Dynamics near QCD critical point by dynamic renormalization group

Abstract

We work out the basic analysis of dynamics near QCD critical point (CP) by dynamic renormalization group (RG). In addition to the RG analysis by coarse graining, we construct the nonlinear Langevin equation as a basic equation for the critical dynamics. Our construction is based on the generalized Langevin theory and the relativistic hydrodynamics. Applying the dynamic RG to the constructed equation, we derive the RG equation for the transport coefficients and analyze their critical behaviors. We find that the resulting RG equation turns out to be the same as that for the liquid-gas CP except for an insignificant constant. Therefore, the bulk viscosity and the thermal conductivity strongly diverge at the QCD CP. We also show that the thermal and viscous diffusion modes exhibit critical slowing down with the dynamic critical exponents $z_{\mathrm{thermal}}\sim 3$ and $z_{\mathrm{viscous}}\sim 2$, respectively. In contrast, the sound propagating mode shows critical speeding up with the negative exponent $z_{\mathrm{sound}}\sim -0.8$.

16 pages, 4 figures. accepted version by PRD. A comment on a frame dependence is added in Sec. V

References in corpus (8)

• New Critical Point Induced by the Axial Anomaly in Dense QCD
• Dynamic universality class of the QCD critical point
• Influence of vector interaction and Polyakov loop dynamics on inhomogeneous chiral symmetry breaking phases
• Spectral sum rules for the quark-gluon plasma
• Heavy Quark Diffusion with Relativistic Langevin Dynamics in the Quark-Gluon Fluid
• Phase structure, collective modes, and the axial anomaly in dense QCD
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Cited by in corpus (10)

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• Dynamical evolution of critical fluctuations and its observation in heavy ion collisions
• Shear Viscosity and Phase Diagram from Polyakov$-$Nambu$-$Jona-Lasinio model
• Transport coefficients of O(N) scalar field theories close to the critical point
• Indications for a critical point in the phase diagram for hot and dense nuclear matter
• Ising-QCD phenomenology close to the critical point
• Viscosity of a net-baryon fluid near the QCD critical point
• Generalized nonlinear Langevin equation from quantum nonlinear projection operator
• New dynamic critical phenomena in nuclear and quark superfluids
• Dynamic density correlations in a baryon rich fluid using Mori-Zwanzig-Nakjima projection operator method