The $B_c$-decays $B_c^+ \to J/ψπ^+π^-π^+$, $η_c π^+π^-π^+$

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

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