# Effective Field Theory Models for Thermal QCD

## TL;DR

This paper develops an effective field theory framework for studying thermal QCD with quarks, including mean field analysis and pion fluctuation models, to understand phase transition behavior.

## Contribution

It introduces a comprehensive effective field theory model for finite-temperature QCD with quarks, linking mean field results to pion fluctuation theories and predicting critical line curvature.

## Key findings

- Predicted the curvature of the QCD critical line.
- Formulated a pionic effective theory from the quark-based model.
- Analyzed mean field parameters and their impact on phase transitions.

## Abstract

We present an effective field theory model for QCD at finite temperature with quarks. We discuss the mean field theory, the fixing of parameters, and a prediction for the curvature of the critical line. We proceed to write down a pionic theory of fluctuations around the mean field, and discuss how the parameters of this pionic effective theory descend from the model with quarks.