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Register a new userExtrapolation for meson screening masses from imaginary to real chemical potential
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We first extend our formulation for the calculation of $pi$- and $sigma$-meson screening masses to the case of finite chemical potential $mu$. We then consider the imaginary-$mu$ approach, which is an extrapolation method from imaginary chemical potential ($mu=i mu_{rm I}$) to real one ($mu=mu_{rm R}$). The feasibility of the method is discussed based on the entanglement Polyakov-loop extended Nambu--Jona-Lasinio (EPNJL) model in 2-flavor system. As an example, we investigate how reliable the imaginary-$mu$ approach is for $pi$- and $sigma$-meson screening masses, comparing screening masses at $mu_{rm R}$ in the method with those calculated directly at $mu_{rm R}$. We finally propose the new extrapolation method and confirm its efficiency.
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Temperature dependence of pion and sigma-meson screening masses is evaluated by the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model with the entanglement vertex. We propose a practical way of calculating meson screening masses in the NJL-type effective models. The method based on the Pauli-Villars regularization solves the well-known difficulty that the evaluaton of screening masses is not easy in the NJL-type effective models.The PNJL model with the entanglement vertex and the Pauli-Villars regularization well reproduces lattice QCD results on temperature dependence of the chiral condensate and the Polyakov loop. The method is applied to analyze temperature dependence of pion screening mass calculated with state-of-the-art lattice simulations with success in reproducing the lattice QCD results.
We extract the imaginary part of the heavy-quark potential using classical-statistical simulations of real-time Yang-Mills dynamics in classical thermal equilibrium. The $r$-dependence of the imaginary part of the potential is extracted by measuring the temporal decay of Wilson loops of spatial length $r$. We compare our results to continuum expressions obtained using hard thermal loop theory and to semi-analytic lattice perturbation theory calculations using the hard classical loop formalism. We find that, when plotted as a function of $m_D r$, where $m_D$ is the hard classical loop Debye mass, the imaginary part of the heavy-quark potential is independent of the lattice spacing at small $r$ and agrees well with the semi-analytic hard classical loop result. For large quark-antiquark separations, we quantify the magnitude of the non-perturbative long-range corrections to the imaginary part of the heavy-quark potential. We present our results for a wide range of temperatures, lattice spacings, and lattice volumes. Based on our results, we extract an estimate of the heavy-quark transport coefficient $kappa$ from the short-distance behavior of the classical potential and compare our result with $kappa$ obtained using hard thermal loops and hard classical loops. This work sets the stage for extracting the imaginary part of the heavy-quark potential in an expanding non-equilibrium Yang Mills plasma.
Properties of QCD at finite imaginary chemical potential are revisited to utilize for the model building of QCD in low energy regimes. For example, the electric holonomy which is closely related to the Polyakov-loop drastically affects thermodynamic quantities beside the Roberge-Weiss transition line. To incorporate several properties at finite imaginary chemical potential, it is important to introduce the holonomy effects to the coupling constant of effective models. This extension is possible by considering the entanglement vertex. We show justifications of the entanglement vertex based on the derivation of the effective four-fermi interaction in the Nambu--Jona-Lasinio model and present its general form with the local approximation. To discuss how to remove model ambiguities in the entanglement vertex, we calculate the chiral condensate with different $mathbb{Z}_3$ sectors and the dual quark condensate.
The Polyakov loop extended Nambu--Jona-Lasinio (PNJL) model with imaginary chemical potential is studied. The model possesses the extended ${mathbb Z}_{3}$ symmetry that QCD does. Quantities invariant under the extended ${mathbb Z}_{3}$ symmetry, such as the partition function, the chiral condensate and the modified Polyakov loop, have the Roberge-Weiss (RW) periodicity. The phase diagram of confinement/deconfinement transition derived with the PNJL model is consistent with the RW prediction on it and the results of lattice QCD. The phase diagram of chiral transition is also presented by the PNJL model.
We evaluate quark number densities at imaginary chemical potential by lattice QCD with clover-improved two-flavor Wilson fermion. The quark number densities are extrapolated to the small real chemical potential region by assuming some function forms. The extrapolated quark number densities are consistent with those calculated at real chemical potential with the Taylor expansion method for the reweighting factors. In order to study the large real chemical potential region, we use the two-phase model consisting of the quantum hadrodynamics model for the hadron phase and the entanglement-PNJL model for the quark phase. The quantum hadrodynamics model is constructed to reproduce nuclear saturation properties, while the entanglement-PNJL model reproduces well lattice QCD data for the order parameters such as the Polyakov loop, the thermodynamic quantities and the screening masses. Then, we calculate the mass-radius relation of neutron stars and explore the hadron-quark phase transition with the two-phase model.
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