[Paper Review] Resummed lattice QCD equation of state at finite baryon density: strangeness neutrality and beyond

Szabolcs Borsányi, Zoltán Fodor+6 more|arXiv (Cornell University)|Feb 11, 2022

High-Energy Particle Collisions ResearchPhysics and Astronomy94 references44 citations

TL;DR

This paper presents a resummed lattice QCD equation of state at finite baryon density along the strangeness-neutral line (⟨S⟩ = 0), extending a novel scaling-based resummation scheme to non-zero strange quark chemical potential. By combining continuum extrapolation of 4stout-improved staggered fermions with a physically motivated resummation and Stefan-Boltzmann corrections, it achieves a stable equation of state up to μB/T = 3.5, overcoming unphysical oscillations from truncated Taylor expansions and enabling hydrodynamic simulations with local strangeness neutrality.

ABSTRACT

We calculate a resummed equation of state with lattice QCD simulations at imaginary chemical potentials. This work presents a generalization of the scheme introduced in 2102.06660 to the case of non-zero $\mu_S$, focusing on the line of strangeness neutrality. We present results up to $\mu_B/T \leq 3.5$ on the strangeness neutral line $\left\langle S ight angle = 0$ in the temperature range $130 m{MeV} \leq T \leq 280 m{MeV}$. We also extrapolate the finite baryon density equation of state to small non-zero values of the strangeness-to-baryon ratio $R=\left\langle S ight angle / \left\langle B ight angle$. We perform a continuum extrapolation using lattice simulations of the 4stout-improved staggered action with 8, 10, 12 and 16 timeslices.

Motivation & Objective

• To extend the resummation scheme from μS = 0 to the physically relevant strangeness-neutral line (⟨S⟩ = 0) in finite-density QCD.
• To overcome unphysical oscillations in truncated Taylor expansions of the equation of state at finite baryon density.
• To provide a reliable, continuum-extrapolated equation of state for use in relativistic hydrodynamic simulations of heavy-ion collisions.
• To generalize the resummation approach to small non-zero strangeness-to-baryon ratios R = ⟨S⟩/⟨B⟩, enabling studies beyond strict strangeness neutrality.

Proposed method

• Employing the 4stout-improved staggered fermion action with Nt = 8, 10, 12, 16 for continuum extrapolation.
• Using imaginary chemical potentials to compute Taylor expansion coefficients without the sign problem.
• Applying a physically motivated resummation ansatz based on an approximate scaling variable T(1 + κ²(T)ˆµ²B + ...), where the scaling coefficient κ²(T) is temperature-dependent.
• Introducing a Stefan-Boltzmann correction to improve convergence at high temperatures where the scaling ansatz breaks down.
• Performing continuum extrapolation of the equation of state using multiple lattice spacings and fitting the resummed form to data at fixed μB/T.
• Extending the framework to compute coefficients for small R = ⟨S⟩/⟨B⟩, allowing for non-zero strangeness-to-baryon ratios.

Experimental results

Research questions

• RQ1 Can the resummation scheme based on an approximate scaling variable be successfully extended from zero strange quark chemical potential to the strangeness-neutral line?
• RQ2 How does the resummed equation of state perform in the crossover region at μB/T ≤ 3.5 along the strangeness-neutral line, compared to truncated Taylor expansions?
• RQ3 To what extent does the inclusion of a Stefan-Boltzmann correction improve the convergence of the resummation at high temperatures?
• RQ4 Can the resummation framework be generalized to describe the equation of state at small, non-zero values of the strangeness-to-baryon ratio R = ⟨S⟩/⟨B⟩?
• RQ5 What is the quantitative behavior of the equation of state in the high-temperature, high-density regime beyond the crossover?

Key findings

• The resummed equation of state is successfully computed up to μB/T = 3.5 along the strangeness-neutral line (⟨S⟩ = 0), with no unphysical oscillations observed.
• The resummation scheme based on the approximate scaling variable T(1 + κ²(T)ˆµ²B + ...) effectively suppresses the unphysical oscillations that plague fixed-order Taylor expansions beyond μB/T ≈ 2.5.
• The continuum extrapolation using Nt = 8, 10, 12, 16 confirms the stability and convergence of the resummed results.
• The inclusion of a Stefan-Boltzmann correction significantly improves the high-temperature behavior of the resummed equation of state.
• The framework is generalized to compute the equation of state at small non-zero R = ⟨S⟩/⟨B⟩, enabling studies of systems with mild strangeness excess.
• The results are consistent with the expectation of a constant crossover width at small μB, supporting the validity of the scaling ansatz in the low-density regime.