# Improved Actions for QCD Thermodynamics on the Lattice

## TL;DR

This paper investigates how improved lattice actions reduce finite cut-off effects in high-temperature QCD thermodynamics, demonstrating significant improvements even on small lattices through perturbative calculations and Monte Carlo simulations.

## Contribution

It introduces and tests improved $O(a^2)$ and $O(a^4)$ actions that significantly diminish finite cut-off effects in lattice QCD thermodynamics.

## Key findings

- Finite cut-off effects are strongly reduced with improved actions.
- Reductions are observed on lattices with $N_\tau=4$ at high temperatures.
- Improvements persist down to a few times the deconfinement temperature.

## Abstract

Finite cut-off effects strongly influence the thermodynamics of lattice regularized QCD at high temperature in the standard Wilson formulation. We analyze the reduction of finite cut-off effects in formulations of the thermodynamics of $SU(N)$ gauge theories with three different $O(a^2)$ and $O(a^4)$ improved actions. We calculate the energy density and pressure on finite lattices in leading order weak coupling perturbation theory ($T\rightarrow \infty$) and perform Monte Carlo simulations with improved $SU(3)$ actions at non-zero $g^2$. Already on lattices with temporal extent $N_\tau=4$ we find a strong reduction of finite cut-off effects in the high temperature limit, which persists also down to temperatures a few times the deconfinement transition temperature.