Collision geometry fluctuations and triangular flow in heavy-ion collisions

TL;DR

This work introduces participant triangularity and triangular flow to explain ridge-like structures in heavy-ion two-particle azimuthal correlations. Using AMPT simulations and long-range data from PHOBOS and STAR, it demonstrates a linear connection between triangularity and triangular flow, and shows that most of the measured third Fourier component arises from triangular flow. The comparison of V3Δ/V2Δ between data and AMPT reveals qualitative agreement in centrality and momentum dependence, suggesting triangular flow as a major contributor to the ridge and broad away-side features. Overall, the paper provides a geometry-driven framework for understanding initial-state fluctuations and the subsequent collective expansion in heavy-ion collisions, with three-particle correlations offering further validation of triangular flow signatures.

Abstract

We introduce the concepts of participant triangularity and triangular flow in heavy-ion collisions, analogous to the definitions of participant eccentricity and elliptic flow. The participant triangularity characterizes the triangular anisotropy of the initial nuclear overlap geometry and arises from event-by-event fluctuations in the participant-nucleon collision points. In studies using a multi-phase transport model (AMPT), a triangular flow signal is observed that is proportional to the participant triangularity and corresponds to a large third Fourier coefficient in two-particle azimuthal correlation functions. Using two-particle azimuthal correlations at large pseudorapidity separations measured by the PHOBOS and STAR experiments, we show that this Fourier component is also present in data. Ratios of the second and third Fourier coefficients in data exhibit similar trends as a function of centrality and transverse momentum as in AMPT calculations. These findings suggest a significant contribution of triangular flow to the ridge and broad away-side features observed in data. Triangular flow provides a new handle on the initial collision geometry and collective expansion dynamics in heavy-ion collisions.

Figures (8)

• Figure 1: Top: azimuthal correlation functions for mid-central (10-20%) Au+Au collisions at $\sqrt{s_{{{\rm NN}}}} =$ 200 GeV obtained from projections of two-dimensional $\Delta\eta,\Delta\phi$ correlation measurements by PHOBOS Alver:2009idAlver:2008gk and STAR Abelev:2008un. The transverse momentum and pseudorapidity ranges are indicated on the figures. Errors bars are combined systematic and statistical errors. The first three Fourier components are shown in solid lines. Bottom: the residual correlation functions after the first three Fourier components are subtracted.
• Figure 2: Distribution of \ref{['fig:glauecc']} eccentricity, $\varepsilon_{2}$, and \ref{['fig:glautria']} triangularity, $\varepsilon_{3}$, as a function of number of participating nucleons, $N_{\rm part}$, in $\sqrt{s_{{{\rm NN}}}} =$ 200 GeV Au+Au collisions.
• Figure 3: Distribution of nucleons on the transverse plane for a $\sqrt{s_{{{\rm NN}}}} =$ 200 GeV Au+Au collision event with $\varepsilon_{3}$=0.53 from Glauber Monte Carlo. The nucleons in the two nuclei are shown in gray and black. Wounded nucleons (participants) are indicated as solid circles, while spectators are dotted circles.
• Figure 4: Top: average elliptic flow, $\left\langle v_2 \right\rangle$, as a function of eccentricity, $\varepsilon_{2}$; bottom: average triangular flow, $\left\langle v_3 \right\rangle$, as a function of triangularity, $\varepsilon_{3}$, in $\sqrt{s_{{{\rm NN}}}} =$ 200 GeV Au+Au collisions from the AMPT model in bins of number of participating nucleons. Error bars indicate statistical errors. A linear fit to the data is shown.
• Figure 5: Dashed lines show \ref{['fig:AMPT_meanv22andv2_2vsNpart_2_1']} second Fourier coefficient, ${\mathbf V}_{2\Delta}$, and \ref{['fig:AMPT_meanv32andv3_2vsNpart_2_1']} third Fourier coefficient, ${\mathbf V}_{3\Delta}$, of azimuthal correlations as a function of number of participating nucleons, $N_{\rm part}$, in $\sqrt{s_{{{\rm NN}}}} =$ 200 GeV Au+Au collisions from the AMPT model. Solid lines show the contribution to these coefficients from flow calculated with respect to the minor axis of (a) eccentricity and (b) triangularity.