Approaching the continuum with anisotropic lattice thermodynamics

TL;DR

This work advances finite-temperature QCD thermodynamics by employing highly anisotropic lattices to enhance temporal resolution for spectral analyses. The authors perform coordinated tuning of a four-parameter anisotropic lattice action at both 3-flavour and 2+1 flavours using the Symanzik flow method and dispersion relations to set $a_s$, $\xi_g$, $\xi_f$, and $m_\pi$, generating ensembles across $T\approx$ 100–530 MeV. They report a chiral transition near $T_c\sim 178$–$182$ MeV with emerging vector–axial degeneracy and perform a bottomonium NRQCD study with spectral-function reconstruction, finding no definitive large thermal mass shift within current uncertainties. Overall, Gen3 demonstrates improved spectral reconstruction capabilities and lays the groundwork for physical-pion-mass ensembles and broader spectroscopy, including charm and light-baryon sectors.

Abstract

The FASTSUM collaboration has a long-standing programme of using anisotropic lattice QCD to investigate strong interaction thermodynamics, and in particular spectral quantities. Here we present first results from our new ensemble which has a temporal lattice spacing a_t=15am and anisotropy xi=a_s/a_t=7, giving unprecedented resolution in the temporal direction. We show results for the chiral transition, vector-axial-vector degeneracy, and heavy quarkonium, and compare them with earlier results with coarser time resolution.

Figures (6)

• Figure 1: Gauge anisotropy (top) and lattice spacing (bottom) from the Wilson flow. Left: $N_f=3$, including linear and quadratic fits. Right: $N_f=2+1$, including quadratic fits.
• Figure 2: Left: light pseudoscalar and vector dispersion relation for the $N_f=3$ and $N_f=2+1$ ensembles. Right: Light and strange meson dispersion relations for the $N_f=2+1$ ensemble. Note that the blue circles and green diamonds are the same in both plots.
• Figure 3: Left: The squared pseudoscalar-to-vector meson mass ratio as a function of the bare quark mass (inverse hopping parameter), for a number of valence quark masses on the 3-flavour ensemble. Right: The strange pseudoscalar-to-vector mass ratio on an $N_f=2+1$ background.
• Figure 4: Left: The dimensionless bare subtracted chiral condensate. Right: The dimensionless chiral susceptibility. The dashed lines are there to guide the eye, while the continuous lines are fits to \ref{['eq:transition-fits']}, using the data points represented by the orange diamonds.
• Figure 5: Left: The $V-A$ degeneracy ratio $\mathcal{R}_{V\!A}(\tau)$ for all temperatures. Right: The summed degeneracy ratio $\mathcal{R}_{V\!A}$ as a function of temperature.