The 3-D O(4) universality class and the phase transition in two-flavor QCD

TL;DR

This paper determines the critical equation of state for the 3D O(4) universality class, relevant for the chiral transition in two-flavor QCD, using polynomial parametric representations and small-field expansions.

Contribution

It introduces a systematic approximation scheme for the O(4) critical equation of state that respects analytic properties and Goldstone singularities, providing universal amplitude ratios.

Findings

Estimated universal amplitude ratios for the O(4) universality class.

Validated polynomial parametric representations across the critical regime.

Connected the O(4) critical behavior to the finite-temperature chiral transition in QCD.

Abstract

We determine the critical equation of state of the three-dimensional O(4) universality class. We first consider the small-field expansion of the effective potential (Helmholtz free energy). Then, we apply a systematic approximation scheme based on polynomial parametric representations that are valid in the whole critical regime, satisfy the correct analytic properties (Griffiths' analyticity), take into account the Goldstone singularities at the coexistence curve, and match the small-field expansion of the effective potential. From the approximate representations of the equation of state, we obtain estimates of several universal amplitude ratios. The three-dimensional O(4) universality class is expected to describe the finite-temperature chiral transition of quantum chromodynamics with two light flavors. Within this picture, the O(4) critical equation of state relates the reduced temperature, the quark masses, and the condensates around T_c in the limit of vanishing quark masses.