Relating eccentricity fluctuations to density fluctuations in heavy-ion collisions

The magnitude of anisotropic flow in a nucleus–nucleus collision is determined by the energy-density field, ρ(x, y, z), created right after the collision occurs. Specifically, elliptic flow, v₂, and triangular flow, v₃, are proportional to the anisotropy coefficients ε₂ and ε₃, which are functionals of ρ. We express the mean and the variance of ε₂ and ε₃ as a function of the 1- and 2-point functions of ρ. 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.