arXiv subjects
Publications and source records attributed to A. H. Blin.
We review the effect on vacuum properties and magnetic catalysis, of adding the most general 0-spin 8-quark (8q) interactions to the combined SU(3) flavor Nambu--Jona-Lasinio (NJL) and 6-quark (6q) 't Hooft interaction Lagrangian.
An attempt is made to resolve certain incongruities within the Nambu - Jona-Lasinio (NJL) and Polyakov loop extended NJL models (PNJL) which currently are used to extract the thermodynamic characteristics of the quark-gluon system. It is argued that the most attractive resolution of these incongruities is the possibility to obtain the thermodynamic potential directly from the corresponding extremum conditions (gap equations) by integrating them, an integration constant being fixed in accordance with the Stefan-Boltzmann law. The advantage of the approach is that the regulator is kept finite both in divergent and finite valued integrals at finite temperature and chemical potential. The Pauli-Villars regularization is used, although a standard 3D sharp cutoff can be applied as well.
Several advantages in the use of a Pauli-Villars regularization procedure in extended Nambu--Jona-Lasinio models with Polyakov loop are discussed.
The extension of the Nambu-Jona-Lasino Model with six and eight quark interactions to include the Polyakov loop is analysed. Several interesting features are determined to be an effect of the choice of the regularization procedure. The use of a Pauli-Villars covariant regularization enables a coherent and correct description of several quantities.
It is shown that the endpoint of the first order transition line which merges into a crossover regime in the phase diagram of the Nambu--Jona-Lasinio model, extended to include the six-quark 't Hooft and eight-quark interaction Lagrangians, is pushed towards vanishing chemical potential and higher temperatures with increasing strength of the OZI-violating eight-quark interactions. We clarify the connection between the location of the endpoint in the phase diagram and the mechanism of chiral symmetry breaking at the quark level. We show how the 8q interactions affect the number of effective quark degrees of freedom. We are able to obtain the correct asymptotics for this number at large temperatures by using the Pauli-Villars regularization.
It is shown that the endpoint of the first order transition line which merges into a crossover regime in the phase diagram of the Nambu--Jona-Lasinio model, extended to include the six-quark 't Hooft and eight-quark interaction Lagrangians, is pushed towards vanishing chemical potential and higher temperatures with increasing strength of the OZI-violating eight-quark interactions. We clarify a connection between the location of the endpoint in the phase diagram and the mechanism of chiral symmetry breaking at the quark level. Constraints on the coupling strengths based on groundstate stability and physical considerations are explained.
We present the results obtained in the three-flavour ($N_f=3$) Nambu--Jona-Lasinio model which is extended by the $U(1)_A$ breaking six-quark 't Hooft interaction and eight-quark interactions. We address the problem of stability, and some phenomenological consequences of the models with multi-quark interactions.
The influence of a constant magnetic field on the order parameter of the four-dimensional Nambu and Jona-Lasinio model extended by the 't Hooft six-quark term and eight-quark interactions is considered. It is shown that the multi-quark interactions cause the order parameter to increase sharply (secondary magnetic catalysis) with increasing strength of the field at the characteristic scale $H\sim 10^{14}Λ^2$ G/MeV^2.
In this talk attention is drawn to thermal properties due to the addition of eight quark interactions in the standard $SU(3)\times SU(3)$ chiral Nambu-Jona-Lasinio model (NJL) with 't Hooft interaction (NJLH). The schematic SU(3) flavor limit with massless current quarks as well as the realistic case $m_u=m_d\ne m_s$ are discussed.
A NJL Lagrangian extended to six and eight quark interactions is applied to study temperature effects (SU(3) flavor limit, massless case), and (realistic massive case). The transition temperature can be considerably reduced as compared to the standard approach, in accordance with recent lattice calculations. The mesonic spectra built on the spontaneously broken vacuum induced by the 't Hooft interaction strength, as opposed to the commonly considered case driven by the four-quark coupling, undergoes a rapid crossover to the unbroken phase, with a slope and at a temperature which is regulated by the strength of the OZI violating eight-quark interactions. This strength can be adjusted in consonance with the four-quark coupling and leaves the spectra unchanged, except for the sigma meson mass, which decreases. A first order transition behavior is also a possible solution within the present approach.
The thermodynamic potential and thermal dependence of low lying mass spectra of scalars and pseudoscalars are evaluated in a generalized Nambu -- Jona-Lasinio model, which incorporates eight-quark interactions. These are necessary to stabilize the scalar effective potential for the light and strange quark flavors, which would be otherwise unbounded from below. In addition it turns out that they are also crucial to i) lower the temperature of the chiral transition, in conformity with lattice calculations, ii) sharpen the temperature interval in which the crossover occurs, iii) or even allow for first order transitions to occur with realistic quark mass values, from certain critical values of the parameters. These are unprecedented results which cannot be obtained within the NJL approaches restricted to quartic and six-quark interactions.
This work is a follow-up of our recent observation that in the SU(3) flavor limit with vanishing current quark masses the temperature for the chiral transition is substantially reduced by adding eight-quark interactions to the Nambu - Jona-Lasinio Lagrangian with U_A(1) breaking. Here we generalize the case to realistic light and strange quark masses and confirm our prior result. Additionally, we demonstrate that depending on the strength of OZI violating eight-quark interactions, the system undergoes either a rapid crossover or a first order phase transition. The meson mass spectra of the low lying pseudoscalars and scalars at T=0 are not sensitive to the difference in the parameter settings that correspond to these two alternatives, except for the singlet-octet mixing scalar channels, mainly the sigma meson.
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~10^{19} 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.
It is shown that eight-quark interactions, which are needed to stabilize the ground state of the combined three flavor Nambu -- Jona-Lasinio and 't Hooft Lagrangians, play also an important role in determining the critical temperature at which transitions occur from the dynamically broken chiral phase to the symmetric phase.
We show that single and multislit experiments involving matter waves may be constructed to assess correlations between the position and momentum of a single free particle. These correlations give rise to position dependent phases which develop dynamically and may play an important role in the interference patterns. For large enough transverse coherence lenght such interference patterns are noticeably different from those of a classical dispersion free wave.
The necessity of adding higher order multiquark interactions to the three flavor NJL model with $U_A(1)$ breaking, in order to stabilize its vacuum, is discussed.
We use proper-time regularizations to define the one-loop fermion determinant in the form suggested by Gasser and Leutwyler some years ago. We show how to obtain the polynomial by which this definition of ln det D needs to be modified in order to arrive at the fermion determinant whose modulus is invarinat under chiral transformations. As an example it is shown how the fundamental symmetries associated with the NJL model are preserved in a consistent way.
The problem of the $ρ$ meson resonance solution in the extended NJL model is studied. It has been shown previously that the solution for the $ρ$ meson changes smoothly from a bound state to a "virtual state" when the vector channel attraction becomes too weak to support bound state solutions. We have found that together with these solutions a separate resonance branch appears which is not connected smoothly with the bound state solutions. At small values of constituent quark mass, $m\sim 200$ MeV, it corresponds to the physical vector meson resonance solution in the quark-continuum region. The $a_1$ and $σ$ resonances are also discussed.