[Paper Review] Collision Geometry and Flow in Uranium+Uranium Collisions

A. Goldschmidt, Zhigang Qiu+2 more|arXiv (Cornell University)|Feb 2, 2015

High-Energy Particle Collisions Research4 citations

TL;DR

This study uses event-by-event viscous hydrodynamics and the two-component Monte Carlo Glauber model to simulate uranium+uranium collisions, revealing a 'knee'-like structure in elliptic flow ($v_2$) at ~0.5% centrality due to tip-on-tip geometry preference under high-multiplicity triggers. However, the absence of this knee in STAR data rules out the two-component MC-Glauber model for initial energy and entropy production, and highlights the need for ZDC-based event-shape engineering to enrich tip-tip and body-body configurations with higher purity than multiplicity-triggering alone.

ABSTRACT

Using event-by-event viscous fluid dynamics to evolve fluctuating initial density profiles from the Monte-Carlo Glauber model for U+U collisions, we report a "knee"-like structure in the elliptic flow as a function of collision centrality, located near 0.5% centrality as measured by the final charged multiplicity. This knee is due to the preferential selection of tip-on-tip collision geometries by a high-multiplicity trigger. Such a knee structure is not seen in the STAR data. This rules out the two-component MC-Glauber model for initial energy and entropy production. An enrichment of tip-tip configurations by triggering solely on high-multiplicity in the U+U collisions thus does not work. On the other hand, using the Zero Degree Calorimeters (ZDCs) coupled with event-shape engineering, we identify the selection purity of body-body and tip-tip events in the full-overlap U+U collisions. With additional constraints on the asymmetry of the ZDC signals one can further increases the probability of selecting tip-tip events in U+U collisions.

Motivation & Objective

• To investigate whether the prolate deformation of uranium nuclei leads to a distinct 'knee'-like structure in elliptic flow ($v_2$) as a function of collision centrality.
• To test the validity of the two-component Monte Carlo Glauber model for initial energy and entropy production in U+U collisions by comparing simulated $v_2$ trends with STAR experimental data.
• To develop and evaluate improved experimental event selection strategies—using Zero Degree Calorimeters (ZDCs), multiplicity, and initial eccentricity ($\varepsilon_2$)—to enrich pure tip-tip and body-body collision geometries.
• To quantify the purity and efficiency of selecting specific collision geometries (tip-tip, body-body) using combined ZDC signal correlations and $\varepsilon_2$ cuts, reducing model dependence.

Proposed method

• Simulated initial energy density profiles using the two-component Monte Carlo Glauber model, incorporating binary collisions and wounded nucleons with $\Gamma$-distributed fluctuations.
• Modeled deformed uranium nuclei using a Woods-Saxon density distribution with quadrupole ($\beta_{20}=0.28$) and hexadecupole ($\beta_{40}=0.093$) deformations.
• Evolved initial density profiles through event-by-event viscous relativistic fluid dynamics to compute final-state $v_2$ and eccentricity $\varepsilon_2$.
• Used ZDC signals and participant number differences ($\Delta N_{\text{part}}$) as proxies for event geometry, with low $\Delta N_{\text{part}}$ indicating symmetric, full-overlap configurations.
• Applied event-shape engineering by cutting on $\varepsilon_2$ and $v_2$ to enrich body-body (high $\varepsilon_2$) and tip-tip (low $\varepsilon_2$) events.
• Evaluated selection purity by comparing the fraction of true tip-tip and body-body events within selected samples, using $\Delta N_{\text{part}}$ to filter asymmetric 'tip-body' configurations.

Experimental results

Research questions

• RQ1 Does the two-component MC-Glauber model predict a 'knee'-like structure in $v_2$ as a function of centrality in U+U collisions due to preferential tip-on-tip geometry at high multiplicity?
• RQ2 Is the predicted knee structure in $v_2$ consistent with STAR experimental data, or does its absence rule out the two-component MC-Glauber model?
• RQ3 Can ZDC signal correlations and $\Delta N_{\text{part}}$ cuts improve the purity of tip-tip and body-body event selection beyond simple multiplicity triggering?
• RQ4 What is the maximum achievable purity for selecting tip-tip and body-body configurations using $\varepsilon_2$ cuts and ZDC-based event engineering?
• RQ5 How do multiplicity fluctuations and binary collision admixture affect the reliability of event selection strategies in U+U collisions?

Key findings

• The two-component MC-Glauber model predicts a 'knee'-like structure in $v_2$ at approximately 0.5% centrality, arising from preferential selection of tip-on-tip geometries under high-multiplicity triggers.
• The absence of this knee structure in STAR data rules out the two-component MC-Glauber model as a valid description of initial energy and entropy production in U+U collisions.
• Triggering solely on high multiplicity fails to enrich tip-tip configurations effectively, as the resulting sample purity is limited to about 25%.
• Using ZDC signals and cutting on low $\Delta N_{\text{part}}$ (a proxy for symmetric spectator emission) increases the selection efficiency of tip-tip events by a factor of 1.4 and boosts purity to approximately 35%.
• Cutting on high $\varepsilon_2$ (or $v_2$) enriches body-body events to a purity of about 40%, while low-$\varepsilon_2$ cuts yield tip-tip samples with ~25% purity, which can be enhanced to ~35% with symmetric ZDC signal constraints.
• ZDC-based event engineering, particularly using $\Delta N_{\text{part}}$ to filter asymmetric configurations, provides a more robust and less model-dependent method for selecting pure collision geometries than multiplicity-based triggers.