$\ddot{I}{„}^{-}\to \hat{I}\cdot \ddot{I}{€}^{-}\ddot{I}{€}^0\hat{I}{½}_{\ddot{I}}„$ and $\ddot{I}ƒ(e^{+}{e}^{-}\to \hat{I}\cdot \ddot{I}{€}^{+}\ddot{I}{€}^{-})$ at low energies

Abstract

We analyze the hadronization structure of $\ddot{I}„\to \hat{I}\cdot \ddot{I}{€}^{-}\ddot{I}{€}^0\hat{I}{½}_{\ddot{I}}„$ decays. In the isospin limit only the vector current contributes to this process. We compute the relevant form factor within Resonance Chiral Theory, at leading order in the $1/N_C$ expansion, and considering only the contribution of the lightest vector resonances. The couplings in the resonance theory are constrained by imposing the asymptotic behaviour of vector spectral functions ruled by $QCD$. We reproduce the branching ratio of this mode and predict the low-energy behaviour of $\ddot{I}ƒ\left(e^{+}{e}^{-}\to \hat{I}\cdot \ddot{I}{€}^{+}\ddot{I}{€}^{-}\right)$ using isospin symmetry.

4 pages, 3 figures. To appear in the Proceedings of the QCD10 (25th anniversary) 15th International QCD Conference. 28th June - 3rd July 2010 Montpellier (France) (Nucl. Phys. Proc. Suppl.)