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Register a new userQuasiparticle Model of Quark-Gluon Plasma at Imaginary Chemical Potential
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Authors
M. Bluhm
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A quasiparticle model of the quark-gluon plasma is compared with lattice QCD data for purely imaginary chemical potential. Net quark number density, susceptibility as well as the deconfinement border line in the phase diagram of strongly interacting matter are investigated. In addition, the impact of baryo-chemical potential dependent quasiparticle masses is discussed. This accomplishes a direct test of the model for non-zero baryon density. The found results are compared with lattice QCD data for real chemical potential by means of analytic continuation and with a different (independent) set of lattice QCD data at zero chemical potential.
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We investigate chemical-potential ($mu$) dependence of the static-quark free energies in both the real and imaginary $mu$ regions, using the clover-improved two-flavor Wilson fermion action and the renormalization-group improved Iwasaki gauge action. Static-quark potentials are evaluated from Polyakov-loop correlators in the deconfinement phase and the imaginary $mu=imu_{rm I}$ region and extrapolated to the real $mu$ region with analytic continuation. As the analytic continuation, the potential calculated at imaginary $mu=imu_{rm I}$ is expanded into a Taylor-expansion series of $imu_{rm I}/T$ up to 4th order and the pure imaginary variable $imu_{rm I}/T$ is replaced by the real one $mu_{rm R}/T$. At real $mu$, the 4th-order term weakens $mu$ dependence of the potential sizably. Also, the color-Debye screening mass is extracted from the color-singlet potential at imaginary $mu$, and the mass is extrapolated to real $mu$ by analytic continuation. The screening mass thus obtained has stronger $mu$ dependence than the prediction of the leading-order thermal perturbation theory at both real and imaginary $mu$.
We summarize the derivation of the finite temperature, finite chemical potential thermodynamic potential in the bag-model approximation to quantum chromodynamics (QCD) that includes a finite $s$-quark mass in the Feynman diagram contributions for both zero-order and two-loop corrections to the quark interaction. The thermodynamic potential for quarks in QCD is a desired ingredient for computations of the equation of state in the early universe, supernovae, neutron stars, and heavy-ion collisions. The 2-loop contributions are normally divergent and become even more difficult in the limit of finite quark masses and finite chemical potential. We introduce various means to interpolate between the low and high chemical potential limits. Although physically well motivated, we show that the infinite series Pade rational polynomial interpolation scheme introduces spurious poles. Nevertheless, we show that lower order interpolation schemes such as polynomial interpolation reproduce the Pade result without the presence of spurious poles. We propose that in this way one can determine the equation of state for the two-loop corrections for arbitrary chemical potential, temperature and quark mass. This provides a new realistic bag-model treatment of the QCD equation of state. We compute the QCD phase diagram with up to the two-loop corrections. We show that the two-loop corrections decrease the pressure of the quark-gluon plasma and therefore increase the critical temperature and chemical potential of the phase transition. We also show, however, that the correction for finite $s$-quark mass in the two-loop correction serves to decrease the critical temperature for the quark-hadron phase transition in the early universe.
We give the alternative formulation of quasiparticle model of quark gluon plasma with medium dependent dispersion relation. The model is thermodynamically consistent provided the medium dependent contribution to the energy density is taken in to account. We establish the connection of our model with other variants of quasiparticle models which are thermodynamically consistent. We test the model by comparing the equation of state with the lattice gauge theory simulations of SU(3) pure gluodynamics .
Based on the constituent quasiparticle model of the quark-gluon plasma (QGP), color quantum path-integral Monte-Carlo (PIMC) calculations of the thermodynamic properties of the QGP are performed. We extend our previous zero chemical potential simulations to the QGP at finite baryon chemical potential. The results indicate that color PIMC can be applied not only above the QCD critical temperature $T_c$ but also below $T_c$. Besides reproducing the lattice equation of state our approach yields also valuable additional insight into the internal structure of the QGP, via the pair distribution functions of the various quasiparticles. In particular, the pair distribution function of gluons reflects the existence of gluon-gluon bound states at low temperatures and $mu=175$ MeV, i.e. glueballs, while meson-like bound states are not found.
By employing QCD inequalities, we discuss appearance of the pion condensate for both real and imaginary isospin chemical potentials, taking also into account imaginary quark chemical potential. We show that the charged pion can condense for real isospin chemical potential, but not for imaginary one. Furthermore, we evaluate the expectation value of the neutral-pion field for imaginary isospin chemical potential by using framework of the twisted mass. As a result, it is found that the expectation value becomes zero for the finite current-quark mass, whereas the Banks-Casher relation is obtained in the massless limit.
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