As the restriction of the gauge fields to the Gribov region is taken into account, it turns out that the resulting gauge field propagators display a nontrivial infrared behavior, being very close to the ones observed in lattice gauge field theory sim
ulations. In this work, we explore for the first time a higher correlation function in the presence of the Gribov horizon: the ghost-anti-ghost-gluon interaction vertex, at one-loop level. Our analytical results (within the so-called Refined Gribov Zwanziger theory) are fairly compatible with lattice YM simulations, as well as with solutions from the Schwinger-Dyson equations. This is an indication that the RGZ framework can provide a reasonable description in the infrared not only of gauge field propagators, but also of higher correlation functions, such as interaction vertices.
Establishing a description for confinement is not something simple. In order to try to understand a little about this phenomenon, we will explore the thermodynamics of models that try to describe it in terms of propagators with violation of positivit
y. In this work, confinement is always understood in the sense of positivity violation of the propagator of the elementary fields. For simplicity, we will define a model for scalar fields with a momentum dependent and nonlocal mass term. One of our objectives is to verify the thermodynamic properties of this Lagrangian in order to analyze possible inconsistencies. For this we use the functional formalism of Quantum Field Theory at finite temperature, from which we obtain the partition function and, consequently, the thermodynamic variables such as pressure, energy density, entropy density, etc. Then, we obtain the two-point function at finite temperature of the scalar field, in order to study whether or not there is a restoration of positivity (hence, deconfinement, in our language).
We consider Yang-Mills theories quantized in the Landau gauge in the presence of the Gribov horizon via the refined Gribov Zwanziger (RGZ) framework. As the restriction of the gauge path integral to the Gribov region is taken into account, the result
ing gauge field propagators display a nontrivial infrared behavior, being very close to the ones observed in lattice gauge field theory simulations. In this work, we explore a higher correlation function in the Refined Gribov-Zwanziger theory: the ghost-gluon interaction vertex, at one-loop level. We show explicit compatibility with kinematical constraints, as required by the Ward identities of the theory, and obtain analytical expressions in the limit of vanishing gluon momentum. We find that the RGZ results are nontrivial in the infrared regime, being compatible with lattice YM simulations in both SU(2) and SU(3), as well as with solutions from Schwinger-Dyson equations in different truncation schemes, Functional Renormalization Group analysis, and the RG-improved Curci-Ferrari model.
The grand partition function of a model of confined quarks is exactly calculated at arbitrary temperatures and quark chemical potentials. The model is inspired by a softly BRST-broken version of QCD and possesses a quark mass function compatible with
nonperturbative analyses of lattice simulations and Dyson-Schwinger equations. Even though the model is defined at tree level, we show that it produces a nontrivial and stable thermodynamic behaviour at any temperature or chemical potential. Results for the pressure, the entropy and the trace anomaly as a function of the temperature are qualitatively compatible with the effect of nonperturbative interactions as observed in lattice simulations. The finite density thermodynamics is also shown to contain nontrivial features, being far away from an ideal gas picture.
We explore the parameter space of the two-flavor thermal quark-meson model and its Polyakov loop-extended version under the influence of a constant external magnetic field $B$. We investigate the behavior of the pseudo critical temperature for chiral
symmetry breaking taking into account the likely dependence of two parameters on the magnetic field: the Yukawa quark-meson coupling and the parameter $T_0$ of the Polyakov loop potential. Under the constraints that magnetic catalysis is realized at zero temperature and the chiral transition at $B=0$ is a crossover, we find that the quark-meson model leads to thermal magnetic catalysis for the whole allowed parameter space, in contrast to the present picture stemming from lattice QCD.
The possibility of a hadron-quark phase transition in extreme astrophysical phenomena such as the collapse of a supernova is not discarded by the modern knowledge of the high-energy nuclear and quark-matter equations of state. Both the density and th
e temperature attainable in such extreme processes are possibly high enough to trigger a chiral phase transition. However, the time scales involved are an important issue. Even if the physical conditions for the phase transition are favorable (for a system in equilibrium), there may not be enough time for the dynamical process of phase conversion to be completed. We analyze the relevant time scales for the phase conversion via thermal nucleation of bubbles of quark matter and compare them to the typical astrophysical time scale, in order to verify the feasibility of the scenario of hadron-quark phase conversion during, for example, the core-collapse of a supernova.
The phase transition from hadronic to quark matter may take place already during the early post-bounce stage of core collapse supernovae when matter is still hot and lepton rich. If the phase transition is of first order and exhibits a barrier, the f
ormation of the new phase occurs via the nucleation of droplets. We investigate the thermal nucleation of a quark phase in supernova matter and calculate its rate for a wide range of physical parameters. We show that the formation of the first droplet of a quark phase might be very fast and therefore the phase transition to quark matter could play an important role in the mechanism and dynamics of supernova explosions.
We investigate the process of phase conversion in a thermally-driven {it weakly} first-order quark-hadron transition. This scenario is physically appealing even if the nature of this transition in equilibrium proves to be a smooth crossover for vanis
hing baryonic chemical potential. We construct an effective potential by combining the equation of state obtained within Lattice QCD for the partonic sector with that of a gas of resonances in the hadronic phase, and present numerical results on bubble profiles, nucleation rates and time evolution, including the effects from reheating on the dynamics for different expansion scenarios. Our findings confirm the standard picture of a cosmological first-order transition, in which the process of phase conversion is entirely dominated by nucleation, also in the case of a weakly first-order transition. On the other hand, we show that, even for expansion rates much lower than those expected in high-energy heavy ion collisions, nucleation is very unlikely, indicating that the main mechanism of phase conversion is spinodal decomposition. Our results are compared to those obtained for a strongly first-order transition, as the one provided by the MIT bag model.
We present numerical results on bubble profiles, nucleation rates and time evolution for a weakly first-order quark-hadron phase transition in different expansion scenarios. We confirm the standard picture of a cosmological first-order phase transiti
on, in which the phase transition is entirely dominated by nucleation. We also show that, even for expansion rates much lower than those expected in heavy-ion collisions nucleation is very unlikely, indicating that the main phase conversion mechanism is spinodal decomposition.
