The $B_c$-decays $B_c^{+}\to J/\psi {\pi }^{+}{\pi }^{-}{\pi }^{+}$, ${\eta }_c{\pi }^{+}{\pi }^{-}{\pi }^{+}$

Abstract

In this article, we study the three-pion $B_c$-decays $B_c^{+}\to J/\psi {\pi }^{+}{\pi }^{-}{\pi }^{+}$, ${\eta }_c{\pi }^{+}{\pi }^{-}{\pi }^{+}$ with dominance of the intermediate axial-vector meson $a_1(1260)$ and vector meson $\rho (770)$ in the ${\pi }^{+}{\pi }^{-}{\pi }^{+}$ and ${\pi }^{+}{\pi }^{-}$ invariant mass distributions respectively, and make predictions for the branching fractions and differential decay widths. The ratio between the decays $B_c^{+}\to J/\psi {\pi }^{+}{\pi }^{-}{\pi }^{+}$ and $B_c^{+}\to J/\psi {\pi }^{+}$ is compatible with the experimental data within uncertainties, other predictions can be confronted with the experimental data in the future at the LHCb.

9 pages, 6 figures, slight revision

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