Narrow Results

We consider the model, which contains a nonminimal coupling of Dirac spinors to torsion. Due to the action for torsion that breaks parity, the left–right asymmetry of the spinors appears. This construction is used in order to provide dynamical electroweak symmetry breaking. Namely, we arrange all Standard Model fermions in the left-handed spinors. The additional technifermions are arranged in right-handed spinors. Due to the interaction with torsion, the technifermions are condensed and, therefore, cause appearance of the gauge boson masses. In order to provide all fermions with masses, we consider two possibilities. The first one is related to an additional coupling of a real massive scalar field to the considered spinors. The second possibility is to introduce the explicit mass term for the mentioned Dirac spinors composed of the Standard Model fermions and the technifermions.

We have shown that the possibility of the existence of the mixed phase of the non-uniform chiral (NCh) and the color superconducting (2SC) ground state depends significantly on the choice of the parameters and type of the regularization scheme. Our calculations indicate that irrespective of the choice of regularization type, in a moderate baryon density region, there is a local minimum of a system corresponding to the NCh/2SC related phase. In the 3d cutoff regularization scheme, the mixed region of the NCh and the 2SC phases exists for a broad set of NJL model parameters. However, in the Schwinger regularization scheme, if parameters are set to the vacuum values of f_π, m_π and , then the mixed region of the NCh and the 2SC phases does not exist.

In this paper, the width of the decay $\tau \to K^{-}{\pi }^0{\nu }_{\tau }$ is calculated in the framework of the Nambu–Jona-Lasinio (NJL) model. The contributions of the intermediate vector $K^{\ast }(892)$ and scalar $K_0^{\ast }(800)$ mesons are taken into account. It is shown that the main contribution to the width of this decay is given by the subprocesses with the intermediate $W$-boson and vector $K^{\ast }(892)$ meson. The scalar channel with the intermediate $K_0^{\ast }(800)$ meson gives an insignificant contribution. In Appendix A, it is shown that the contribution of the subprocess with the intermediate ${K^{\ast }}^{\prime }(1410)$ meson is negligible as well. The obtained results are in satisfactory agreement with the experimental data.

The full and differential widths of the decay $\tau \to K^0{K}^{-}{\nu }_{\tau }$ are calculated in the framework of the extended Nambu–Jona-Lasinio model.The contributions of the subprocesses with the intermediate vector mesons $\rho$(770) and $\rho$(1450) are taken into account. The obtained results are in satisfactory agreement with the experimental data.

In this work, the mixing angle of the vector $\omega (782)$ and $\varphi (1020)$ mesons is estimated in the framework of Nambu–Jona-Lasinio model. The decay $\varphi \to {\pi }^0\gamma$ is considered as a basic process to determine this angle. The obtained value is compared with the results of the other authors. Besides, the width of the decay $\varphi \to 3\pi$ and the cross-section of the process $e^{+}{e}^{-}\to {\pi }^0\varphi$ are calculated by using this angle.

The branching fractions of the decays ${\eta }^{\prime }\to \pi \rho$ and $\rho \to \pi \eta$ are calculated in the chiral quark NJL model. The decays exist due to the mass difference between $u$- and $d$-quarks leading to ${\pi }^0-{\eta }^{\prime }$ and ${\pi }^0-\eta$ mixing. Two different approaches are applied: the approximate calculation of this process, taking into account the transitions ${\pi }^0-{\eta }^{\prime }$ and ${\pi }^0-\eta$ explicitly without diagonalization and a more precise approach consisting in the diagonalization of the singlet and octet states leading to the physical fields ${\pi }^0$, $\eta$ and ${\eta }^{\prime }$. The obtained results are in satisfactory agreement with current experimental data.

In this exploratory study, I present, for the first time, the implications of the charge symmetry breaking (CSB) that arise from the $u$ and $d$ quark-mass differences on gluon and sea quark distribution functions of the pion and kaon in the framework of the Nambu–Jona-Lasino (NJL) model, which is a quark-level chiral effective theory of QCD, with the help of the proper-time regularization scheme to simulate color confinement of QCD. From the analysis, one finds that the charge symmetry (CS) gluon distribution for the pion has a good agreement with the prediction results obtained from the recent lattice QCD simulation and JAM global fit QCD analysis at a higher scale of $Q^2=5$GeV². The size of the CSB effects on gluon and sea quark distributions for the pion with the realistic ratios of $m_u/m_d=0.5$ at $Q^2=5$GeV² are, respectively, estimated by 1.3% and 2.0% at $x\simeq 1$ in comparison with those for $m_u/m_d=1.0$, while those for the kaon are approximately about 0.3% and 0.5% at $x\simeq 1$, respectively. A remarkable result is found that the CSB effects on gluon distribution for the kaon are smaller than that for the pion, which has a similar prediction result as that for the CS case.

In this paper, we study the 2-flavor equation of state of the quantum chromodynamics at zero temperature and finite chemical potentials with a modified Nambu–Jona–Lasinio model, where the beta equilibrium and electric charge neutrality conditions of the system (including u, d quarks, electrons and muons) are considered. The related chiral phase transition is also discussed in this paper. For comparison, we show the results with four different parameter sets, and find only quantitative differences. As chemical potential increases, the crossover instead of first-order chiral phase transition happens. Finally, we calculate the binding energy per baryon for different parameter sets, and find that the 2-flavor quark system with a smaller $G_1$ (or a larger m) possesses the lower binding energy per baryon, indicated to be more stable than the other case.

Radiative decays of pseudoscalar and vector mesons are calculated in the frames of chiral Nambu–Jona-Lasinio (NJL) model. We use triangle quark loops of anomalous type. During the evaluation of this loop integrals we used two methods. In the first method we neglect the dependence of external momenta. In that case we reproduce the Wess–Zumino–Witten terms of effective chiral meson Lagrangian. In the second method we take into account the momenta dependence of loop integrals omitting their imaginary part. This enables us to take into account quark confinement. The application of both methods are in qualitative agreement with each other and with experimental data. The second method allows us to describe the electron–positron annihilation with production pseudoscalar and vector mesons in center-of-mass energy range from 1 to 5 GeV. Comparisons with the recent experimental data are presented.

Differential distributions in the π₀π₀γ system created in the annihilation channel of an electron–positron collision are considered. The energy fractions of the pions (Dalitz-plot) distribution are presented in a general form and in approximation of intermediate vector mesons (excited and ordinary ones). It is pointed out that in relevant experiments the generalized polarizability of the neutral pion can be measured. Numerical illustrations are presented.

The first radial excitations of axial-vector mesons are considered in the framework of the extended U(3) × U(3) Nambu–Jona-Lasinio model. We calculate the mass spectrum of a₁, f₁ and also strange axial-vector mesons. For description of radially excited states, we used the form factors of polynomial type of the second order in transverse quark momentum. For the ground- and excited-state mesons consisting of light quarks we have calculated the widths of a number of strong and radiative decays. We got satisfactory agreement with experimental data for the ground states. A set of predictions for the excited states of mesons is given.

In the extended Nambu–Jona-Lasinio model the decay widths $\tau \to \rho (770)({\rho }^{\prime }(1450)){\nu }_{\tau }$ and $\tau \to K^{\ast }(892)(K^{\ast \prime }(1410)){\nu }_{\tau }$ are studied in the quark one-loop approximation. Our estimations of the decay widths $\tau \to K^{\ast }(892)(K^{\ast \prime }(1410)){\nu }_{\tau }$ are in satisfactory agreement with experimental data. In the paper, the decay widths $\tau \to \rho (770)({\rho }^{\prime }(1450)){\nu }_{\tau }$ are also calculated.

In the mean field approximation of (2 + 1)-flavor Nambu–Jona-Lasinio model, we strictly derive several sets of coupled equations for the chiral susceptibility, the quark number susceptibility, etc. at finite temperature and quark chemical potential. The critical exponents of these susceptibilities in the vicinity of the QCD critical end point (CEP) are presented in SU(2) and SU(3) cases, respectively. It is found that these various susceptibilities share almost the same critical behavior near the CEP. The comparisons between the critical exponents for the order parameters and the theoretical predictions are also included.

The processes $e^{+}{e}^{-}\to K^{\pm }{K}^{\ast \mp }(892)$ and $e^{+}{e}^{-}\to \eta \varphi (1020)$ are calculated in the framework of the extended Nambu–Jona-Lasinio model. The intermediate vector mesons $\rho (770)$, $\omega (782)$, $\varphi (1020)$ and their first radially excited states are taken into account. The obtained results are in satisfactory agreement with the experimental data. The predictions for the cross-sections of the reactions $e^{+}{e}^{-}\to K^{\pm }{K}^{\ast \mp }(1410)$, $e^{+}{e}^{-}\to {\eta }^{\prime }(958)\varphi (1020)$ and $e^{+}{e}^{-}\to \eta \varphi (1680)$ were made.

The processes $e^{+}{e}^{-}\to (f_1(1285),a_1(1260))\gamma$ in the threshold domain are considered in the framework of the extended Nambu–Jona-Lasinio model. The channels with the ground $\rho (770)$, $\omega (782)$ and radially excited $\rho (1450)$, $\omega (1420)$ intermediate meson states are taken into account. It is shown that in the process $e^{+}{e}^{-}\to f_1(1285)\gamma$, the probability of the subprocesses with $\rho$-mesons significantly exceeds the probability of the subprocesses with $\omega$-mesons, whereas, in the process $e^{+}{e}^{-}\to a_1(1260)\gamma$, $\rho$- and $\omega$-channels give approximately equal contributions. The mechanism of this effect is discussed. The radiative decay widths of $\rho (1450)\to f_1(1285)\gamma$, $\omega (1420)\to f_1(1285)\gamma$, $\rho (1450)\to a_1(1260)\gamma$ and $\omega (1420)\to a_1(1260)\gamma$ are calculated.

In the extended Nambu–Jona-Lasinio (NJL) model, the decay widths of $\tau \to (K,K(1460)){\nu }_{\tau }$, $(K,K(1460))\to \mu {\nu }_{\mu }$ are calculated. The contributions from intermediate axial-vector mesons $K_1(1270)$, $K_1(1400)$ and the first radially excited state $K_1(1650)$ are taken into account. Estimates for the weak decay constants $F_K$ and $F_{K^{\prime }}$ are given. Predictions are made for the width of $\tau \to K(1460){\nu }_{\tau }$ decay and $F_{K^{\prime }}$ constant.

In the extended Nambu–Jona-Lasinio model, the branching fraction of $\tau \to K^{\ast 0}(892)K^{-}{\nu }_{\tau }$ is calculated. The contributions from the contact diagram and the diagrams with intermediate axial-vector, vector and pseudoscalar mesons in the ground and first radially excited states are taken into account. It is shown that an axial-vector and vector channel with a contact diagram give a dominant contribution to the branching fraction. The obtained results for the branching fraction $\tau \to K^{\ast 0}(892)K^{-}{\nu }_{\tau }$ are in satisfactory agreement with experimental data. A prediction for the differential distribution over the invariant mass of the meson pair $K^{\ast 0}(892)K^{-}$ is given.

The effect of the interaction of mesons in the final state is additionally considered within the description of $\tau \to \pi \eta ({\eta }^{\prime }){\nu }_{\tau }$ decays. This interaction is taken into account at the level of production of intermediate pions. One of them, in turn, might be transited into $\eta$ or ${\eta }^{\prime }$ mesons. Our results do not exceed the experimentally established branching fractions, and they are in agreement with the results of other theoretical studies.

We prove that Nambu–Jona-Lasinio model is an exact description of infrared Quantum ChromoDynamics (QCD) deriving it from QCD Lagrangian. The model we obtain is renormalizable and confining but, taking very small momenta fixes completely all the parameters of the Nambu–Jona-Lasinio model through those of QCD. The choice of the infrared propagator is done consistently with recent numerical results from lattice and Dyson–Schwinger equations for Yang–Mills theory. The model we get coincides, once the ultraviolet contribution is removed, with the one proposed by Langfeld, Kettner and Reinhardt [Nucl. Phys. A608 (1996) 331].

Two-loop corrections for the standard Abelian Nambu–Jona-Lasinio model are obtained with the optimized perturbation theory (OPT) method. These contributions improve the usual mean-field and Hartree–Fock results by generating a 1/N_c suppressed term, which only contributes at finite chemical potential. We take the zero temperature limit observing that, within the OPT, chiral symmetry is restored at a higher chemical potential μ, while the resulting equation of state is stiffer than the one obtained when mean-field is applied to the standard version of the model. In order to understand the physical nature of these finite N_c contributions, we perform a numerical analysis to show that the OPT quantum corrections mimic effective repulsive vector–vector interaction contributions. We also derive a simple analytical approximation for the mass gap, accurate at the percent level, matching the mean-field approximation extended by an extra vector channel to OPT. For μ ≳ μ_c the effective vector coupling matching OPT is numerically close (for the Abelian model) to the Fierz-induced Hartree–Fock value G/(2N_c), where G is the scalar coupling, and then increases with μ in a well-determined manner.