Composite antisymmetric-tensor Nambu-Goldstone bosons in a four-fermion interaction model and the Higgs mechanism

Starting from the Fierz transform of the two-flavour 't Hooft interaction (a four-fermion Lagrangian with antisymmetric Lorentz tensor interaction terms augmented by an NJL type Lorentz scalar inetraction responsible for dynamical symmetry breaking and quark mass generation), we show that: (1) antisymmetric tensor Nambu-Goldstone bosons appear provided that the scalar and tensor couplings stand in the proportion of two to one, which ratio appears naturally in the Fierz transform of the two-flavour 't Hooft interaction; (2) non-Abelian vector gauge bosons coupled to this system acquire a non-zero mass. Axial-vector fields do not mix with antisymmetric tensor fields, so there is no mass shift there.Comment: 13 pages, RevTex, 2 EPS figure

Discriminating between effective theories of U_{A}(1) symmetry breaking

We address the question if one can empirically distinguish between the two proposed solutions to the ``$U_A (1)$ problem'': the 't Hooft, and the Veneziano-Witten $U_{A}(1)$ symmetry breaking effective interactions. Two hadronic observables are offered as discriminants: (1) The scalar ($0^{+}$) meson spectrum; (2) Weinberg's second spectral sum rule. Their present experimental status is discussed.Comment: 6 pages, 1 eps file, Yonsei "Hadrons and Nuclei" conference proceeding

A Lagrangian for the Chiral (1/2,0) + (0,1/2) Quartet Nucleon Resonances

We study the nucleon and three N* resonances' properties in an effective linear realization chiral SU_L(2) x SU_R(2) and U_A(1) symmetric Lagrangian. We place the nucleon fields into the so-called "naive" (1/2,0) + (0, 1/2) and "mirror" (0, 1/2) + (1/2,0) (fundamental) representations of SU_L(2) x SU_R(2), two of each -distinguished by their U_A(1) chiral properties, as defined by an explicit construction of the nucleon interpolating fields in terms of three quark (Dirac) fields. We construct the most general one-meson-baryon chiral interaction Lagrangian assuming various parities of these four nucleon fields. We show that the observed masses of the four lowest lying nucleon states can be well reproduced with the effective Lagrangian, after spontaneous symmetry breakdown, without explicit breaking of U_A(1) symmetry. This does not mean that explicit U_A(1) symmetry breaking does not occur in baryons, but rather that it does not have a unique mass prediction signature that exists e.g. in the case of spinless mesons. We also consider briefly the axial couplings with chiral representation mixing.Comment: Published in International Journal of Modern Physics

Nucleon axial couplings and [(1/2,0) + (0,1/2)]-[(1,1/2) + (1/2,1)] chiral multiplet mixing

Three-quark nucleon interpolating fields in QCD have well-defined SU_L(2) x SU_R(2) and U_A(1) chiral transformation properties. Mixing of the [(1,1/2) + (1/2,1)] chiral multiplet with one of [(1/2,0) + (0,1/2)] or [(0,1/2) + (1/2,0)] representation can be used to fit the isovector axial coupling g_A(1) and thus predict the isoscalar axial coupling g_A(0) of the nucleon, in reasonable agreement with experiment. We also use a chiral meson-baryon interaction to calculate the masses and one-pion-interaction terms of J=1/2 baryons belonging to the [(0,1/2) + (1/2,0)] and [(1,1/2) + (1/2,1)] chiral multiplets and fit two of the diagonalized masses to the lowest-lying nucleon resonances thus predicting the third J=1/2 resonance at 2030 MeV, not far from the (one-star PDG) state Delta(2150).Comment: To appear in Modern Physics Letters

Pseudoscalar Mesons in the SU(3) Linear Sigma Model with Gaussian Functional Approximation

We study the SU(3) linear sigma model for the pseudoscalar mesons in the Gaussian Functional Approximation (GFA). We use the SU(3) linear sigma model Lagrangian with nonet scalar and pseudo-scalar mesons including symmetry breaking terms. In the GFA, we take the Gaussian Ansatz for the ground state wave function and apply the variational method to minimize the ground state energy. We derive the gap equations for the dressed meson masses, which are actually just variational parameters in the GFA method. We use the Bethe-Salpeter equation for meson-meson scattering which provides the masses of the physical nonet mesons. We construct the projection operators for the flavor SU(3) in order to work out the scattering T-matrix in an efficient way. In this paper, we discuss the properties of the Nambu-Goldstone bosons in various limits of the chiral $U_L(3)\times U_R(3)$ symmetry.Comment: 28 pages, comments and suggestions welcom