Triangular flow in hydrodynamics and transport theory (1007.5469v2)

Abstract: In ultrarelativistic heavy-ion collisions, the Fourier decomposition of the relative azimuthal angle, \Delta \phi, distribution of particle pairs yields a large cos(3\Delta \phi) component, extending out to large rapidity separations \Delta \eta >1. This component captures a significant portion of the ridge and shoulder structures in the \Delta \phi distribution, which have been observed after contributions from elliptic flow are subtracted. An average finite triangularity due to event-by-event fluctuations in the initial matter distribution, followed by collective flow, naturally produces a cos(3\Delta \phi) correlation. Using ideal and viscous hydrodynamics, and transport theory, we study the physics of triangular (v_3) flow in comparison to elliptic (v_2), quadrangular (v_4) and pentagonal (v_5) flow. We make quantitative predictions for v_3 at RHIC and LHC as a function of centrality and transverse momentum. Our results for the centrality dependence of v_3 show a quantitative agreement with data extracted from previous correlation measurements by the STAR collaboration. This study supports previous results on the importance of triangular flow in the understanding of ridge and shoulder structures. Triangular flow is found to be a sensitive probe of initial geometry fluctuations and viscosity.

• The paper demonstrates that triangular flow (v3) arises from initial geometry fluctuations, evidenced by a significant cos(3Δφ) term in particle correlations.
• It employs both ideal and viscous hydrodynamics along with transport theory, achieving quantitative predictions for v3 that align with RHIC and LHC data.
• The findings indicate that v3’s strong sensitivity to viscous damping makes it a powerful probe for studying the quark-gluon plasma's transport properties.

Triangular Flow in Hydrodynamics and Transport Theory

In the study of ultrarelativistic heavy-ion collisions, the analysis of particle correlations holds a crucial role in unraveling the underlying physics of these events. The paper "Triangular flow in hydrodynamics and transport theory," authored by Alver et al., explores the intricacies of triangular flow ($v_3$) within the framework of both hydrodynamics and kinetic transport theory. The research investigates the characteristics and implications of $v_3$ by comparing it with other flow coefficients such as elliptic ($v_2$), quadrangular ($v_4$), and pentagonal ($v_5$) flows.

Key Findings and Methodology

1. Triangular Flow Component: The Fourier decomposition of particle pair distributions in heavy-ion collisions reveals a significant $\cos(3\Delta\phi)$ term, indicative of triangular flow. The paper attributes this to event-by-event fluctuations in initial matter distribution resulting in an effective triangularity of the initial geometry.
2. Modeling Approach: The authors employed both ideal and viscous hydrodynamics alongside transport theory to study the evolution of triangular flow. They analyzed the effect of viscosity and the initial geometry on $v_3$ and compared with experimental data from RHIC and LHC.
3. Predictions for $v_3$: Quantitative predictions were made for $v_3$ as a function of centrality and transverse momentum. The results showed a good agreement with the STAR collaboration's previously extracted data, confirming the significance of triangular flow.
4. Viscous Damping: The study highlighted how viscous effects dampen flow coefficients, with $v_3$ being substantially more sensitive to viscosity than $v_2$. The paper emphasizes that this sensitivity makes triangular flow an excellent probe for the properties of the medium, such as its viscosity.
5. Comparisons to Other Flow Components: The findings suggest that $v_3$, unlike $v_2$, arises predominantly from fluctuations rather than geometrical anisotropy. Interestingly, $v_3/\varepsilon_3$ is of a similar magnitude to $v_2/\varepsilon_2$, whereas higher harmonics like $v_4$ and $v_5$ are substantially smaller.

Implications and Future Directions

The elucidation of triangular flow has substantial implications for the theoretical understanding of initial geometry fluctuations and the medium's transport properties during a collision. Findings suggest that $v_3$ could provide insights into the degree of thermalization and the viscosity of the quark-gluon plasma. The paper proposes that simultaneous analysis of $v_2$ and $v_3$ could provide stringent constraints on theoretical models of heavy-ion collisions.

Given the distinct nature of triangular flow, future research could focus on refining initial condition models to better capture fluctuations that give rise to $v_3$. Additionally, more sophisticated treatments of viscous effects at different collision energies, possibly incorporating temperature-dependent viscosities, would be beneficial. As experimental precision increases at facilities like the LHC, more accurate data could further validate and refine these theoretical constructs.

In conclusion, this study on triangular flow not only complements existing analyses of collective flow phenomena but also opens new avenues for probing the quark-gluon plasma's intrinsic properties. By advancing both theoretical and experimental investigations in this domain, researchers can further unravel the complex dynamics governing high-energy nuclear collisions.