arXiv subjects

A. A. Osipov

Publications and source records attributed to A. A. Osipov.

85 records · Page 5Linked to original sources

arXiv2007

OZI violating eight-quark interactions as a thermometer for chiral transitions

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.

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arXiv2007

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~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.

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arXiv2006

Lowering the critical temperature with eight-quark interactions

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.

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arXiv2006

Stable Multiquark Interactions

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.

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arXiv2006

pi pi scattering in a nonlocal Nambu -- Jona-Lasinio model

We consider a nonlocal version of the Nambu and Jona-Lasinio model. The nonlocality is contained in the quark-antiquark bilinears of the four-quark vertices as a form factor of the Gaussian type. The model has three parameters which can be fixed in favour of the values of the pion mass, the pion decay constant f_pi, and the current quark mass. The pi pi scattering amplitude is obtained by calculating the quark box and the sigma-pole diagrams, where sigma is the scalar isoscalar meson. It is shown that this amplitude satisfies the well-known Weinberg relation. We obtain the s, p, d wave scattering lengths in all isotopic channels and the s wave slope parameters. The results are in satisfactory agreement with both phenomenological data and the basic requirements of low-energy theorems, thus supporting to the form factor used.

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arXiv2005

Symmetries and Ambiguities in the linear sigma model with light quarks

We investigate the role of undetermined finite contributions generated by radiative corrections in a $SU(2)\times SU(2)$ linear sigma model with quarks. Although some of such terms can be absorbed in the renormalization procedure, one such contribution is left in the expression for the pion decay constant. This arbitrariness is eliminated by chiral symmetry.

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arXiv2004

Long distance expansion for the NJL model with SU(3) and U_A(1) breaking

This work is a follow up of recent investigations, where we study the implications of a generalized heat kernel expansion, constructed to incorporate non-perturbatively the effects of a non-commutative quark mass matrix in a fully covariant way at each order of the expansion. As underlying Lagrangian we use the Nambu -- Jona-Lasinio model of QCD, with $SU_f(3)$ and $U_A(1)$ breaking, the latter generated by the 't Hooft flavour determinant interaction. The associated bosonized Lagrangian is derived in leading stationary phase approximation (SPA) and up to second order in the generalized heat kernel expansion. Its symmetry breaking pattern is shown to have a complex structure, involving all powers of the mesonic fields allowed by symmetry. The considered Lagrangian yields a reliable playground for the study of the implications of symmetry and vacuum structure on the mesonic spectra, which we evaluate for the scalar and pseudoscalar meson nonets and compare with other approaches and experiment.

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arXiv1999

One-Loop Determinant of Dirac Operator in Non-Renormalizable Models

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.

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arXiv1997

Quark-antiquark resonances in the NJL model

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.

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arXiv1996

Low-energy dynamics of the $γγ\toππ$ reaction

We calculate the one-quark-loop amplitude for the low energy $γγ\toππ$ collision in the context of the Nambu and Jona-Lasinio model with scalar and pseudoscalar four quark couplings to all orders in the external momenta. We show that the NJL predictions for the $γγ\toπ^+π^-$ reaction are not far from the Born amplitude, which is close to the data, and is compatible with the chiral perturbation theory estimations. We determine the corrections given by the NJL model in leading order of $1/N_c$ to the chiral loop amplitude for $γγ\toπ^0π^0$. Numerical results for the $γγ\rightarrowππ$ cross sections and for pion polarizabilities are given.

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arXiv1995

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 to $ππ$ scattering. Unlike the case in earlier published papers, we obtain the $ππ$ scattering 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 constant $f_π$ are obtained. The low-energy $ππ$ phase shifts are compared to the available data. We also study the scalar form factor of the pion.

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arXiv1994

The Rho-Meson as a Collective Excitation

A model of the rho-meson as a collective excitation of $q\bar{q}$ pairs in a system that obeys the modified Nambu--Jona-Lasinio Lagrangian is proposed. The rho emerges as a dormant Goldstone boson. The origin of the rho-meson mass is understood as a result of spontaneous chiral symmetry breaking. The low-energy dynamics of rho, pi, omega and gamma is consistently described in this new framework. The model accounts for the origin of the celebrated Kawarabayashi--Suzuki--Riazuddin--Fayyazuddin relation.

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arXiv1993

The Momentum--Space Bosonization of the Nambu--Jona-Lasinio Model with Vector and Axial-Vector Mesons

The momentum-space bosonization method is extended to the case of a Nambu--Jona-Lasinio type model with vector and axial-vector mesons. The method presented gives the possibility of deriving any meson vertex function to all orders in momenta and to the leading order in $1/N_c$. Two-point functions, which describe one-particle transitions to the hadronic vacuum, and meson self-energies are considered. We find new relations which generalize the well-known KSFR relation and both the first and the second Weinberg sum rules. These result from a consistent treatment of higher order terms in the momentum expansion.

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