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The solitonic sector of the Nambu - Jona-Lasinio model with baryon number one is solved in the presence of an external medium. The calculations fully include the polarization of both the Dirac sea and the medium as well as the Pauli blocking effect. We found that with an increasing density the medium destabilizes the soliton. At finite medium density the soliton mass gets reduced whereas the mean square baryon radius shows an increase - a swelling of the soliton. At some critical density of about two times nuclear matter density there is no localized solution - the soliton disappears.
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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.
We estimate the axion properties i.e. its mass, topological susceptibility and the self-coupling within the framework of Polyakov loop enhanced Nambu-Jona-Lasinio (PNJL) model at finite temperature and quark chemical potential. PNJL model, where quarks couple simultaneously to the chiral condensate and to a background temporal quantum chromodynamics (QCD) gauge field, includes two important features of QCD phase transition, i.e. deconfinement and chiral symmetry restoration. The Polyakov loop in PNJL model plays an important role near the critical temperature. We have shown significant difference in the axion properties calculated in PNJL model compared to the same obtained using Nambu-Jona-Lasinio (NJL) model. We find that both the mass of the axion and its self-coupling are correlated with the chiral transition as well as the confinement-deconfinement transition. We have also estimated the axion properties at finite chemical potential. Across the QCD transition temperature and/or quark chemical potential axion mass and its self-coupling also changes significantly. Since the PNJL model includes both the fermionic sector and the gauge fields, it can give reliable estimates of the axion properties, i.e. its mass and the self-coupling in a hot and dense QCD medium. We also compare our results with the lattice QCD results whenever available.
We treat quantum chromodynamics (QCD) using a set of Dyson-Schwinger equations derived, in differential form, with the Bender-Milton-Savage technique. In this way, we are able to derive the low energy limit that assumes the form of a non-local Nambu-Jona-Lasinio model with all the parameters properly fixed by the QCD Lagrangian and the determination of the mass gap of the gluon sector.
The effects of meson fluctuations are studied in a nonlocal generalization of the Nambu-Jona-Lasinio model, by including terms of next-to-leading order (NLO) in 1/N_c. In the model with only scalar and pseudoscalar interactions NLO contributions to the quark condensate are found to be very small. This is a result of cancellation between virtual mesons and Fock terms, which occurs for the parameter sets of most interest. In the quark self-energy, similar cancellations arise in the tadpole diagrams, although not in other NLO pieces which contribute at the sim 25% level. The effects on pion properties are also found to be small. NLO contributions from real $pipi$ intermediate states increase the sigma meson mass by $sim 30%$. In an extended model with vector and axial interactions, there are indications that NLO effects could be larger.
Within the context of an extended Nambu - Jona-Lasinio model, we analyze the role of the axial-vector $a_1(1260)$ and $a_1(1640)$ mesons in the decay $tauto u_tau rho^0pi^-$. The contributions of pseudoscalar $pi$ and $pi (1300)$ states are also considered. The form factors for the decay amplitude are determined in terms of the masses and widths of these states. To describe the radial excited states $pi (1300)$ and $a_1(1640)$ we introduce two additional parameters which can be estimated theoretically, or fixed from experiment. The decay rate and $rhopi$ mass spectrum are calculated.
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