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

We investigate the decay of $a_1^{+}(1260)\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$ with the assumption that the $a_1(1260)$ is dynamically generated from the coupled channel $\rho \pi$ and $\bar{K}{K}^{\ast }$ interactions. In addition to the tree level diagrams that proceed via $a_1^{+}(1260)\to {\rho }^0{\pi }^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$, we take into account also the final state interactions of $\pi \pi \to \pi \pi$ and $K\bar{K}\to \pi \pi$. We calculate the invariant ${\pi }^{+}{\pi }^{-}$ mass distribution and also the total decay width of $a^+_1(1260) \to \pi^+ \pi^+ \pi^-$asafunctionofthemassof$a_1(1260)$. 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 $\rho \pi$ component in the $a_1(1260)$ wave function.