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

Abstract

The momentum-space bosonization method of a Nambu and Jona-Lasinio type model with vector and axial-vector mesons is applied to $\pi \pi$ scattering. Unlike the case in earlier published papers, we obtain the $\pi \pi$ 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 $f_{\pi }$ are obtained. The low-energy $\pi \pi$ phase shifts are compared to the available data. We also study the scalar form factor of the pion.

39 pp, LaTeX file, uses epsf, 7 figures (appended as compressed tar files in pion.uu)

Cited by in corpus (39)

• Spontaneous electromagnetic superconductivity of vacuum in strong magnetic field: evidence from the Nambu--Jona-Lasinio model
• Quark matter under rotation in the NJL model with vector interaction
• Multi-quark interactions with a globally stable vacuum
• Chirally symmetric quark description of low energy π-πscattering
• Quark magnetar in three-flavor Nambu--Jona-Lasinio model with vector interaction and magnetized gluon potential
• Consistency in Regularizations of the Gauged NJL Model at One Loop Level
• Analytic proof that the Quark Model complies with the PCAC theorems
• Dynamical chiral symmetry breaking by a magnetic field and multi-quark interactions
• $\pi \pi$ scattering in the $\rho$-meson channel at finite temperature
• Extension of the Nambu--Jona-Lasinio model at high densities and temperatures by using an implicit regularization scheme
• Electromagnetic superconductivity of vacuum induced by strong magnetic field
• Aspects of U_A(1) breaking in the Nambu and Jona-Lasinio model
• Effective Chiral Meson Lagrangian For The Extended Nambu-Jona-Lasinio Model
• The Role of hidden ambiguities in the Linear Sigma Model with fermions
• Neutral quark matter in a Nambu-Jona Lasinio model with vector interaction
• Implications of the fermion vacuum term in the extended SU(3) Quark Meson model on compact stars properties
• The anomalous decay $f_1(1285)\to \rho \gamma$ and related processes
• Effects of Renormalizing the chiral SU(2) Quark-Meson-Model
• A predictive formulation of the Nambu--Jona-Lasinio model
• A general framework to diagonalize vector--scalar and axial-vector--pseudoscalar transitions in the effective meson Lagrangian
• Implications of a New Effective Chiral Meson Lagrangian
• $\tau \to f_1(1285){\pi }^{-}{\nu }_{\tau }$ decay in the extended Nambu -- Jona-Lasinio model
• Meson Properties in a renormalizable version of the NJL model
• An effective field theory for warm QCD
• The ${\pi }^0-\eta -{\eta }^{\prime }$ mixing in a generalized multi-quark interaction scheme
• Vector and axial vector mesons in a nonlocal chiral quark model
• From scale properties of physical amplitudes to a predictive formulation of the Nambu-Jona-Lasinio model
• Quark-antiquark resonances in the NJL model
• Current algebra and soft pionic modes in asymmetric quark matter
• Low-energy theorem for $\gamma \to 3\pi$: surface terms against $\pi a_1$-mixing
• rho -> pi pi decay in nuclear medium
• $1/N_c$ approximation and universality of vector mesons
• Collective modes and current-algebraic sum rules in nuclear medium
• Ratios of the light quark masses: Cubic curve vs ellipse
• Quadrupole polarizabilities of the pion in the Nambu--Jona-Lasinio model
• Masses of the lowest spin-0 and spin-1 meson nonets: explicit symmetry breaking effects
• Anomalous decay $f_1(1285)\to {\pi }^{+}{\pi }^{-}\gamma$ in the Nambu - Jona-Lasinio model
• Process eta -> pi^0 gamma gamma in the Nambu-Jona-Lasinio model
• One-Loop Determinant of Dirac Operator in Non-Renormalizable Models