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arXiv · 1712.05572

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

Xu Zhang·Ju-Jun Xie
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Abstract

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

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Xu Zhang, Ju-Jun Xie. 2018-08-09. The three-pion decays of the $a_1(1260)$. https://doi.org/10.1088/0253-6102%2F70%2F1%2F60

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