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Register a new userFaddeev calculation of pentaquark $Theta^+$ in the Nambu-Jona-Lasinio model-based diquark picture
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A Bethe-Salpeter-Faddeev (BSF) calculation is performed for the pentaquark $Theta^+$ in the diquark picture of Jaffe and Wilczek in which $Theta^+$ is a diquark-diquark-${bar s}$ three-body system. Nambu-Jona-Lasinio (NJL) model is used to calculate the lowest order diagrams in the two-body scatterings of ${bar s}D$ and $D D$. With the use of coupling constants determined from the meson sector, we find that ${bar s}D$ interaction is attractive in s-wave while $DD$ interaction is repulsive in p-wave. With only the lowest three-body channel considered, we do not find a bound $ frac 12^+$ pentaquark state. Instead, a bound pentaquark $Theta^+$ with $ frac 12^-$ is obtained with a unphysically strong vector mesonic coupling constants.
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A Bethe-Salpeter-Faddeev (BSF) calculation is performed for the pentaquark $Theta^+$ in the diquark picture of Jaffe and Wilczek in which $Theta^+$ is a diquark-diquark-${bar s}$ three-body system. Nambu-Jona-Lasinio (NJL) model is used to calculate the lowest order diagrams in the two-body scatterings of ${bar s}D$ and $D D$. With the use of coupling constants determined from the meson sector, we find that ${bar s}D$ interaction is attractive while $DD$ interaction is repulsive, and there is no bound $frac 12^+$ pentaquark state. A bound pentaquark $Theta^+$ can only be obtained with unphysically strong vector mesonic coupling constants.
We investigate theta-vacuum effects on the QCD phase diagram for the realistic 2+1 flavor system, using the three-flavor Polyakov-extended Nambu-Jona-Lasinio (PNJL) model and the entanglement PNJL model as an extension of the PNJL model. The theta-vacuum effects make the chiral transition sharper. For large theta-vacuum angle the chiral transition becomes first order even if the quark number chemical potential is zero, when the entanglement coupling between the chiral condensate and the Polyakov loop is taken into account. We finally propose a way of circumventing the sign problem on lattice QCD with finite theta.
We study the thermo-magnetic properties of the strong coupling constant G and quark mass M entering the Nambu-Jona-Lasinio model. For this purpose, we compute the quark condensate and compare it to lattice QCD (LQCD) results to extract the behavior of G and M as functions of the magnetic field strength and temperature. We find that at zero temperature, where the LQCD condensate is found to monotonically increase with the field strength, M also increases whereas G remains approximately constant. However, for temperatures above the chiral/deconfinement phase transitions, where the LQCD condensate is found to monotonically decrease with increasing field, M and G also decrease monotonically. For finite temperatures, below the transition temperature, we find that both G and M initially grow and then decrease with increasing field strength. To study possible consequences of the extracted temperature and magnetic field dependence of G and M, we compute the pressure and compare to LQCD results, finding an excellent qualitative agreement. In particular, we show that the transverse pressure, as a function of the field strength, is always negative for temperatures below the transition temperature whereas it starts off being positive and then becomes negative for temperatures above the transition temperature, also in agreement with LQCD results. We also show that for the longitudinal pressure to agree with LQCD calculations, the system should be described as a diamagnet. We argue that the turnover of M and G as functions of temperature and field strength is a key element that drives the behavior of the quark condensate going across the transition temperature and provides clues for a better understanding of the inverse magnetic catalysis phenomenon.
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.
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.
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