Variable hadronic bag pressure effect in colorless deconfining phase transition: Thermodynamic lower bounds for hadronic bag pressure and hadronic bag surface tension

Abstract

The Quantum Chromo Dynamics (QCD), with its two main properties of confinement and asymptotic freedom, is considered as the fundamental theory of the strong interaction from which the phenomenology of string model and hadronic bag models can be derived as particular cases. In QCD, besides quark masses, there is only one parameter, the renormalization scale parameter [Formula: see text], which comes into play. In nonperturbative models, like string model and bag models, the string constant [Formula: see text], the hadronic bag surface tension [Formula: see text] and the concept of the hadronic bag pressure [Formula: see text] emerge naturally. Since these parameters characterize the same color confining force, this explains the existence of simple mathematical relationships that connect them. Although in most applications of the MIT bag model, considering [Formula: see text] with its phenomenologically determined value as a constant does not generate any inconsistency, however, there are some indications that [Formula: see text] is not a universal constant. The concept of hadronic bag pressure [Formula: see text] as a parameter was introduced long before, and we plan in this work to extrapolate the concept of [Formula: see text] to become a full-fledged thermodynamic variable and to explore the consequences of its variability in the context of our colorless MIT bag model. To achieve this, we carry out a detailed thermodynamic study based on the three variables [Formula: see text] using an improved [Formula: see text]-method and considering the hadronic bag pressure [Formula: see text] as a thermodynamic variable like the temperature [Formula: see text] and volume [Formula: see text]. The findings in the small [Formula: see text] region, in themselves, are very unexpected and exciting that essentially concern the abnormal behavior of the order parameter [Formula: see text]. This shows that, from an experimental point of view, a low value of the hadronic bag pressure [Formula: see text] would have dramatic consequences. Thus, it is argued that the abnormal behavior observed in the order parameter [Formula: see text] well reflects the appearance of the mixed state at low temperature before the deconfining process. We also indicate how this result might be avoided by imposing a lower bound on the hadronic bag pressure: [Formula: see text]. A detailed study of the global properties of the order parameter [Formula: see text] as function on the three variables is given, and as an illustration of our ideas we construct three different criteria from which we extract the lower bound of the hadronic bag pressure [Formula: see text]. We succeeded to show that the physically genuine colorless deconfining phase transition is feasible only if the thermodynamic lower bound is taken as [Formula: see text][Formula: see text]MeV. As a consequence, the corresponding lower bound of the hadronic bag surface tension is [Formula: see text][Formula: see text]MeV. Our results are consistent with each other, and seem to corroborate the results obtained by other approaches, such as the thermodynamic model of chromo-magnetism. We focus not only on certain technical details, but also on physical understanding and interpretation. The results are relevant for the parton phenomenology of stars and for URHIC experiments. We review some of the underlying physics and discuss outstanding questions regarding this variability.