Abstract
The Quantum Chromo Dynamics (QCD), with its two main properties of confnement 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 A, which comes into play. In nonperturbative models, like string model and bag models, the string constant a, the hadronic bag surface tension E and the concept of the hadronic bag pressure B emerge naturally. Since these parameters characterize the same color confning force, this explains the existence of simple mathematical relationships that connect them. Although in most applications of the MIT bag model, considering B with its phenomenologically determined value as a constant does not generate any inconsistency, however, there are some indications that B is not a universal constant. The concept of hadronic bag pressure B as a parameter was introduced long before, and we plan in this work to extrapolate the concept of B 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 (T, V, B) using an improved L-m,L-n-method and considering the hadronic bag pressure B as a thermodynamic variable like the temperature T and volume V. The fndings in the small B region, in themselves, are very unexpected and exciting that essentially concern the abnormal behavior of the order parameter H(T, V, B). This shows that, from an experimental point of view, a low value of the hadronic bag pressure B would have dramatic consequences. Thus, it is argued that the abnormal behavior observed in the order parameter H(T, V, B) 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: B >= B-min. A detailed study of the global properties of the order parameter H(T, V, B) 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 B-min. We succeeded to show that the physically genuine colorless deconfining phase transition is feasible only if the thermodynamic lower bound is taken as B-1/4 (min)? 56 MeV. As a consequence, the corresponding lower bound of the hadronic bag surface tension is sigma(1/3)(min)? 47:77 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.