Equivalence Between Vector Meson Dominance and Unitarised Chiral Perturbation Theory

It is explicitly shown that the solution of the integral equation for the inverse of the form factor or the Padé approximant method to resum the one loop Chiral Perturbation Theory (CPTH) are equivalent to the standard vector meson dominance (VMD) models using the vector meson coupling to two pseudoscalars given by the KSRF relation. Inconsistencies between the one loop CPTH and its unitarised version for the vector pion form factor and the related P-wave ππ scattering are pointed out. The situation is better for the CPTH calculation of the scalar form factor and the related S-wave ππ scattering. The branching ratios of τ → ππν, τ → Kπν, τ → Kην and τ → KK̄0ν using only two inputs as the ρ and K masses, or the two corresponding rms radii, agree with the experimental data. Applications to the Next Linear Colliders and Large Hadron Collider physics are also discussed.