Triangle singularities in $B^-\rightarrow D^{*0}\pi^-\pi^0\eta$ and $B^-\rightarrow D^{*0}\pi^-\pi^+\pi^-$

Abstract

The possible role of the triangle mechanism in the $B^-$ decay into $D^{*0}\pi^-\pi^0\eta$ and $D^{*0}\pi^-\pi^+\pi^-$ is investigated. In this process, the triangle singularity appears from the decay of $B^-$ into $D^{*0}K^-K^{*0}$ followed by the decay of $K^{*0}$ into $\pi^-K^+$ and the fusion of the $K^+K^-$ which forms the $a_0(980)$ or $f_0(980)$ which finally decay into $\pi^0\eta$ or $\pi^+\pi^-$ respectively. The triangle mechanism from the $\bar{K}^*K\bar{K}$ loop generates a peak around 1420 MeV in the invariant mass of $\pi^-a_0$ or $\pi^-f_0$, and gives sizable branching fractions $Br(B^-\rightarrow D^{*0}\pi^- a_0;a_0 \rightarrow \pi^0\eta)= 1.66 \times 10^{-6}$ and $Br(B^-\rightarrow D^{*0}\pi^- f_0 ; f_0 \rightarrow \pi^+\pi^-)= 2.82 \times 10^{-6}$.