Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userRegularization dependence on phase diagram in Nambu-Jona-Lasinio model
109
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study the regularization dependence on meson properties and the phase diagram of quark matter by using the two flavor Nambu-Jona-Lasinio model. We find that the meson properties and the phase structure do not show drastically difference depending the regularization procedures. We also find that the location or the existence of the critical end point highly depends on the regularization methods and the model parameters. Then we think that regularization and parameters are carefully considered when one investigates the QCD critical end point in the effective model studies.
rate research
Read More
We investigate the phase diagram on temperature-chemical potential plane in the Nambu-Jona-Lasinio model with the dimensional regularization. While the structure of the resulting diagram shows resemblance to the one in the frequently used cutoff regularization, some results of our study indicate striking difference between these regularizations. The diagram in the dimensional regularization exhibits strong tendency of the first order phase transition.
We investigate the phase diagram of the so-called Polyakov--Nambu--Jona-Lasinio model at finite temperature and nonzero chemical potential with three quark flavours. Chiral and deconfinement phase transitions are discussed, and the relevant order-like parameters are analyzed. The results are compared with simple thermodynamic expectations and lattice data. A special attention is payed to the critical end point: as the strength of the flavour-mixing interaction becomes weaker, the critical end point moves to low temperatures and can even disappear.
The Nambu--Jona-Lasinio model is investigated in the $1/N_c$ expansion with the dimensional regularization. At the four-dimensional limit the meson propagators have simple forms in the leading order of the $1/N_c$ expansion. Thus the next to leading order calculation reduces to an ordinary one loop calculation. Here we obtain an explicit form of the $1/N_c$ correction and numerically evaluate the $N_c$ dependence for the gap equation.
Based on the Cornwall-Jackiw-Tomboulis effective potential, we extensively study nonperturbative renormalization of the gauged Nambu-Jona-Lasinio model in the ladder approximation with standing gauge coupling. Although the pure Nambu-Jona-Lasinio model is not renormalizable, presence of the gauge interaction makes it possible that the theory is renormalized as an interacting continuum theory at the critical line in the ladder approximation. Extra higher dimensional operators (``counter terms) are not needed for the theory to be renormalized. By virtue of the effective potential approach, the renormalization (``symmetric renormalization) is performed in a phase-independent manner both for the symmetric and the spontaneously broken phases of the chiral symmetry. We explicitly obtain $beta$ function having a nontrivial ultraviolet fixed line for the renormalized coupling as well as the bare one. In both phases the anomalous dimension is very large ($ ge 1$) without discontinuity across the fixed line. Operator product expansion is explicitly constructed, which is consistent with the large anomalous dimension owing to the appearance of the nontrivial extra power behavior in the Wilson coefficient for the unit operator. The symmetric renormalization breaks down at the critical gauge coupling, which is cured by the generalized renormalization scheme (``$tM$-dependent renormalization). Also emphasized is the formal resemblance to the four-fermion theory in less than four dimensions which is renormalizable in $1/N$ expansion.
It is shown that the endpoint of the first order transition line which merges into a crossover regime in the phase diagram of the Nambu--Jona-Lasinio model, extended to include the six-quark t Hooft and eight-quark interaction Lagrangians, is pushed towards vanishing chemical potential and higher temperatures with increasing strength of the OZI-violating eight-quark interactions. We clarify the connection between the location of the endpoint in the phase diagram and the mechanism of chiral symmetry breaking at the quark level. We show how the 8q interactions affect the number of effective quark degrees of freedom. We are able to obtain the correct asymptotics for this number at large temperatures by using the Pauli-Villars regularization.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
