Abstract
We analyze the evolution of hydrodynamic fluctuations for QCD matter below $T_c$ in the chiral limit, where the pions (the Goldstone modes) must be treated as additional non-abelian superfluid degrees of freedom, reflecting the broken $SU_L(2) \times SU_R(2)$ symmetry of the theory. In the presence of a finite pion mass $m_{\pi}$, the hydrodynamic theory is ordinary hydrodynamics at long distances, and superfluid-like at short distances. The presence of the superfluid degrees of freedom then gives specific contributions to the bulk viscosity, the shear viscosity, and diffusion coefficients of the ordinary theory at long distances which we compute. This determines, in some cases, the leading dependence of the transport parameters of QCD on the pion mass. We analyze the predictions of this computation, as the system approaches the $O(4)$ critical point.
Highlights
Viscous hydrodynamics, based on the conservation of energy and momentum, is remarkably successful at describing a wide range of correlations observed in heavy ion collisions and has become a kind of “standard model” for heavy ion events [1,2]
Below the transition temperature, these modes should be added to the usual hydrodynamic modes associated with energy momentum and charge conservation, leading to an effective theory which is analogous to a non-Abelian superfluid [3,4]
A distinct advantage of the hydrokinetic approach is that it can be simulated in expanding environments, capturing the physics associated with the chiral fluctuations
Summary
Viscous hydrodynamics, based on the conservation of energy and momentum, is remarkably successful at describing a wide range of correlations observed in heavy ion collisions and has become a kind of “standard model” for heavy ion events [1,2]. Below the transition temperature, these modes should be added to the usual hydrodynamic modes associated with energy momentum and charge conservation, leading to an effective theory which is analogous to a non-Abelian superfluid [3,4]. Mass the theory should be superfluidlike for modes with wavelength l ∼ m−π 1 and should asymptote to ordinary hydrodynamics for l ≫ m−π 1, with the superfluid modes correcting the ordinary transport coefficients of QCD. The standard observable proposed to detect the soft dynamics of pions induced by the chiral phase transition is the multiplicity ratio of charged pions with the neutral one [10]. IV, we discuss the expected scaling behavior of the computed transport coefficients in the vicinity of the critical point
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