# Real time warm pions from the lattice using an effective theory

## TL;DR

This paper explores how to analytically continue long-distance correlation functions from Euclidean to Minkowski space in finite-temperature lattice QCD, focusing on the challenges of defining real-time masses.

## Contribution

It investigates the analytic continuation of screening and pole masses from Euclidean to Minkowski space using an effective theory derived from lattice data.

## Key findings

- Analytic continuation of masses is non-trivial at finite temperature.
- Euclidean screening and pole masses differ from real-time masses.
- Effective theory helps understand the transition from Euclidean to Minkowski space.

## Abstract

Lattice measurements provide adequate information to fix the parameters of long distance effective field theories in Euclidean time. Using such a theory, we examine the analytic continuation of long distance correlation functions of composite operators at finite temperature from Euclidean to Minkowski space time. There are two definitions of mass in each regime; in Euclidean these are the screening and pole masses. The analytic continuation of these mass parameters to real time is non-trivial. This is in contrast to the situation at zero temperature.