The dispersive two-photon contribution to the $K_L\to {\mu }^{+}{\mu }^{-}$ decay amplitude is analyzed, using chiral perturbation theory techniques and large- $N_C$ considerations. A consistent description of the decays ${\pi }^0\to e^{+}{e}^{-}$, $\eta \to {\mu }^{+}{\mu }^{-}$, and $K_L\to {\mu }^{+}{\mu }^{-}$ is obtained. As a by-product, one predicts $B(\eta \to e^{+}{e}^{-})=(5.8\pm 0.2)\times {10}^{-9\mathrm{}}$ and $B(K_L\to e^{+}{e}^{-})=(9.0\pm 0.4)\times {10}^{-12\mathrm{}}$.

Within the resonance chiral effective theory we study the dressed propagators of the spin-1 fields, which arise from a Dyson-Schwinger resummation perturbatively constructed from loop diagrams with absorptive contributions in the s channel. We apply the procedure to the vector pion form factor and elastic $\pi \pi$ scattering to obtain the off-shell width of the ${\rho }^0$ meson. We adopt a definition of the off-shell width of spin-1 meson resonances that satisfies the requirements of analyticity, unitarity, chiral symmetry, and asymptotic behavior ruled by QCD. To satisfy these constraints the resummation procedure cannot consist only of self-energy diagrams. Our width definition is shown to be independent of the formulation used to describe the spin-1 meson resonances.

$\overrightarrow{\tau }\pi \pi \pi {\nu }_{\tau }$ decays are analyzed within the framework of the resonance effective theory of QCD. We work out the relevant Lagrangian that describes the axial-vector current hadronization contributing to these processes, in particular the local $a_1\mathrm{}\left(1260\right)-\rho \mathrm{}\left(770\right)\mathrm{}$-Goldstone interactions. The new coupling constants are constrained by imposing the asymptotic behavior of the corresponding spectral function within QCD. Hence we compare the theoretical framework with the experimental data, obtaining a good quality fit from the ALEPH spectral function and branching ratio. We also get values for the mass and on-shell width of the $a_1\mathrm{}\left(1260\right)\mathrm{}$ resonance. In this way we are able to provide the structure functions that have been measured by OPAL and CLEO-II and we find an excellent agreement.

We present a comparative analysis of chiral quark models which include nonlocal covariant four-fermion couplings. We consider two alternative ways of introducing the nonlocality, as well as various shapes for the momentum-dependent form factors governing the effective interactions. In all cases we study the behavior of model parameters and analyze numerical results for constituent quark masses and quark propagator poles. Advantages of these covariant nonlocal schemes over instantaneous nonlocal schemes and the standard NJL model are pointed out.

We analyze the role played by the Polyakov loop in the description of the chiral phase transition within the framework of nonlocal SU(3) chiral models with flavor mixing. We show that its presence provides a substantial enhancement of the predicted critical temperature, bringing it to a better agreement with the most recent results of lattice calculations.