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$U(1)_A$ symmetry restoration at finite temperature with mesonic correlators

Ryan Bignell, Gert Aarts, Chris Allton, Benjamin Jäger, Seyong Kim, Jon-Ivar Skullerud, Antonio Smecca

TL;DR

This work tackles the question of whether the $U(1)_A$ anomaly is effectively restored at finite temperature in QCD by examining the degeneracy between the pseudoscalar $( ext{π})$ and flavour non-singlet scalar $( ext{δ})$ correlators. Using anisotropic FASTSUM Generation 3 lattice ensembles with Wilson-Clover fermions, the authors develop smeared, mid-point-normalised, and integrated correlator ratios to suppress ultraviolet and Wilson artefacts and to isolate infrared restoration signals. They find that the integrated, smeared ratio indicates an effective $U(1)_A$ restoration at $T_{U(1)_A}=317(4)$ MeV, significantly above the chiral transition temperature $T_{ m pc} oughly180$ MeV for their pion mass $m_ ext{π} oughly380$ MeV. This suggests that, for their setup, $U(1)_A$ restoration is not coincident with chiral restoration and provides a robust framework for future systematic studies across different pion masses and lattice parameters to map the QCD phase structure more precisely.

Abstract

The $U(1)_A$ symmetry of the massless QCD Lagrangian is explicitly broken in the quantised theory by the anomaly. It may be effectively restored at some finite temperature, which would have important consequences for the order of the chiral transition and the QCD phase diagram. It has been argued in the literature that one way to probe the effective restoration of $U(1)_A$ is to check for the degeneracy of pseudoscalar and flavour non-singlet scalar correlators. In this work, we consider a new method of examining this degeneracy based upon hadron correlation functions on the anisotropic FASTSUM ensembles. The anisotropic nature and our newest Generation 3 ensembles aid in a determination of the effective restoration of the $U(1)_A$ symmetry which we find to be $T_{U(1)_A} \sim 320$ MeV, well above the chiral transition temperature, which is $T_{\rm pc} \sim 180$ MeV for our choice of Wilson-Clover fermions.

$U(1)_A$ symmetry restoration at finite temperature with mesonic correlators

TL;DR

This work tackles the question of whether the anomaly is effectively restored at finite temperature in QCD by examining the degeneracy between the pseudoscalar and flavour non-singlet scalar correlators. Using anisotropic FASTSUM Generation 3 lattice ensembles with Wilson-Clover fermions, the authors develop smeared, mid-point-normalised, and integrated correlator ratios to suppress ultraviolet and Wilson artefacts and to isolate infrared restoration signals. They find that the integrated, smeared ratio indicates an effective restoration at MeV, significantly above the chiral transition temperature MeV for their pion mass MeV. This suggests that, for their setup, restoration is not coincident with chiral restoration and provides a robust framework for future systematic studies across different pion masses and lattice parameters to map the QCD phase structure more precisely.

Abstract

The symmetry of the massless QCD Lagrangian is explicitly broken in the quantised theory by the anomaly. It may be effectively restored at some finite temperature, which would have important consequences for the order of the chiral transition and the QCD phase diagram. It has been argued in the literature that one way to probe the effective restoration of is to check for the degeneracy of pseudoscalar and flavour non-singlet scalar correlators. In this work, we consider a new method of examining this degeneracy based upon hadron correlation functions on the anisotropic FASTSUM ensembles. The anisotropic nature and our newest Generation 3 ensembles aid in a determination of the effective restoration of the symmetry which we find to be MeV, well above the chiral transition temperature, which is MeV for our choice of Wilson-Clover fermions.
Paper Structure (9 sections, 4 equations, 4 figures, 1 table)

This paper contains 9 sections, 4 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Ensembles
  3. Results using local correlation functions
  4. Standard Definition
  5. Normalise and cutoff
  6. Normalised Ratio
  7. Smeared Ratio
  8. Integrated Ratio
  9. Conclusions and Future Work

Figures (4)

  • Figure 1: Left: Subtracted susceptibilities $\chi_\pi-\chi_\delta$, see Eq. $\left(\ref{['eqn:def1']}\right)$. Right: Subtracted normalised susceptibilities $\tilde{\chi}_\pi^{\rm norm}-\tilde{\chi}_\delta^{\rm norm}$, see Eq. $\left(\ref{['eqn:def2']}\right)$. Here the correlator has been normalised at the mid-point first and the sum starts at $\tau_{\text{min}}\,T = 0.2$.
  • Figure 2: Left: Ratio of normalised correlators $\mathcal{R}\!\left(\tau\right)$, see Eq. $\left(\ref{['eqn:def3']}\right)$. Note that the data corresponds to the legend in the figure on the right, with the temperature increasing vertically along the left-hand side of the plot. Right: Ratio $\mathcal{R}\!\left(\tau\right)$ for free Wilson correlators on lattices of the same dimensions as Generation 3.
  • Figure 3: Ratio $\mathcal{R}\!\left(\tau\right)$, see Eq. $\left(\ref{['eqn:def3']}\right)$, for four different smearing radii (including none) at $T\sim160$ MeV (left) and $T\sim356$ MeV (right). Note that the vertical scales are different.
  • Figure 4: Left: Ratio $\mathcal{R}\!\left(\tau\right)$, see Eq. $\left(\ref{['eqn:def3']}\right)$, using smeared correlators. Right: Corresponding integrated ratio $R$, see Eq. $\left(\ref{['eqn:def3:int']}\right)$. The orange curve is a spline interpolation used to find the intercept of the curve with zero.