# Normalized symmetric cumulants as a measure of QCD phase transition: a viscous hydrodynamic study

## TL;DR

This study demonstrates that normalized symmetric cumulants of charged pions can distinguish between different QCD equations of state in viscous hydrodynamic models, aiding in identifying the QCD critical point.

## Contribution

The paper introduces the use of normalized symmetric cumulants as a novel observable to differentiate QCD equations of state in hydrodynamic simulations.

## Key findings

- Normalized symmetric cumulants distinguish between crossover and first-order phase transition EoSs.
- Results are consistent across various initial conditions and shear viscosities.
- These cumulants can serve as an EoS meter in experimental analyses.

## Abstract

Finding the existence and the location of the QCD critical point is one of the main goals of the RHIC beam energy scan program. To make theoretical predictions and corroborate with the experimental data requires modeling the space-time evolution of the matter created in heavy-ion collisions by dynamical models such as the relativistic hydrodynamics with an appropriate Equation of State (EoS). In the present exploratory study, we use a viscous 2+1 dimensional event-by-event (e-by-e) hydrodynamic code at finite baryon densities with two different EoSs (i) Lattice QCD + HRG with a crossover transition and (ii) EoS with a first-order phase transition to studying the normalized symmetric cumulants of charged pions $v_n$ $(n=2-4)$. We show that the normalized symmetric cumulants can differentiate the two EoSs while all other conditions remain the same. The conclusion does not change for various initial conditions and shear viscosity. This indicates that these observables can be used to gain information about the QCD EoS from experimental data and can be used as an EoS meter.