Jona-Lasinio Type Model Research Articles

Heavy-quark spin polarization induced by the Kondo effect in a magnetic field

We propose a new mechanism of the heavy-quark spin polarization (HQSP) in quark matter induced by the Kondo effect under external magnetic field. The Kondo effect is caused by a condensate between a heavy and a light quark called the Kondo condensate leading to a mixing of the heavy and light quark spins. Thus the HQSP is driven through the Kondo effect from light quarks coupling with the magnetic field in quark matter. For demonstration, we employ the Nambu--Jona-Lasinio type model under a magnetic field, and investigate the HQSP within the linear response theory with vertex corrections required by the $U(1)_{\rm EM}$ electromagnetic gauge invariance. As a result, we find that the HQSP arises significantly with the appearance of the Kondo effect. Our findings are testable in future sign-problem-free lattice simulations.

Chiral transformations of spin-1 mesons in the non-symmetric vacuum

A new sort of chiral transformations for spin-1 states is obtained as a result of a linearized diagonalization of πa1 mixing in the effective meson Lagrangian. Using this symmetry argument, we argue that there is no physical distinction between such theory and the theory in which a covariant nonlinear diagonalization is used instead. As an illuminating example, the Nambu–Jona-Lasinio type model with the broken SU(2)×SU(2) chiral symmetry in the one-quark-loop approximation is considered.

Some properties of two Nambu-Jona-Lasinio -type models with inputs from lattice QCD

We investigate the phase diagram of the so-called Polyakov--Nambu--Jona-Lasinio (PNJL) model at finite temperature and nonzero chemical potential. The calculations are performed in the light and strange quark sectors ($u$, $d$, $s$), which includes the 't Hooft instanton induced interaction term that breaks the axial symmetry, and the quarks are coupled to the (spatially constant) temporal background gauge field. On one hand, a special attention is payed to the critical end point (CEP). The strength of the flavor-mixing interaction alters the CEP location, since when it becomes weaker the CEP moves to low temperatures and can even disappear. On the other hand, we also explore the connection between QCD, a nonlocal Nambu--Jona-Lasinio type model and the Landau gauge gluon propagator. Possible links between the quenched gluon propagator and low energy hadronic phenomenology are investigated.

What does low energy physics tell us about the zero momentum gluon propagator

The connection between QCD, a nonlocal Nambu–Jona-Lasinio type model and the Landau gauge gluon propagator is explored. This two point function is parameterized by a functional form which is compatible with Dyson–Schwinger and lattice QCD results. Demanding the nonlocal model to reproduce the experimental values for the pion mass, the pion decay constant, Γπ→γγ and the light quark condensate we conclude that low energy physics does not distinguish between the so-called decoupling and scaling solutions of the Dyson–Schwinger equations. This result means that, provided that the model parameters are chosen appropriately, one is free to choose any of the above scenarios. Furthermore, the nonlocal Nambu–Jona-Lasinio quark model considered here is chiral invariant and satisfies the GMOR relation at the 1% level of precision.

Thermodynamics and critical behavior in the Nambu–Jona-Lasinio model of QCD

We investigate the phase diagram of strongly interacting matter as a function of temperature and baryonic density/chemical potential, within Nambu--Jona-Lasinio type models. We perform a systematic study concerning the existence, location, and properties of a critical end point/tricritical point, both in SU(2) and SU(3) versions of the model. We verify that, for ${m}_{u}={m}_{d}=0$ and up to a critical strange quark mass, there is a tricritical point, which becomes a critical end point in a world with realistic values of the current quark masses. The properties of physical observables, such as the baryon number susceptibility and the specific heat, are analyzed in the vicinity of the critical end point, with special focus on their critical exponents. The behavior of mesons in the $T\ensuremath{-}{\ensuremath{\mu}}_{B}({\ensuremath{\rho}}_{B})$ plane is analyzed in connection with possible signatures of partial and effective restoration of chiral symmetry.

Dynamical chiral symmetry breaking by a magnetic field and multi-quark interactions

Catalysis of dynamical symmetry breaking by a constant magnetic field in (3+1) dimensions is considered. We use the three flavour Nambu–Jona-Lasinio type model with 't Hooft and eight-quark interaction terms. It is shown that the multi-quark interactions introduce new additional features to this phenomenon: (a) the local minimum of the effective potential catalyzed by the constant magnetic field is smoothed out with increasing strength of the field at the characteristic scale H∼1019 G, (b) the multi-quark forces generate independently another local minimum associated with a larger dynamical fermion mass. This state may exist even for multi-quark interactions with a subcritical set of couplings, and is globally stable with respect to a further increase of the magnetic field.

Manifestation of instabilities in Nambu–Jona-Lasinio type models

We study a Nambu-Jona-Lasinio (NJL) type model with two-flavor quark matter in $\beta$-equilibrium. It turns out that the system develops instabilities in the dispersion relations of the diquark fields, i.e., the velocity squared $v^2$ becomes negative in a certain region of the electron chemical potential. The critical point is the same as that of the chromomagnetic instability. The results imply the existence of spatially inhomogeneous diquark condensates in the genuine vacuum. We also discuss gauge equivalent classes between the inhomogeneous diquark condensates and gluon condensates.

Abnormal number of Nambu-Goldstone bosons in the color-asymmetric dense color superconducting phase of a Nambu–Jona-Lasinio–type model

We consider an extended Nambu--Jona-Lasinio model including both (q \bar q)- and (qq)-interactions with two light-quark flavors in the presence of a single (quark density) chemical potential. In the color superconducting phase of the quark matter the color SU(3) symmetry is spontaneously broken down to SU(2). If the usual counting of Goldstone bosons would apply, five Nambu-Goldstone (NG) bosons corresponding to the five broken color generators should appear in the mass spectrum. Unlike that expectation, we find only three gapless diquark excitations of quark matter. One of them is an SU(2)-singlet, the remaining two form an SU(2)-(anti)doublet and have a quadratic dispersion law in the small momentum limit. These results are in agreement with the Nielsen-Chadha theorem, according to which NG-bosons in Lorentz-noninvariant systems, having a quadratic dispersion law, must be counted differently. The origin of the abnormal number of NG-bosons is shown to be related to a nonvanishing expectation value of the color charge operator Q_8 reflecting the lack of color neutrality of the ground state. Finally, by requiring color neutrality, two massive diquarks are argued to become massless, resulting in a normal number of five NG-bosons with usual linear dispersion laws.

Chiral symmetry breaking, color superconductivity and quark matter phase diagram: a variational approach

We discuss in this note simultaneous existence of chiral symmetry breaking and color superconductivity at finite temperature and density in a Nambu–Jona–Lasinio type model. The methodology involves an explicit construction of a variational ground state and minimisation of the thermodynamic potential. There exist nontrivial solutions to the gap equations at finite densities with both quark–antiquark as well as diquark condensates for the “ground” state. However, such a phase is thermodynamically unstable with the pressure being negative in this region. We also compute the equation of state, and obtain the structure of the phase diagram in the model.

Pion Observables in the Extended NJL Model with Vector and Axial-Vector Mesons

The momentum-space bosonization method of a Nambu and Jona-Lasinio type model with vector and axial-vector mesons is applied toππscattering. Unlike the case in earlier published papers, we obtain theππscattering amplitude using the linear and nonlinear realizations of chiral symmetry and fully taking into account the momentum dependence of meson vertices. We show the full physical equivalence between these two approaches. The chiral expansion procedure in this model is discussed in detail. Chiral expansions of the quark mass, pion mass and constantfπare obtained. The low-energyππphase shifts are compared to the available data. We also study the scalar form factor of the pion.

Regularization in the gauged Nambu-Jona-Lasinio model.

Various prescriptions employed for regulating gauged Nambu--Jona-Lasinio type models such as the top-quark condensate model are discussed. The use of dimensional regularization maintains gauge invariance but destroys the quadratic divergence in the gap equation. If instead a simple ultraviolet momentum cutoff is used to regulate loop integrals, then gauge invariance is destroyed by a quadratically divergent term as well as by ambiguities associated with arbitrary routing of loop momenta. Finally it is shown that one can use dispersion relations to regulate the top-quark condensate model. This prescription maintains gauge invariance and does not depend on arbitrary shifts in loop momenta.

Nambu—Jona-Lasinio Model: An Effective Lagrangian for Quantum Chromodynamics at Intermediate Length Scales

A Nambu--Jona-Lasinio type model is proposed as an effective Lagrangian for quantum chromodynamics at intermediate length scales. It is shown that the SU(n) x SU(n) nonlinear sigma model, including the Wess-Zumino term, can be derived from it in the low-energy limit. Also presented is the effective nonminimal action whose minima correspond to baryons in the many-color limit.