The three-pion decays of the $a_1(1260)$

Abstract

We investigate the decay of $a_1^{+}(1260)\to \ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ with the assumption that the $a_1(1260)$ is dynamically generated from the coupled channel $\ddot{I}\ddot{I}€$ and $\bar{K}{K}^{\ast }$ interactions. In addition to the tree level diagrams that proceed via $a_1^{+}(1260)\to \ddot{I}{}^0\ddot{I}{€}^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$, we take into account also the final state interactions of $\ddot{I}€\ddot{I}€\to \ddot{I}€\ddot{I}€$ and $K\bar{K}\to \ddot{I}€\ddot{I}€$. We calculate the invariant $\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ mass distribution and also the total decay width of $a_1^{+}(1260)\to \ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ as a function of the mass of $a_1(1260)$. The calculated total decay width of $a_1(1260)$ is significantly different from other model calculations and tied to the dynamical nature of the $a_1(1260)$ resonance. The future experimental observations could test of model calculations and would provide vary valuable information on the relevance of the $\ddot{I}\ddot{I}€$ component in the $a_1(1260)$ wave function.

Published version