# Relative flow fluctuations as a probe of initial state fluctuations

## TL;DR

This paper investigates how relative flow fluctuations can serve as a direct probe of initial state fluctuations in heavy-ion collisions, using hydrodynamic simulations to analyze deviations from linear scaling.

## Contribution

It identifies conditions where flow fluctuations directly reflect initial density fluctuations and provides predictions for higher-order cumulants in various collision systems.

## Key findings

- Flow fluctuations match initial density fluctuations when deviations are negligible.
- Existing models overestimate flow fluctuations in central Pb+Pb collisions.
- Predictions made for higher-order cumulants in noncentral Pb+Pb and high-multiplicity p+Pb collisions.

## Abstract

Elliptic flow, $v_2$, and triangular flow, $v_3$, are to a good approximation linearly proportional to the corresponding spatial anisotropies of the initial density profile, $\varepsilon_2$ and $\varepsilon_3$. Using event-by-event hydrodynamic simulations, we point out when deviations from this linear scaling are to be expected. When these deviations are negligible, relative $v_n$ fluctuations are equal to relative $\varepsilon_n$ fluctuations, and one can directly probe models of initial conditions using ratios of cumulants, for instance $v_n\{4\}/v_n\{2\}$. We argue that existing models of initial conditions tend to overestimate flow fluctuations in central Pb+Pb collisions, and to underestimate them in peripheral collisions. We make predictions for $v_3\{6\}$ in noncentral Pb+Pb collisions, and for $v_3\{4\}$ and $v_3\{6\}$ in high-multiplicity p+Pb collisions.