Probing the finite density equation of state of QCD via resummed perturbation theory

TL;DR

This thesis investigates the thermodynamics of hot, dense quark-gluon plasma at finite density using resummed perturbation theory, achieving good agreement with lattice data and validating convergence methods for higher order calculations.

Contribution

It applies resummed perturbation theory frameworks to finite density QCD, providing new insights into the equation of state and charge fluctuations near the deconfinement transition.

Findings

Good agreement with lattice QCD data down to low temperatures

Validation of fast convergence in mass parameter expansions

Comparison of two perturbative schemes showing consistent results

Abstract

In this Ph.D. thesis, the primary goal is to present a recent investigation of the finite density thermodynamics of hot and dense quark-gluon plasma. As we are interested in a temperature regime, in which naive perturbation theory is known to lose its predictive power, we clearly need to use a refined approach. To this end, we adopt a resummed perturbation theory point of view and employ two different frameworks. We first use hard-thermal-loop perturbation theory (HLTpt) at leading order to obtain the pressure for nonvanishing quark chemical potentials, and next, inspired by dimensional reduction, resum the known four-loop weak coupling expansion for the quantity. We present and analyze our findings for various cumulants of conserved charges. This provides us with information, through correlations and fluctuations, on the degrees of freedom effectively present in the quark-gluon plasma right above the deconfinement transition. Moreover, we compare our results with state-of-the-art lattice Monte Carlo simulations as well as with a recent three-loop mass truncated HTLpt calculation. We obtain very good agreement between the two different perturbative schemes, as well as between them and lattice data, down to surprisingly low temperatures right above the phase transition. We also quantitatively test the convergence of an approximation, which is used in higher order loop calculations in HTLpt. This method based on expansions in mass parameters, is unavoidable beyond leading order, thus motivating our investigation. We find the ensuing convergence to be very fast, validating its use in higher order computations.