Pion and Kaon Electromagnetic Form Factors

Abstract

We study the electromagnetic form factor of the pion and kaons at low-energies with the use of Chiral Perturbation Theory. The analysis is performed within the three flavour framework and at next-to-next-to-leading order. We explain carefully all the relevant consistency checks on the expressions, present full analytical results for the pion form factor and describe all the assumptions in the analysis. From the phenomenological point of view we make use of our expression and the available data to obtain the charge radius of the pion obtaining $<r^2{>}_V^{\pi }=(0.452+-0.013)f{m}^2$, as well as the low-energy constant $L_9^r(m_{\rho })=(5.93+-0.43)10^{-3}$. We also obtain experimental values for 3 combinations of order $p^6$ constants.

50 pages

References in corpus (5)

• Resonance estimates of O(p^6) low-energy constants and QCD short-distance constraints
• QCD Isospin Breaking in Meson Masses, Decay Constants and Quark Mass Ratios
• A new measurement of K+(e4) decay and the s-wave pi-pi-scattering length a00
• The vector form factor of the pion from unitarity and analyticity: a model-independent approach
• K_l3 form factors at order p^6 in chiral perturbation theory

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