Sea quark effects in non-topological chiral soliton models and the Nambu-Jona-Lasinio approach

The Nambu-Jona-Lasinio model (NJL) in the chiral invariant SU (2)-sector with scalar couplings is solved numerically in the Hartree approximation (zero boson loop) for baryon number B=1. To this end first the polarized vacuum solution (B=0) is constructed using appropriately parametrized non-dynamic meson fields on the chiral circle. The cut-off Λ is fixed to reproduce the pion decay constant. With this choice a full treatment of the polarized vacuum is shown in second-order gradient expansion to be equivalent to considering kinetic energies of the mesons. Solutions of the NJL model with baryon number B=1 are obtained by adding N_c=3 valence quarks to the full polarized vacuum and subjecting them to the same meson fields. If one adds the valence quarks to the kinetic energy of the mesons the usual chiral soliton model with valence quarks (CSM) is obtained. For both, NJL and CSM, the equilibrium radii of the B=1 solution are evaluated and shown to be rather close to each other. The present approach shows no vacuum instabilities. The resulting radii are different from those of the renormalized one-quark-loop model.     

Strange and heavy flavoured hypernuclei in chiral soliton models

The extension of the chiral soliton approach to hypernuclei --strange or heavy flavoured-- becomes more reliable due to the success in describing other properties of nuclei, e.g. the symmetry energy of nuclei with atomic numbers up to ∼ 30 . The binding energies of the ground states of light hypernuclei with S = - 1 have been described in qualitative agreement with data. The existence of charmed or beautiful hypernuclei and Theta-hypernuclei (strange, charmed or beautiful) with large binding energy is expected within same approach.     

Hard soliton excitation regime: Stability investigation

The problem of the stability of one-dimensional solitons in the hard regime of soliton excitation, where the matrix element of the four-wave interaction has an additional smallness, is studied. It is that shown for optical solitons striction can weaken the Kerr nonlinearity. It is shown that solitons with a finite amplitude discontinuity at the critical soliton velocity, equal to the minimum phase velocity of linear waves, are unstable while solitons with a soft transition remain stable with respect to one-dimensional perurbations. Two-and three-dimensional solitons near threshold are unstable with respect to modulation perturbations. Zh. éksp. Teor. Fiz. 116, 299–317 (July 1999)     

关于修正的一维分子晶体模型的孤子激发

从立方型相互作用的一维分子晶体模型出发,在加入本征值平方项的近似下,运用能量极小原理和连续化近似,得到了考虑本征值平方项和立方型相互作用后一维分子晶体模型的孤子激发的修正解.在忽略了立方型相互作用和本征值平方项的近似下,孤子激发的修正解回复于通常的极化子解.并计算了孤子激发的峰宽、峰值和电子自陷势阱,分析了本征值平方项和立方型相互作用对孤子激发的峰值、峰宽和电子自陷势阱的影响.     

Phase transition and the nucleon as a soliton in the Nambu-Jona-Lasinio model at finite temperature and density

We study some bulk thermodynamical characteristics, meson properties and the nucleon as a baryon-number-one soliton in hot quark matter in the NJL model as well as in hot nucleon matter in a hybrid NJL model in which the Dirac sea of quarks is combined with a Fermi sea of nucleons. In both cases, working in the mean-field approximation, we find a chiral phase transition from the Goldstone to the Wigner phase. At finite density the chiral order parameter and the constituent quark mass have a non-monotonic temperature dependence — at finite temperatures not close to the critical one they are less affected than in cold matter. Whereas quark matter is rather soft against thermal fluctuations and the corresponding chiral phase transition is smooth, nucleon matter is much stiffer and the chiral phase transition is very sharp. The thermodynamical variables show large discontinuities which is an indication for a first-order phase transition. We solve the B = 1 solitonic sector of the NJL model in the presence of external hot quark and nucleon media. In the hot medium at intermediate temperature the soliton is more bound and less swelled than in the case of cold matter. At some critical temperature, which for nucleon matter coincides with the critical temperature for the chiral phase transition, we find no more a localized solution. According to this model scenario one should expect a sharp phase transition from nucleon to quark matter.     

Frequency selection by soliton excitation in nondegenerate intracavity down-conversion

We show that soliton excitation in intracavity down-conversion naturally selects a strictly defined frequency difference between the signal and idler fields. In particular, this phenomenon implies that if the signal has smaller losses than the idler then its frequency is pulled away from the cavity resonance and the idler frequency is pulled towards the resonance and vice versa. The frequency selection is shown to be closely linked with the relative energy balance between the idler and signal fields.     

Heavy mesons in the Nambu-Jona-Lasinio model

We propose an extended Nambu-Jona-Lasinio model to include heavy mesons with heavy quark symmetry.The quark current-current interaction is generalized to include the heavy quark currents. In order to comply with the heavy quark spin symmetry at the heavy quark limit,the dependence of the quark mass on the interaction strength is introduced. The light and heavy pseudo-scalar and vector mesons,their masses and the weak decay constants are calculated in the unified frame.     

Nambu-Jona-Lasinio Model Beyond the Mean-Field Approximation

1. Department of Technical Physics, Peking University, Beijing 100871, China;
2. Department of Physics, Peking University, Beijing 100871, China     

Strange-quark matter within the Nambu-Jona-Lasinio model

The equation of state of baryon-rich quark matter is studied within the SU(3) Nambu-Jona-Lasinio model with flavor-mixing interaction. Possible bound states (strangelets) and chiral phase transitions in this matter are investigated at various values of the strangeness fraction r _s. Model predictions are very sensitive to the ratio of the vector and scalar coupling constants, ξ=G _V/G _S. At ξ=0.5 and zero temperature, the binding energy takes a maximum value of about 15 MeV per baryon at r _s?0.4. Such strangelets are negatively charged and have typical lifetimes of about 10^?7s. Calculations are performed at finite temperatures as well. According to these calculations, bound states exist up to temperatures of about 15 MeV. The model predicts a first-order chiral phase transition at finite baryon densities. The parameters of this phase transition are calculated as functions of r _s.     

Nonstandard magnetic oscillations in the Nambu-Jona-Lasinio model

The Nambu-Jona-Lasinio model at nonzero values of an external magnetic field H and of the chemical potential is considered in the strong-coupling region G>G _c. The phase portrait of the model exhibits an infinitely large number of massless chiral-invariant phases and massive phases resulting from a spontaneous breakdown of chiral invariance. This phase structure is responsible for aperiodic oscillations of some thermodynamic parameters of the system, including the dynamical fermion mass, as functions of H ^?1.     

Electromagnetic form factors in the Nambu-Jona-Lasinio model

The original Nambu-Jona-Lasinio model is treated to leading order in 1/N. The electromagnetic form factors of the constituent quarks and the pion, and the anomalous π⁰ → 2γ decay amplitude are obtained. Their dependence on the cutoff of the model is made explicit. Two distinct limits (depending on the ratio of the cutoff to the constituent quark mass) in which the cutoff can be taken to infinity are also discussed. We find that to leading order of 1/N the model in one limit corresponds to the linear and in the other to the nonlinear sigma model.