Transport and hydrodynamics in the chiral limit

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 $S{U}_L(2)\times S{U}_R(2)$ 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.

27 pages, 2 figures. Correct a mistake, some of the results are slightly modified the conclusion are not changed .Corrected typos. Added references

References in corpus (6)

• Spectral sum rules for the quark-gluon plasma
• A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion
• The eightfold way to dissipation
• Bose-Einstein condensation of pions in heavy-ion collisions at the CERN Large Hadron Collider (LHC) energies
• Chiral dynamics in the low-temperature phase of QCD
• Multiplicity fluctuations at the quark-hadron phase transition from a fluid dynamical model