Importance of Multiplicity Fluctuations in Entropy Scaling

TL;DR

This paper investigates how different models of initial energy density fluctuations, especially those inspired by the Color-Glass Condensate framework, impact entropy scaling and eccentricity calculations in heavy-ion collisions.

Contribution

It compares multiplicity fluctuation models based on $T_A T_B$ scaling with those from Bayesian analyses, highlighting implications for eccentricity and viscosity extraction.

Findings

$T_A T_B$ scaling with log-normal fluctuations is a plausible model.

Different fluctuation models lead to significant differences in eccentricity.

Choice of fluctuation model affects the interpretation of viscosity in small systems.

Abstract

One of the greatest uncertainties in heavy-ion collisions is the description of the initial state. Different models predict a wide range of initial energy density distributions based on their underlying assumptions. Final flow harmonics are sensitive to these differences in the initial state due to the nearly linear mapping between eccentricities and anisotropic flow harmonics. The Trento code uses a model-agnostic approach by phenomenologically parameterizing the initial state and constraining those parameters from a Bayesian analysis. There the multiplicity fluctuations were determined by a one parameter $\Gamma$ distribution. However, initial-state models arising from the Color-Glass Condensate (CGC) framework lead to an initial energy density which is outside the functional form considered in Trento and its later Bayesian analyses because they rely on log-normal multiplicity fluctuations. We compare $T_{A}T_{B}$ scaling (CGC-like) to $\sqrt{T_{A}T_{B}}$ scaling (preferred from a Trento Bayesian analysis) and find that the $T_A T_B$ form together with log-normal fluctuations is a reasonable candidate to describe the multiplicity fluctuations but leads to larger eccentricities, which would affect the extraction of viscosity in small systems.