario, allowing these collisions of deformed ions to be used as a powerful discriminator between models. We also find that sub-nucleonic fluctuations have a systematic effect on the elliptic and triangular flow harmonics which are most discriminating in $0-1\%$ ultracentral symmetric collisions of small deformed ions and in $0-10\%$ $\mathrm{d} {}^{197}\mathrm{Au}$ collisions. The collision systems we consider are ${}^{238}\mathrm{U} {}^{238}\mathrm{U}$, $\mathrm{d} {}^{197}\mathrm{Au}$, ${}^{9}\mathrm{Be} {}^{197}\mathrm{Au}$, ${}^{9}\mathrm{Be} {}^{9}\mathrm{Be}$, ${}^{3}\mathrm{He} {}^{3}\mathrm{He}$, and ${}^{3}\mathrm{He} {}^{197}\mathrm{Au}$.

Motivation & Objective

• To test whether ultracentral collisions of deformed ions can serve as a sensitive probe to distinguish between hydrodynamic and color glass condensate (CGC) descriptions of collective flow in small systems.
• To examine how nuclear deformation and sub-nucleonic fluctuations affect the multiplicity dependence of flow harmonics $v_2\{2\}$ and $v_3\{2\}$ in both hydrodynamic and CGC frameworks.
• To identify specific collision systems and kinematic regimes where the predictions of the two models diverge most significantly, enabling experimental discrimination.
• To analyze the role of initial condition geometry—particularly tip-on-tip vs. side-on-side collisions—in modifying flow harmonics and multiplicity scalings in ultracentral events.
• To determine whether the $T_A T_B$ scaling of flow harmonics, expected in CGC, is violated in realistic collision geometries with large density gradients and nuclear deformations.

Proposed method

• Simulates initial conditions using the TRENTO model for hydrodynamic scenarios, employing a linear response approximation to compute final-state flow harmonics.
• Applies the CGC framework to compute two-gluon correlations in the high-$p_T$ "(semi)dilute-(semi)dilute" regime, expressing flow harmonics in terms of the nuclear density profile.
• Compares multiplicity scalings of $v_2\{2\}$ and $v_3\{2\}$ under $T_A T_B$ and $\sqrt{T_A T_B}$ scaling assumptions across different collision systems.
• Uses smooth optical Glauber profiles with ellipsoidal deformation (e.g., $^{238}$U) to model nuclear geometry and compute the ratio $[v_2\{2\}]_{\text{tip}}/[v_2\{2\}]_{\text{side}}$ to quantify deformation effects.
• Introduces event-by-event multiplicity fluctuations and lumpy nuclear profiles to assess robustness of scalings under realistic sub-nucleonic structure.
• Analyzes asymmetric systems like $^9$Be-Au and $^3$He-Au to explore intermediate-scale deformation effects beyond symmetric collisions.

Experimental results

Research questions

• RQ1 How does nuclear deformation in $^{238}$U-$^{238}$U collisions alter the multiplicity dependence of $v_2\{2\}$ and $v_3\{2\}$ in the CGC framework compared to hydrodynamics?
• RQ2 To what extent do sub-nucleonic fluctuations in the nuclear density profile flatten or distort the $T_A T_B$ scaling of flow harmonics in the CGC model?
• RQ3 In which collision systems—such as $^9$Be-$^9$Be or $^3$He-$^3$He—do the predictions of hydrodynamics and CGC show the largest qualitative differences in flow harmonic multiplicity scalings?
• RQ4 Does the $v_2\{2\}$ scaling with multiplicity transition from constant to increasing due to deformation, as predicted in Ref. Kovchegov and Wertepny (2014), and is this effect visible in $^{238}$U-$^{238}$U and $^9$Be-Au systems?
• RQ5 Can the anticorrelation between elliptic flow magnitude and multiplicity in ultracentral collisions be reproduced in the CGC model, and how does it differ from the hydrodynamic prediction?

Key findings

• In the CGC scenario, $v_2\{2\}$ for $^{238}$U-$^{238}$U collisions shows a positive slope with multiplicity when nuclear deformation is included, violating the $T_A T_B$ scaling that holds for smooth, undeformed systems.
• For smooth optical Glauber profiles, the ratio $[v_2\{2\}]_{\text{tip}}/[v_2\{2\}]_{\text{side}} \approx 1.26$ due to deformation, indicating a measurable geometric dependence in the CGC framework.
• In $^9$Be-Au collisions, the $v_2\{2\}$ scaling with $T_A T_B$ exhibits a small negative slope, suggesting incomplete manifestation of deformation effects in asymmetric, ultracentral systems.
• Sub-nucleonic fluctuations significantly flatten the $v_2\{2\}$ and $v_3\{2\}$ scalings in the CGC model, especially in $0-1\%$ ultracentral symmetric collisions of small deformed ions.
• The $T_A T_B$ scaling of $v_2\{2\}$ and $v_3\{2\}$ is robust in $\mathrm{p}^{208}\mathrm{Pb}$ collisions with smooth profiles but is strongly violated in systems with large density gradients, such as $^{208}\mathrm{Pb}$-$^{208}\mathrm{Pb}$.
• The largest discriminating power between hydrodynamics and CGC models is found in $0-1\%$ ultracentral $^3$He-$^3$He and $0-10\%$ d-$^{197}$Au collisions due to systematic effects from sub-nucleonic fluctuations on flow harmonics.