Relating eccentricity fluctuations to density fluctuations in heavy-ion collisions

Abstract

The magnitude of anisotropic flow in a nucleus-nucleus collision is determined by the energy density field, $\rho (x,y,z)$, created right after the collision occurs. Specifically, elliptic flow, $v_2$, and triangular flow, $v_3$, are proportional to the anisotropy coefficients ${\epsilon }_2$ and ${\epsilon }_3$, which are functionals of $\rho$. We express the mean and the variance of ${\epsilon }_2$ and ${\epsilon }_3$ as a function of the 1- and 2-point functions of $\rho$. These results generalize results obtained previously, that were valid only for central collisions, or only for identical point-like sources. We apply them to the color glass condensate effective theory, using the recently derived expression of the 2-point function.

12 pages, 2 figures. v2: minor changes in figures, acknowledgments added. Proceedings of XXV Epiphany conference on Advances in Heavy Ion Physics, Cracow, Poland, 8-11 January 2019