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Register a new userSoft Modes at the Critical End Point in the Chiral Effective Models
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H. Fujii
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At the critical end point in QCD phase diagram, the scalar, vector and entropy susceptibilities are known to diverge. The dynamic origin of this divergence is identified within the chiral effective models as softening of a hydrodynamic mode of the particle-hole--type motion, which is a consequence of the conservation law of the baryon number and the energy.
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This paper has been withdrawn by the authors, due to its incompleteness.
We investigate the role played by the Polyakov loop in the dynamics of the chiral phase transition in the framework of the so-called PNJL model in the SU(2)sector. We present the phase diagram where the inclusion of the Polyakov loop moves the critical points to higher temperatures, compared with the NJL model results. The critical properties of physical observables, such as the baryon number susceptibility and the specific heat, are analyzed in the vicinity of the critical end point, with special focus on their critical exponents. The results with the PNJL model are closer to lattice results and we also recover the universal behavior of the critical exponents of both the baryon susceptibility and the specific heat.
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.
We analyze the critical phenomena in the theory of strong interactions at high temperatures starting from first principles. The model is based on the dual Yang-Mills theory with scalar degrees of freedom - the dilatons. The latter are produced due to the spontaneous breaking of an approximate scale symmetry. The phase transitions are considered in systems where the field conjugate to the order parameter has the (critical) chiral end mode. The hiral end point (ChEP) is a distinct singular feature existence of which is dictated by the chiral dynamics. The physical approach the effective ChEP is studied via the influence fluctuations of two-body Bose-Einstein correlation function for observed particles to which the chiral end mode couples.
In this article we explore the critical end point in the $T-mu$ phase diagram of a thermomagnetic nonlocal Nambu--Jona-Lasinio model in the weak field limit. We work with the Gaussian regulator, and find that a crossover takes place at $mu, B=0$. The crossover turns to a first order phase transition as the chemical potential or the magnetic field increase. The critical end point of the phase diagram occurs at a higher temperature and lower chemical potential as the magnetic field increases. This result is in accordance to similar findings in other effective models. We also find there is a critical magnetic field, for which a first order phase transition takes place even at $mu=0$.
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