Transport properties and equation-of-state of hot and dense QGP matter near the critical endpoint in the phenomenological dynamical quasiparticle model

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We extend the effective dynamical quasiparticle model (DQPM)---constructed for the description of nonperturbative QCD phenomena of the strongly interacting quark-gluon plasma (QGP)---to large baryon chemical potentials, ${\ensuremath{\mu}}_{B}$, including a critical endpoint (CEP) and a first-order phase transition. The DQPM description of quarks and gluons is based on partonic propagators with complex self-energies where the real part of the self-energies is related to the quasiparticle mass and the imaginary part to a finite width of their spectral functions (i.e., the imaginary parts of the propagators). In DQPM the determination of complex self-energies for the partonic degrees of freedom at zero and finite ${\ensuremath{\mu}}_{B}$ has been performed by adjusting the entropy density to the lattice QCD data. The temperature-dependent effective coupling (squared) ${g}^{2}(T/{T}_{c})$, as well as the effective masses and widths of the partons are based on this adjustments. The novel extended dynamical quasiparticle model, named ``DQPM-CP,'' makes it possible to describe thermodynamical and transport properties of quarks and gluons in a wide range of temperature, $T$, and baryon chemical potential, ${\ensuremath{\mu}}_{B}$, and reproduces the equation of state of lattice QCD calculations in the crossover region of finite $T,{\ensuremath{\mu}}_{B}$. We apply a scaling ansatz for the strong coupling constant near the CEP, located at $({T}^{\mathrm{CEP}},{\ensuremath{\mu}}_{B}^{\mathrm{CEP}})=(0.100,0.960)\text{ }\text{ }\mathrm{GeV}$. We show the equation of state as well as the speed of sound for $T>{T}_{c}$ and for a wide range of ${\ensuremath{\mu}}_{B}$, which can be of interest for hydrodynamical simulations. Furthermore, we consider two settings for the strange quark chemical potentials, (I) ${\ensuremath{\mu}}_{q}={\ensuremath{\mu}}_{u}={\ensuremath{\mu}}_{s}={\ensuremath{\mu}}_{B}/3$ and (II) ${\ensuremath{\mu}}_{s}=0,{\ensuremath{\mu}}_{u}={\ensuremath{\mu}}_{d}={\ensuremath{\mu}}_{B}/3$. The isentropic trajectories of the quark-gluon plasma matter are compared for these two cases. The phase diagram of DQPM-CP is close to PNJL calculations. The leading order pQCD transport coefficients of both approaches differ. This elucidates that the knowledge of the phase diagram alone is not sufficient to describe the dynamical evolution of strongly interacting matter.