Extended non-chiral quark models confronting QCD

Journal of Mathematical Sciences, 2000

We compare two QCD-inspired quark models with four-fermion interaction, without and with the remnant coupling to low-energy gluons, in the regime of dynamical chiral symmetry breaking (DCSB). The first one, the Nambu-Jona-Lasinio (NJL) model ensures the factorization of scalar and pseudoscalar meson poles in correlators, the well-known Nambu relation between the scalar meson mass and the dynamical quark mass, m σ = 2m dyn , and the residual chiral symmetry in coupling constants characteristic for the linear σ-model. The second one, the Gauged NJL model, happens to be qualitatively different from the NJL model, namely, the Nambu relation is not valid and the factorization of light meson poles does not entail the residual chiral symmetry, i.e. it does not result in a linear σ-model. The more complicated DCSB pattern in the GNJL model is fully explained in terms of excited meson states with the same quantum numbers. The asymptotic restrictions on parameters of scalar and pseudoscalar meson states are derived from the requirement of chiral symmetry restoration at high energies.

2009

Using a ladder-rainbow kernel previously established for light quark hadron physics, we explore the extension to masses and electroweak decay constants of ground state pseudoscalar and vector quarkonia and heavy-light mesons in the c- and b-quark regions. We make a systematic study of the effectiveness of a constituent mass concept as a replacement for a heavy quark dressed propagator for such states. The difference between vector and axial vector current correlators is explored within the same model to provide an estimate of the four quark chiral condensate and the leading distance scale for the onset of non-perturbative phenomena in QCD.

Physical Review D, 1996

Journal of Physics G-nuclear and Particle Physics, 2009

We present a nonextensive version of the recently discussed QCD-based Nambu - Jona-Lasinio (NJL) model of many-body field theory describing behavior of strongly interacting matter. It is based on the nonextensive generalization of the Boltzmann-Gibbs (BG) statistical mechanics used in NJL model, which was taken in the form proposed by Tsallis and characterized by a dimensionless nonextensivity parameter q (for q -> 1 one recovers the usual BG case). This is a new phenomenological parameter of the model which accounts summarily for all possible (so far unspecified) effects leading to departure from the conditions required by the usual BG approach to be fully applicable. It turns out that temperature dependencies of chiral symmetry restoration, masses of pion and sigma meson and characteristic features of spinodal decomposition are sensitive to the departures from the usual BG case.

1997

A generalization to any dimension of the fermion field transformation which allows to derive the solution of the massless Schwinger model in the path integral framework is identified. A derivation based on this transformation of a Nambu-Jona-Lasinio (NJL) like model for the low energy limit of a gauge theory in dimension greater than two is presented. Our result confirms the spontaneous chiral symmetry breaking picture conjectured by Nambu many years ago and it also provides a link between QCD, NJL and chiral models. PACS number(s): 12.38-t, 12.38.Aw Typeset using REVTEX

2012

In this thesis, we focus on some aspects concerning hadronic phenomena at low energy, below 1 GeV, under which the spontaneous breaking of chiral symmetry takes place. Under this scale, the spectrum of Quantum Chromodynamics reduces to an octet of light pseudo-scalar mesons (π, K and η). But because of the confinement property, QCD under 1 GeV is highly non-perturbative, it is thus not possible to describe at low energy the dynamics of these mesons in terms of gluons and quarks (in that case the three light quarks u,d, and s). Two main alternatives exist to circumvent this major obstacle: Lattice QCD and Effective Field Theories. Lattice QCD is concerned with the numerical computations of various hadronic observables, while Effective Field Theories correspond to analytical frameworks adapted to a particular energy scale. In the case of QCD at low energy, this role is devoted to Chiral Perturbation Theory (ChiPT). This theory can be built either from two quark flavours (u and d), or ...

1994

In this talk I concentrate on the role of chiral symmetry realisation by spin-1 fields in the low energy QCD effective lagrangian. I assume that chiral symmetry is nonlinearly realised and that spin-1 fields transform homogeneously under chiral rotations, which is in sharp contrast to previous works where the ρ and the a1 mesons were treated as approximate gauge bosons of some chiral group. I emphasise the role played by four-meson couplings which in our scheme are essential for the theory to make sense. By requiring the kinetic energy density of the theory to be bounded from below we find inequalities relating three- and four-point meson couplings. It is finally shown how the combination of our analysis and of unitarity requirements naturally leads to a low-energy phenomenological lagrangian for the nonanomalous sector of πρa1 strong interactions. 1.

2011

A low energy effective field theory model for QCD with a scalar color octet field is discussed. The model relates the gluon mass, the constituent quark masses and the quark condensate. The gluon mass comes about √ N c Λ QCD with the quark condensate being proportional to the gluon mass squared. The model suggests that the restoration of chiral symmetry and the deconfinement transition occur at the same temperature and that, near the transition, the critical exponent for the condensate is twice the gluon mass one. The model also favors the decoupling like solution for the gluon propagator.

The application of effective field theory methods to the low energy structure of QCD is discussed. The analysis relies on the fact that three of the quark masses happen to be light, so that QCD exhibits an approximate chiral symmetry. The Goldstone bosons associated with the spontaneous breakdown of this symmetry represent the essential degrees of freedom at low energies. I emphasize the universal structure of the corresponding effective Lagrangian, which only depends on the symmetry properties of the theory, and then discuss the physics of the effective coupling constants. The implications of the effective theory for the masses of the light quarks are analyzed in some detail.

Nuclear Physics B, 1977

We review the subject of chiral sytmnetry breaking and its connection with the quark model. When the light plane SU(3) charges and quark field density matrix elements are transformed back to the usual static basis it becomes clear that expectation values of chiral breaking operators, such as qXiq, do not necessarily have simple SU(3) transformation properties. Starting with the standard current quark chiral Hamiltonian H' = rnuKU + mddd + ruffs, we then use current quark light-cone distribution function concepts in combination with constraints from (i) Compton amplitude fixed poles, (ii) baryon octet and decuplet mass differences, (iii) ~rN and KN a terms, (iv) GA/GV, (v) lowenergy ~r photoproduction multipoles, (vi) Goldberger-Treiman discrepancies, (vii) meson mass ratios in PCAC and, (viii) meson mass differences to determine in = ½(m u + rod) and m s in more than four independent ways. Our results are all mutually consistent and yield the values ~z ~ mrr and ms/~Z ~ 5. In particular the independent baryon and meson sectors of the theory are completely compatible.