Two- and Three-Point Functions in the Extended NJL Model

Abstract

The two-point functions in generalized Nambu--Jona-Lasinio models are calculated to all orders in momenta and quark masses to leading order in $1/N_c$. The use of Ward identities and the heat-kernel expansion allows for a large degree of regularization independence. We also show how this approach works to the same order for three-point functions on the example of the vector-pseudoscalar-pseudoscalar three-point function. The inclusion of the chiral anomaly effects at this level is shown by calculating the pseudoscalar-vector-vector three-point function to the same order. Finally we comment on how (vector-)meson-dominance comes out in the presence of explicit chiral symmetry breaking in both the anomalous and the non-anomalous sectors.

Latex, 42 pages, 3 latex figures, 7 postscript figures included, NORDITA 94/11 N,P. Improvement in the regularization procedure for the PVV three point function

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• Chiral expansions of the pi0 lifetime
• QCD Short-distance Constraints and Hadronic Approximations
• On covariant nonlocal chiral quark models with separable interactions
• The $B_K$ Parameter in the $1/N_c$ Expansion
• Vector Meson Masses in Chiral Perturbation Theory
• Constraints on Chiral Perturbation Theory Parameters from QCD Inequalities
• $\pi \pi$ scattering in the $\rho$-meson channel at finite temperature
• The role of momentum dependent dressing functions and vector meson dominance in hadronic light-by-light contributions to the muon g-2
• The $\gamma \gamma \to {\pi }^0{\pi }^0$ and $\eta \to {\pi }^0\gamma \gamma$ Transitions in the Extended NJL Model
• $\gamma \gamma \to {\pi }^0{\pi }^0$ and $\eta \to {\pi }^0\gamma \gamma$ at low energy within the Extended Nambu Jona-Lasinio Model
• Scalar-involved three-point Green functions and their phenomenology
• Chiral anomaly and nucleon properties in the Nambu--Jona-Lasinio model with vector mesons
• The $B_K$ Kaon Parameter in the Chiral Limit
• Meson Properties in a renormalizable version of the NJL model
• Low-energy dynamics of the $\gamma \gamma \to \pi \pi$ reaction
• Hadronic Matrix Elements for Kaons
• The $\Delta I=1/2$ Rule for Kaons
• The role of vector meson dominance and running masses in the hadronic contributions to the muon $g-2$