[Paper Review] Meson correlation functions at high temperature QCD: $SU(2)_{CS}$ symmetry vs. free quarks

Christian Rohrhofer, Yasumichi Aoki+4 more|arXiv (Cornell University)|Sep 1, 2018

Quantum Chromodynamics and Particle Interactions4 references3 citations

TL;DR

This study investigates meson correlation functions in high-temperature QCD using domain-wall fermions on lattices with $N_s = 32$ and $n_f = 2$ flavors. It finds that at $T \sim 2T_c$, spatial correlation functions exhibit approximate $SU(2)_{CS}$ symmetry due to dominant chromo-electric interactions, while at $T > 700$ MeV, the system approaches the free quark limit where $SU(2)_{CS}$ symmetry is broken, indicating a transition from strongly correlated quark-like excitations to asymptotically free quarks.

ABSTRACT

We report on the progress of understanding spatial correlation functions in high temperature QCD. We study isovector meson operators in $N_f=2$ QCD using domain-wall fermions on lattices of $N_s=32$ and different quark masses. It has previously been found that at $\sim 2T_c$ these observables are not only chirally symmetric but in addition approximately $SU(2)_{CS}$ and $SU(4)$ symmetric. In this study we increase the temperature up to $5T_c$ and can identify convergence towards an asymptotically free scenario at very high temperatures.

Motivation & Objective

• To investigate the emergence of $SU(2)_{CS}$ and $SU(4)$ symmetries in spatial meson correlation functions at high temperatures in $n_f=2$ QCD.
• To determine whether the approximate $SU(2)_{CS}$ symmetry observed near $2T_c$ persists or breaks at higher temperatures.
• To compare the behavior of interacting quarks with that of free quarks in the high-temperature limit.
• To understand the role of chromo-electric vs. chromo-magnetic interactions in shaping the spectral structure of mesons at high $T$.
• To clarify the nature of quark excitations in the $T \sim 2T_c$ regime, distinguishing them from free quarks.

Proposed method

• Lattice QCD simulations using Möbius domain wall fermions for two degenerate light quark flavors with masses between 2–15 MeV.
• Gauge configurations generated with the tree-level improved Symanzik action at varying $eta$ and $N_t$, enabling access to temperatures from $T \simeq 1.2T_c$ to $5.5T_c$.
• Spatial correlation functions $C_{ar{ ho}}(n_z)$ computed for isovector bilinear operators $\mathcal{O}_{ ho}(x) = \bar{q}(x)\vec{\tau}\Gamma q(x)$, grouped into $S$, $PS$, $\mathbf{V}$, $\mathbf{A}$, $\mathbf{T}$, $\mathbf{X}$, and non-propagating channels.
• Ratios of correlation functions connected by $U(1)_A$ and $SU(2)_{CS}$ transformations are computed to probe symmetry restoration, with comparison to free quark limits.
• The Dirac operator's low-mode truncation is not applied; instead, the focus is on full QCD dynamics at high $T$.
• Theoretical analysis of the QCD Lagrangian in Minkowski space decomposes into chromo-electric ($D_0$) and chromo-magnetic ($D_i$) terms, with only the former invariant under $SU(2)_{CS}$.

Experimental results

Research questions

• RQ1 Does $SU(2)_{CS}$ symmetry emerge in spatial meson correlation functions in $n_f=2$ QCD at temperatures above $2T_c$?
• RQ2 How does the $SU(2)_{CS}$ symmetry ratio evolve with increasing temperature, and does it approach unity at high $T$?
• RQ3 To what extent do interacting quarks at $T \sim 2T_c$ resemble free quarks, and what is the role of chromo-electric vs. chromo-magnetic interactions?
• RQ4 Is the approximate $SU(2)_{CS}$ symmetry at $T \sim 2T_c$ due to the dominance of chromo-electric interactions over chromo-magnetic ones?
• RQ5 How does the system transition from $SU(2)_{CS}$-symmetric behavior to the free quark limit at asymptotically high temperatures?

Key findings

• At $T \sim 220$ MeV ($\sim 1.2T_c$), the $SU(2)_{CS}$ ratio of correlation functions is significantly above 1, indicating strong influence of chromo-magnetic interactions.
• At $T \sim 380$ MeV ($\sim 2.2T_c$), the $SU(2)_{CS}$ ratio approaches approximately 1, signaling the dominance of chromo-electric interactions and approximate $SU(2)_{CS}$ symmetry.
• For $T > 700$ MeV ($\sim 3.8T_c$), the $SU(2)_{CS}$ ratio for interacting quarks converges toward the free quark limit, where it is below 1 due to explicit $SU(2)_{CS}$ breaking in the free Dirac Lagrangian.
• The spatial correlation functions for operators related by $SU(2)_{CS}$ transformations (e.g., $V_x$ and $T_t$) become approximately degenerate at $T \sim 380$ MeV, confirming approximate symmetry restoration.
• The $U(1)_A$ symmetry is approximately restored at $T > 220$ MeV, as evidenced by degeneracy of $PS$ and $S$ correlators, and $\mathbf{T}$ and $\mathbf{X}$ correlators.
• The results suggest that at $T \sim 2T_c$, quark excitations are not free but are instead correlated via chromo-electric fields, forming a 'stringy fluid' with $SU(2)_{CS}$ symmetry, even in the presence of finite chemical potential.