Lattice-QCD-based equations of state at finite temperature and density

TL;DR

This paper discusses two lattice QCD-based equations of state at finite temperature and density, one purely from fundamental theory and another incorporating critical behavior to aid heavy-ion collision modeling and critical point searches.

Contribution

It introduces a lattice QCD-derived EoS using susceptibilities and extends it by including critical phenomena based on universality classes, aiding experimental and theoretical studies.

Findings

Reconstructed EoS using susceptibilities up to b0b4 in baryon chemical potential.

Incorporated critical behavior based on 3D Ising universality class.

Ensured EoS validity for heavy-ion collision applications with strangeness neutrality.

Abstract

The equation of state (EoS) of QCD is a crucial input for the modeling of heavy-ion-collision (HIC) and neutron-star-merger systems. Calculations of the fundamental theory of QCD, which could yield the true EoS, are hindered by the infamous Fermi sign problem which only allows direct simulations at zero or imaginary baryonic chemical potential. As a direct consequence, the current coverage of the QCD phase diagram by lattice simulations is limited. In these proceedings, two different equations of state based on first-principle lattice QCD (LQCD) calculations are discussed. The first is solely informed by the fundamental theory by utilizing all available diagonal and non-diagonal susceptibilities up to $\mathcal{O}(\mu_B^4)$ in order to reconstruct a full EoS at finite baryon number, electric charge and strangeness chemical potentials. For the second, we go beyond information from the lattice in order to explore the conjectured phase structure, not yet determined by LQCD methods, to assist the experimental HIC community in their search for the critical point. We incorporate critical behavior into this EoS by relying on the principle of universality classes, of which QCD belongs to the 3D Ising Model. This allows one to study the effects of a singularity on the thermodynamical quantities that make up the equation of state used for hydrodynamical simulations of HICs. Additionally, we ensure that these EoSs are valid for applications to HICs by enforcing conditions of strangeness neutrality and fixed charge-to-baryon-number ratio.