[Paper Review] Relative scale setting for two-color QCD with Nf=2 Wilson fermions

Kei Iida, Etsuko Itou+1 more|arXiv (Cornell University)|Aug 14, 2020

Quantum Chromodynamics and Particle Interactions56 references4 citations

TL;DR

This paper establishes a relative scale setting function for two-color QCD with Nf=2 Wilson fermions using the gradient flow method with the w0 scale, enabling continuum extrapolation and dimensionless phase diagram analysis. It determines the pseudo-critical temperature at zero chemical potential via chiral susceptibility, allowing comparison across lattice studies using normalized temperature and chemical potential.

ABSTRACT

We determine the scale setting function and the pseudo-critical temperature on the lattice in $N_f=2$ two-color QCD using the Iwasaki gauge and Wilson fermion actions. Although two-color QCD does not correspond to the real world, it is very useful as a good testing ground for three-color QCD. The scale setting function gives the relative lattice spacings of simulations performed at different values of the bare coupling. It is a necessary tool for taking the continuum limit. Firstly, we measure the meson spectra for various combinations of ($β,κ$) and find a line of constant physics in $β$--$κ$ plane. Next, we determine the scale setting function via $w_0$ scale in the gradient flow method. Furthermore, we estimate the pseudo-critical temperature at zero chemical potential from the chiral susceptibility. Combining these results, we can discuss the QCD phase diagram in which both axes are given by dimensionless quantities, namely, the temperature normalized by the pseudo-critical temperature on the lattice and the chemical potential normalized by the pseudoscalar meson mass. It makes it easy to compare among several lattice studies and also makes it possible to compare theoretical analyses and lattice studies in the continuum limit.

Motivation & Objective

• To establish a relative scale setting function for two-color QCD with Nf=2 Wilson fermions, enabling consistent comparison across simulations with different bare couplings.
• To determine the pseudo-critical temperature at zero chemical potential using chiral susceptibility, providing a key reference scale for the phase diagram.
• To enable the construction of a QCD phase diagram in which both axes are dimensionless—temperature normalized by Tc and chemical potential normalized by the pseudoscalar meson mass.
• To overcome the lack of physical reference scales in two-color QCD by using nonperturbative lattice methods to define relative scales.
• To facilitate continuum extrapolation and cross-study comparison by providing a universal scale-setting framework for lattice QCD simulations.

Proposed method

• Measure meson spectra (PS, vector, PCAC) across various (β, κ) values to identify a line of constant physics in the β–κ plane.
• Apply the gradient flow method to compute the w0 scale, which serves as a nonperturbative reference for lattice spacing determination.
• Use the w0 scale to derive the scale setting function relating lattice spacing to the bare coupling β.
• Compute the chiral susceptibility to locate the pseudo-critical temperature Tc at zero chemical potential.
• Construct the phase diagram using dimensionless quantities: T/Tc and μ/mPS, enabling universal comparison across different lattice actions and studies.
• Perform simulations on 16³×32 lattices with varying β and κ, using multiple configurations and trajectories to ensure statistical accuracy.

Experimental results

Research questions

• RQ1 How can a relative scale setting function be nonperturbatively determined in two-color QCD, which lacks physical reference scales?
• RQ2 What is the value of the pseudo-critical temperature Tc at zero chemical potential in Nf=2 two-color QCD with Wilson fermions?
• RQ3 How can the phase diagram be expressed in terms of dimensionless variables to allow comparison across different lattice simulations?
• RQ4 What is the relationship between the lattice spacing and the bare coupling β in this setup, and how does it enable continuum extrapolation?
• RQ5 To what extent can the w0 scale be reliably used as a reference for scale setting in two-color QCD with Wilson fermions?

Key findings

• The scale setting function is successfully determined via the w0 scale in the gradient flow method, enabling relative lattice spacing determination across different β values.
• The pseudo-critical temperature Tc is estimated from the peak of the chiral susceptibility, providing a key reference scale for the phase diagram.
• The phase diagram is constructed in dimensionless units: temperature normalized by Tc and chemical potential normalized by the pseudoscalar meson mass mPS.
• The line of constant physics is identified across multiple (β, κ) points, confirming consistency in meson mass ratios and enabling continuum extrapolation.
• The results allow direct comparison between different lattice studies and theoretical analyses in the continuum limit, despite differing lattice actions.
• The study provides a reproducible framework for scale setting in two-color QCD, crucial for future high-precision lattice QCD studies in finite-density regimes.