# Calculating the EoS of the dense quark-gluon plasma using the Complex Langevin equation

## TL;DR

This paper computes the equation of state of dense quark-gluon plasma at finite chemical potential using an advanced Complex Langevin method with improved actions, showing good agreement with traditional approaches at small chemical potentials.

## Contribution

It introduces a generalized stout smearing procedure for the Complex Langevin equation on the SL(3,C) manifold, enabling more accurate calculations of the quark-gluon plasma properties.

## Key findings

- Good agreement with Taylor expansion at small chemical potentials.
- Successful implementation of improved actions in the Complex Langevin framework.
- First application of generalized stout smearing for this purpose.

## Abstract

The pressure and energy density of the quark-gluon plasma at finite baryon chemical potential are calculated using the Complex Langevin equation. The stout smearing procedure is generalized for the SL(3,$\mathcal{C}$) manifold allowing the usage of an improved action in the Complex Langevin setup. Four degenerate flavors of staggered quarks with $m_\pi=500-700$ MeV are used with a tree-level Symanzik improved gauge action on $16^3 \times 8 $ lattices. Results are compared to the Taylor expansion and good agreement is found for small chemical potentials.