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arXiv · 0708.0800

Elliptic flow in the Gaussian model of eccentricity fluctuations

Sergei A. Voloshin·Arthur M. Poskanzer·Aihong Tang·Gang Wang
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Abstract

We discuss a specific model of elliptic flow fluctuations due to Gaussian fluctuations in the initial spatial $x$ and $y$ eccentricity components $\left\{\mean{(σ_y^2-σ_x^2)/(σ_x^2+σ_y^2)}, \mean{2σ_{xy}/(σ_x^2+σ_y^2)} \right\}$. We find that in this model $\vfour$, elliptic flow determined from 4-particle cumulants, exactly equals the average flow value in the reaction plane coordinate system, $\mean{v_{RP}}$, the relation which, in an approximate form, was found earlier by Bhalerao and Ollitrault in a more general analysis, but under the same assumption that $v_2$ is proportional to the initial system eccentricity. We further show that in the Gaussian model all higher order cumulants are equal to $\vfour$. Analysis of the distribution in the magnitude of the flow vector, the $Q-$distribution, reveals that it is totally defined by two parameters, $\vtwo$, the flow from 2-particle cumulants, and $\vfour$, thus providing equivalent information compared to the method of cumulants. The flow obtained from the $Q-$distribution is again $\vfour=\mean{v_{RP}}$.

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Sergei A. Voloshin, Arthur M. Poskanzer, Aihong Tang, Gang Wang. 2007-10-23. Elliptic flow in the Gaussian model of eccentricity fluctuations. https://doi.org/10.1016/j.physletb.2007.11.043

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