Continuous description of fluctuating eccentricities

Understand

We consider the initial energy density in the transverse plane of a high energy nucleus-nucleus collision as a random field $\rho(\x)$, whose probability distribution $P[\rho]$, the only ingredient of the present description, encodes all possible sources of fluctuations.

• We argue that it is a local Gaussian, with a short-range 2-point function, and that the fluctuations relevant for the calculation of the eccentricities that drive the anisotropic flow have small relative amplitudes.
• In fact, this 2-point function, together with the average density, contains all the information needed to calculate the eccentricities and their variances, and we derive general model independent expressions for these quantities.
• The short wavelength fluctuations are shown to play no role in these calculations, except for a renormalization of the short range part of the 2-point function.