Low-energy processes of meson production in the extended Nambu–Jona-Lasinio model

The processes of meson production in electron–positron collisions at low energies are characterized within the extended Nambu–Jona-Lasinio model. It is demonstrated that intermediate vector mesons (both in the ground state and in the first radially excited one) play a critical part in these processes. The obtained results are in reasonable agreement with the available experimental data. A number of theoretical predictions are made, which can be tested experimentally in the near future.     

Polarization effects of the τ → <Emphasis Type="Italic">K</Emphasis>–π<Superscript>0</Superscript>ν<Subscript>τ</Subscript> process in the Nambu–Jona-Lasinio model

The polarization effects of the τ → K–π⁰ν_τ process are described in the framework of the Nambu–Jona-Lasinio model. The intermediate vector meson K*(892) is taken into account. The contribution of these effects to the differential decay width is obtained.     

Electromagnetic Interactions of Mesons and the π<Emphasis Type="Italic">a</Emphasis><Subscript>1</Subscript> Diagonalization

It has been demonstrated that, contrary to the commonly accepted viewpoint, electromagnetic interactions cannot be consistently included in the Nambu–Jona-Lasinio model within vector meson dominance. This refers to the procedure for removing the πa₁ transition in the effective meson Lagrangian. By the example of the a₁(1260)→γπ⁺π^- radiative decay, it has been demonstrated that the gauge invariance condition for the amplitude gives rise to an electromagnetic vertex describing the direct emission of a photon and a pion by a quark–antiquark pair. Surface terms appearing in the calculation of an anomalous triangular quark diagram, where one of the vertices is the interaction violating the vector-dominance hypothesis, play a key role in satisfying the Ward identities.     

τ → K–π0ντ Decay in the Nambu–Jona-Lasinio Model Including the Final-State Interaction of Mesons

JETP Letters - The $$\tau \to {{K}^{ - }}{{\pi }^{0}}{{\nu }_{\tau }}$$ decay has been described within the Nambu–Jona-Lasinio model including the contact term and the contribution from an...     

Strange quark matter with dynamically generated quark masses

Bulk properties of strange quark matter (SQM) are investigated within the SU(3) Nambu–Jona-Lasinio model. In the chiral limit the model behaves very similarly to the MIT bag model which is often used to describe SQM. However, when we introduce realistic current quark masses, the strange quark becomes strongly disfavored, because of its large dynamical mass. We conclude that SQM is not absolutely stable.     

τ → K–ηντ Decay in the Extended Nambu–Jona-Lasinio Model Including the Final-State Interaction

JETP Letters - The width of the $$\tau \to {{K}^{ - }}\eta {{\nu }_{\tau }}$$ decay has been calculated within the extended Nambu–Jona-Lasinio model including the final-state interaction of...     

On size and shape of the average meson fields in the semibosonized Nambu & Jona-Lasinio model

We consider the bosonized form of a two-flavor Nambu & Jona-Lasinio model involving scalar-isoscalar and pseudoscalar-isovector quark-quark interaction. Solitonic meson fields are obtained by minimizing the effective Euclidean action. In dependence on the constituent quark mass, which is the only free parameter in the model, we evaluate a series of meson profiles and compare them with a properly parameterized reference profile. We show that the self-consistent fields do in fact practically not depend on the constituent quark mass. Their shape can be very well approximated by this reference profile which interpolates between the correct asymptotic behavior for small and large radii. To demonstrate the accuracy of the approximation we evaluate several static properties like energy, mean square radius, axial-vector constant and delta-nucleon mass splitting using both self-consistent and reference profiles. The agreement is found to be very well in the physically relevant mass region.     

Nonlocal Nambu–Jona-Lasinio model and chiral chemical potential

We derive the critical temperature in a nonlocal Nambu–Jona-Lasinio model with the presence of a chiral chemical potential. The model we consider uses a form factor derived from recent studies of the gluon propagator in Yang–Mills theory and has the property to fit in excellent way the form factor arising from the instanton liquid picture for the vacuum of the theory. Nambu–Jona-Lasinio model is derived form quantum chromodynamics providing all the constants of the theory without any need for fits. We show that the critical temperature in this case always exists and increases as the square of the chiral chemical potential. The expression we obtain for the critical temperature depends on the mass gap that naturally arises from Yang–Mills theory at low-energy as also confirmed by lattice computations.     

Calculation of the Width of the τ → K–K 0 ντ Decay in the Extended Nambu–Jona-Lasinio Model with Estimation of the Contribution from the Final-State Interaction

JETP Letters - The partial width of the $$\tau \to {{K}^{ - }}{{K}^{0}}{{\nu }_{\tau }}$$ decay has been calculated within the extended Nambu–Jona-Lasinio model including the contact and...     

τ− → π−π0ντ and e+e− → π+π− Processes in the Chiral Nambu—Jona-Lasinio Model Including the Interaction of Pions in the Final State

JETP Letters - The τ− → π−π0ντ and e+e− → π+π− processes have been described within the chiral Nambu—Jona-Lasinio model...     

Pion–Pion Interaction in a Soluble Two-Level Nambu–Jona-Lasinio Model

We explore the interplay between the few-body aspects of few-pion states and the many-body aspects of their quark structure. We show for a schematic quasispin model similar to the Nambu–Jona-Lasinio model how one can derive rather accurately the pion–pion scattering length from the excitation spectrum in a box.     

Effects of K–K1 Transitions on Kaon-Field Renormalization in the NJL Model Framework

Physics of Particles and Nuclei Letters - An additional kaon-field renormalization dictated by transitions between pseudoscalar and axial-vector fields is derived in the Nambu–Jona-Lasinio...     

Influence of In-medium properties of vector mesons on dilepton production in heavy ion collisions at SIS energies

Dileptons represent a unique probe for nuclear matter under extreme conditions reached in heavy ion collisions. They allow the study of meson properties, like mass and decay width, at various density and temperature regimes. Up to now, in the Tübingen model for dilepton production, modification of meson properties in nuclear medium has been accounted for by allowing a density dependence of the mass (Brown–Rho scaling) together with an ad hoc dependence of the meson decay widths on the same variable. We use the extended vector meson dominance (eVMD) model to extract meson properties in nuclear matter by computing the in-medium meson spectral functions. Dilepton spectra for C+C at 1.0 and 2.0 AGeV are calculated and compared with previous results.     

On the Problem of Spontaneous Isotopic Symmetry Breaking in Nambu–Jona-Lasinio Models

Physics of Particles and Nuclei Letters - The problem of spontaneous isotopic symmetry breaking in Nambu–Jona-Lasinio quark models is considered. It is shown that, in models with light...     

On properties of low-lying spin-1 hadron resonances

Properties of low-lying spin-1 hadron resonances are described in the review. It is shown how the Nambu–Jona-Lasinio model can be extended in the chiral invariant way by new tensor interactions. New mass formulas are obtained, which are not based on unitary symmetry groups but involve particles from different multiplets even with opposite parity. They all are in good agreement with experimental data. Dynamic properties of spin-1 mesons confirmed by the calculations performed using the QCD sum rule technique and the lattice calculations are understood and explained.     

The $$\tau\rightarrow\bar{K}^{*0}(892)\pi^{-}\nu_\tau$$ Decay in the Nambu–Jona-Lasinio Model

The width of the \(\tau\rightarrow\bar{K}^{*0}(892)\pi^{-}\nu_\tau\) decay is calculated within the Nambu–Jona-Lasinio model taking into account four channels of the formation of the \(\tau\rightarrow\bar{K}^{*0}(892)\pi^{-}\) pair—the contact interaction and three channels with intermediate axial-vector, vector, and pseudoscalar mesons. Leading contributions arise from the contact interaction and axial-vector channel with an intermediate ground-state K₁(1270) meson. Our theoretical estimate adequately reproduces the measured \(\tau\rightarrow\bar{K}^{*0}(892)\pi^{-}\nu_\tau\) decay width.     

Do we need to use regularization for the thermal part in the NJL model?

The Nambu–Jona-Lasinio(NJL)model is one of the most useful tools for studying non-perturbative strong interactions in matter.Because it is a nonrenormalizable model,the choice of regularization is a subtle issue.In this paper,we discuss one of the general issues regarding regularization in the NJL model,which is whether we need to use regularization for the thermal part by evaluating the quark chiral condensate and thermal properties in the two-flavor NJL model.The calculations in this work include three regularization schemes that contain both gauge covariant and invariant schemes.We found that,regardless of the regularization scheme we choose,it is necessary to use regularization for the thermal part when calculating physical quantities related to the chiral condensate and to not use regularization for the thermal part when calculating physical quantities related to the grand potential.     

Influence of Self-Interaction ofσ Meson to the Equation of State of Nuclear Matter

In the relativistic σ-ωmodel, the influence of the parameters in self-interaction of a meson to the equation of state of normal nuclear matter, especially, to incompressibility, effective mass, and coupling constants, is studied in detail. We find that these parameters have an intense relationship to the property of nuclear matter. At the same time , we study the relation between the binding energy and pressure of relativestic △-resonance nuclear matter and temperature using using above results in the relativistic σ-ω-π model,and it is interesting to compare it to our prior work. In all these studies, the vacuum fluctuation on nucleon, △-isobar, and σmeson is considered.     

Transport coefficients near chiral phase transition

We analyze the transport properties of relativistic fluid composed of constituent quarks at finite temperature and density. We focus on the shear and bulk viscosities and study their behavior near chiral phase transition. We model the constituent quark interactions through the Nambu–Jona-Lasinio Lagrangian. The transport coefficients are calculated within kinetic theory under relaxation time approximation including in-medium modification of quasi-particles dispersion relations. We quantify the influence of the order of chiral phase transition and the critical end point on dissipative phenomena in such a medium.