Soft pions and transport near the chiral critical point

TL;DR

This paper investigates how critical fluctuations near the QCD chiral transition influence transport properties and soft pion spectra in heavy ion collisions, providing theoretical predictions and phenomenological estimates.

Contribution

It formulates stochastic hydrodynamics near the $O(4)$ critical point and derives scaling behaviors of transport coefficients and pion dispersion relations.

Findings

Scaling functions for shear viscosity and conductivities near the critical point.

Estimate of critical enhancement of soft pion yields matching experimental excess.

Predictions for the impact of chiral fluctuations on QCD transport properties.

Abstract

During the expansion of a heavy ion collision, the system passes close to the $O(4)$ critical point of QCD, and thus the fluctuations of the order parameter $(\sigma, \vec{\pi})$ are expected to be enhanced. Our goal is to compute how these enhanced fluctuations modify the transport coefficients of QCD near the pseudo-critical point. We also make a phenomenological estimate for how chiral fluctuations could effect the momentum spectrum of soft pions. We first formulate the appropriate stochastic hydrodynamic equations close to the $O(4)$ critical point. Then, working in mean field, we determine the correlation functions of the stress tensor and the currents which result from this stochastic real time theory, and use these correlation functions to determine the scaling behavior of the transport coefficients. The hydrodynamic theory also describes the propagation of pion waves, fixing the scaling behavior of the dispersion curve of soft pions. We present scaling functions for the shear viscosity and the charge conductivities near the pseudo-critical point, and estimate the absolute magnitude of the critical fluctuations to these parameters and the bulk viscosity. Using the calculated pion dispersion curve, we estimate the expected critical enhancement of soft pion yields, and this estimate provides a plausible explanation for the excess seen in experiment relative to ordinary hydrodynamic computations. Our results motivate further phenomenological and numerical work on the implications of chiral symmetry on real time properties of thermal QCD near the pseudo-critical point.