Continuous description of fluctuating eccentricities

Abstract

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. As an illustration, we compare to a commonly used model of independent sources, and recover the known results of this model

Primordial non-Gaussianity in heavy-ion collisions

“…In each line, there is one term of order δρ, which is the dominant contribution to the anisotropy, and was the only term kept in [19]. In addition, there are two next-toleading corrections of order (δρ) 2 , which originate from the non-linear relation between ε n and δρ [20].…”

“…One typically expects that the functions C n are short ranged (they vanish unless all the arguments are close to one another) and positive. However, long-range correlations can be induced by energy conservation, i.e., if one requires that all events have the exact same energy [19,20].…”

“…The perturbative expression of c n {2} in terms of the two-point function was derived in [19] to leading order (δρ) 2 . It is obtained by inserting the first term in the right-hand side of Eqs.…”

“…In order to relate the fluctuations of the initial anistotropies to the fluctuations of the initial density pro-file, we carry out a systematic perturbative expansion in powers of the density fluctuations [19,20], which is introduced in Sec. II.…”

What does the matter created in high multiplicity proton-nucleus collisions teach us about the 3-D structure of the proton?

“…Underlying all this is a picture of correlations where the mean and the variance of the eccentricity distribution dominate over higher moments; this is likely the case when the number of fluctuating sources is large [66,67]. While this is superficially like the McLerran-Venugopalan (MV) model [45,46], there are essential and interesting ways in which the two pictures diverge.…”