[Paper Review] QCD transition at the physical point, and its scaling window from twisted mass Wilson fermions

A. Yu. Kotov, Maria Paola Lombardo+1 more|arXiv (Cornell University)|May 20, 2021

High-Energy Particle Collisions Research67 references56 citations

TL;DR

This study investigates the finite-temperature QCD phase transition using Nf = 2+1+1 twisted mass Wilson fermions at the physical pion mass, introducing a novel order parameter ⟨¯ψψ⟩3 that eliminates linear mass contributions. It finds consistent compatibility with the 3D O(4) universality class for T ≈ 120–300 MeV and estimates the chiral critical temperature as T₀ = 134⁺⁶₋₄ MeV, robust across multiple methods and consistent with O(4) scaling.

ABSTRACT

We study the scaling properties of the finite temperature QCD phase transition, for light quark masses ranging from the heavy quark regime to their physical values. The lattice results are obtained in the fixed scale approach from simulations of $N_f=2+1+1$ flavours of Wilson fermions at maximal twist. We identify an order parameter free from the the linear contributions in mass due to additive renormalization and regular terms in the Equation of State, which proves useful for the assessment of the hypothesized universal behaviour. We find compatibility with the 3D $O(4)$ universality class for the physical pion mass and temperatures $120$ MeV $ \lesssim T \lesssim 300$ MeV. We discuss violation of scaling at larger masses and a possible cross-over to mean field behaviour. The chiral extrapolation $T_0 = 134^{+6}_{-4}$ MeV of the pseudocritical temperature is robust against predictions of different universality classes and consistent with its estimate from the $O(4)$ Equation of State for the physical pion mass.

Motivation & Objective

• To assess the scaling window of the QCD chiral phase transition at physical quark masses using lattice QCD simulations.
• To test the hypothesis of 3D O(4) universality class for the finite-temperature transition in QCD with Nf = 2+1+1 flavors.
• To introduce and validate a new order parameter ⟨¯ψψ⟩3 that removes linear mass and additive renormalization contributions.
• To determine the chiral critical temperature T₀ in the physical pion mass regime and assess its consistency across different observables and methods.
• To investigate the onset of mean-field behavior and scaling violations at larger pion masses and higher temperatures.

Proposed method

• Simulations are performed using Nf = 2+1+1 twisted mass Wilson fermions at maximal twist, employing the fixed-scale approach to set the lattice spacing.
• A new order parameter ⟨¯ψψ⟩3 is defined as ⟨¯ψψ⟩ − mₗ ∂⟨¯ψψ⟩/∂mₗ, which eliminates linear mass dependence from the chiral condensate.
• The Equation of State (EoS) for ⟨¯ψψ⟩3 is derived analytically using the 3D O(4) scaling function and compared to mean-field behavior.
• Pseudo-critical temperatures Tc(mπ) are extracted from peak positions of the chiral susceptibility χₗ and the transverse susceptibility χₜ.
• Three independent methods are used to estimate T₀: scaling of ⟨¯ψψ⟩3, fitting to the O(4) EoS, and chiral extrapolation of Tc(mπ) from different observables.
• Scaling violations are assessed by comparing results across pion masses and temperatures, with a focus on the 300 MeV threshold where Griffith analyticity dominates.

Experimental results

Research questions

• RQ1 Is the QCD chiral phase transition at the physical pion mass compatible with the 3D O(4) universality class within the scaling window?
• RQ2 Does the newly introduced order parameter ⟨¯ψψ⟩3 eliminate linear mass contributions and improve the detection of critical behavior?
• RQ3 What is the chiral critical temperature T₀ in the physical pion mass regime, and how robust is it across different observables and fitting methods?
• RQ4 At what pion mass and temperature does scaling break down, and does the system transition to mean-field behavior?
• RQ5 How do scaling violations and dimensional reduction affect the validity of the O(4) EoS at physical quark masses?

Key findings

• The new order parameter ⟨¯ψψ⟩3 successfully removes linear mass and additive renormalization contributions, enabling cleaner identification of critical behavior.
• For physical pion mass (mπ = 139 MeV), the system shows consistent compatibility with the 3D O(4) universality class in the temperature range 120 MeV ≤ T ≤ 300 MeV.
• The chiral critical temperature is estimated as T₀ = 134⁺⁶₋₄ MeV, with robust consistency across three independent methods: scaling of ⟨¯ψψ⟩3, O(4) EoS fitting, and chiral extrapolation of Tc(mπ).
• The pseudo-critical temperature for ⟨¯ψψ⟩3 is T∆₃ = 146.2(21)(1) MeV, serving as an upper bound for T₀ and indicating proximity to true criticality.
• Scaling violations become significant above ~300 MeV, where the high-temperature behavior aligns with Griffith analyticity rather than O(4) scaling.
• The data are also compatible with a Z₂ universality class for a first-order transition, but no definitive discrimination is possible without lower pion masses.