Phase structure and thermodynamics of QCD

We discuss the phase structure and thermodynamics of QCD by means of dynamical chiral effective models. Quark and meson fluctuations are included via the functional renormalization group. We study the influence of confinement in addition to the impact of fluctuations by comparing the results of the chiral models to their Polyakov-loop extended versions. Furthermore, we discuss the mass sensitivity of the phase structure and thermodynamics and find interesting modifications close to the chiral limit.

Figure 1

Partially hadronized version of the FRG flow for QCD. The loops denote the gluon, ghost, quark and meson contributions, respectively. The crosses mark the RG regulator term.

Figure 2

Quark polarization contribution to the gluon propagator representing a contribution to the matter back-coupling.

Figure 3

Phase structure at physical pion masses for the QM (left) and PQM (right) models. Depicted is the chiral (blue, long- and short-dashed) transition line. In the PQM model the Polyakov-loop transitions (black, dot-dashed and dot-dot-dashed lines) are also shown.

Figure 4

Similar to the previous Fig. 3 but for the chiral limit; see text for more details.

Figure 5

Meson $(m_{\pi },m_{\sigma })$ and quark ($m_q$) masses in the chiral limit as a function of $\mu$ for constant temperature $T=30\mathrm{MeV}$. One extra minimum of $m_{\sigma }$ occur in the splitting region while $m_{\pi }$ vanishes until the second chiral transition is reached.

Figure 6

Phase structure of the QM (left) and PQM (right) model for small pion masses $m_{\pi }=50\mathrm{MeV}$. For these masses, the transition splitting persists, while it is washed out for increasing masses towards the physical point, cf. Fig. 3.

Figure 7

Chemical potential derivative of the chiral order parameter vs $\mu$ at physical pion masses and low temperature. Including the $T$ and $\mu$ dependence of the UV potential, ${\Omega }_{\Lambda }(T,\mu )$ as well as the modified version of $T_0(\mu )$ a splitting in the chiral transition can be determined also at physical masses.

Figure 8

Pressure normalized by the Stefan-Boltzmann pressure, Eq. (25), in the QM (upper panels) and PQM (lower panels) model, each for $m_{\pi }=138$, 50, 0 MeV (left to right).

Figure 9

Interaction measure $\Delta /T^4$ in the QM model (upper panels) and PQM model (lower panels); see text for details.

Figure 10

Dependence of the phase structure on our choice of the parameter $\widehat{\gamma }$ in $T_0(N_f,T,\mu )$. The solid lines denote the chiral transition while the dashed lines correspond to the transition related to the Polyakov-loop, $\Phi$. See text for a detailed discussion.

Figure 11

Phase structure at physical masses with (upper lines) and without (lower lines) modified UV potential and ${\theta }_b$.