The first three coefficients of the Taylor’s series expansion of the vevtor pion form factor as a function of the momentum transfer are evaluated using the experimental data on the pion form factor and the P-wave ππ phase shifts. The real part of the form factor as a function of energy is also calculated by dispersion relation. Comparisons there results with Chiral Perturbation Theory and unitarized models are given. | Communications in Physics, Vol. 25, No. 1 (2015), pp. 21-28 DOI: TAYLOR’S SERIES AND DISPERSION RELATION ANALYSES OF THE VECTOR PION FORM FACTOR AND THEIR COMPARISON WITH PERTURBATIVE AND NON PERTURBATIVE CALCULATIONS TRAN NGUYEN TRUONG Centre de Physique Th´eorique, Ecole Polytechnique F91128 Palaiseau, France E-mail: Received 20 November 2014 Accepted for publication 28 November 2014 Abstract. The first three coefficients of the Taylor’s series expansion of the vevtor pion form factor as a function of the momentum transfer are evaluated using the experimental data on the pion form factor and the P-wave ππ phase shifts. The real part of the form factor as a function of energy is also calculated by dispersion relation. Comparisons there results with Chiral Perturbation Theory and unitarized models are given. Keywords: ???. The purpose of this note is three-fold. First, a systematic procedure is given to calculate the coefficients of the Taylor’s series expansion of the form factor around the origin s = 0 in terms of experimental data. Second the real parts of the form factor for a wider range of energy are calculated using also experimental data. Third, these results are compared with those given by existing theoretical calculations in order to evaluate their reliability. It turns out that only models satisfying the elastic unitarity, giving rise to the ρ resonance, are valid. Chiral Perturbation calculations at one and two-loop disagree, at very low energy, with the Taylor’s series expansion and, at moderate energy, with the dispersion relation results. Chiral Perturbation Theory (ChPT) [1–4] is a well-defined perturbative procedure allowing one to calculate systematically low energy phenomenon involving soft pions. It is now widely used to analyze the low energy pion physics not only when the interaction is not strong but also in the presence of the resonance as long as the energy region of interest
