Elliptic Flow from a Beam Energy Scan: a signature of a phase transition to the Quark-Gluon Plasma

TL;DR

This paper uses a relativistic transport model to show that the nearly energy-invariant elliptic flow in heavy-ion collisions suggests a phase transition, with a specific temperature dependence of shear viscosity to entropy ratio.

Contribution

It introduces a method to fix the temperature-dependent shear viscosity to entropy ratio and links its behavior to the observed elliptic flow scaling across energies.

Findings

Elliptic flow $v_2(p_T)$ is nearly invariant with collision energy.

A temperature-dependent $ ext{eta}/s(T)$ with a minimum at $T_c$ explains the flow behavior.

Constant or strongly varying $ ext{eta}/s(T)$ disrupts flow scaling.

Abstract

We employ a relativistic transport theory to describe the fireball expansion of the matter created in ultra-relativistic heavy-ion collisions (uRHICs). Developing an approach to fix locally the shear viscosity to entropy density $\eta/s$, we study the impact of a temperature dependent $\eta/s(T)$ on the build-up of the elliptic flow, $v_2$, a measure of the angular anisotropy in the particle production. Beam Energy Scan from $\sqrt{s_{NN}}= \rm 62.4 GeV$ at RHIC up to 2.76 TeV at LHC has shown that the $v_2(p_T)$ as a function of the transverse momentum $p_T$ appears to be nearly invariant with energy. We show that such a surprising behavior is determined by a rise and fall of $\eta/s(T)$ with a minimum at $T\sim T_c$, as one would expect if the matter undergoes a phase transition or a cross-over. This provides an evidence for phase transition occurring in the uRHIC's and a first constraint on the temperature dependence of $\eta/s$. In particular, a constant $\eta/s$ at all temperatures or a too strong T-dependence would cause a breaking of the scaling of $v_2(p_T)$ with the energy.