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 → π +π 0ν, τ → Kπν, τ → K +ην and τ → K + ¯K0ν using only two inputs as the ρ and K∗ masses, or the two corresponding rms radii, agree with the experimental data. Using the same number of parameters, the corresponding one loop CPTH calculation cannot explain the τ data. | Communications in Physics, Vol. 24, No. 4 (2014), pp. 289-311 DOI: EQUIVALENCE BETWEEN VECTOR MESON DOMINANCE AND UNITARISED CHIRAL PERTURBATION THEORY LE VIET DUNG Centre de Physique Theorique de l’Ecole Polytechnique, 91128 Palaiseau, France and Institute of Physics, Hanoi, Vietnam TRAN NGUYEN TRUONG National Laboratory for High Energy Physics (KEK), Oho 1-1 Tsukuba, Ibaraki 305, Japan and Centre de Physique Theorique de l’Ecole Polytechnique, 91128 Palaiseau, France E-mail: Received 26 November 2014 Accepted for publication 12 December 2014 Abstract. It is explicitly shown that either the approximate solution of the integral equation for the inverse of the pion form facto,r or the result of the Pad´e approximant method of resumming 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 (or the VMD model) 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 → π + π 0 ν, τ → Kπν, τ → K + ην and τ → K + K¯0 ν using only two inputs as the ρ and K ∗ masses, or the two corresponding rms radii, agree with the experimental data. Using the same number of parameters, the corresponding one loop CPTH calculation cannot explain the τ data. Keywords: vector meson dominance, unitarity, chiral perturbation theory, unitarised chiral perturbation theory, tau decays calculations, scalar form factor calculation. I. INTRODUCTION The hypothesis of Vector Meson Dominance (VMD) [1] has proved to be an useful and convenient concept in low energy hadronic physics. It enables us to describe many low energy phenomena, below 1 GeV scale, in a compact and convenient language, although not always correct. An apparently .
