Weinberg sum rules in an effective chiral field theory

It is shown that Weinbergʹs first sum rule is satisfied by the Pauli-Villars regulated spectral densities of the chiral two-flavour Nambu-Jona-Lasinio (NJL) model, with or without vector and axial-vector terms in the Lagrangian. The second sum rule equals −m〈ψψ〉 instead of zero, reflecting the contribution of the finite quark condensate in the spontaneously broken groundstates in both versions of the model. The Das et al. current algebra result for the π± − π0 mass difference is re-evaluated in the extended model.