From cool pions to the chiral phase transition

TL;DR

This paper connects low-energy QCD models using effective field theory and dimensional reduction to better understand the chiral phase transition and provides a generalized formula for the finite temperature pion decay constant.

Contribution

It establishes a theoretical link between the dynamics of cool pions and the critical behavior of the chiral phase transition through effective models.

Findings

Derived a generalized expression for the finite temperature pion decay constant.

Showed the relation between the O(N) nonlinear sigma model and the O(N) Heisenberg magnet.

Reproduced known expressions in specific limits.

Abstract

Using the ideas of effective field theory and dimensional reduction, we relate the parameters of two low energy models of QCD: the O(N) nonlinear sigma model in D=3+1, which describes the dynamics of cool pions, and the O(N) Heisenberg magnet in D=3+0, which is commonly argued to reproduce the correct critical behaviour of the chiral phase transition. As a result, we obtain a generalized expression for the finite temperature pion decay constant which reproduces, in certain limits, the available expressions in the literature.