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

Abstract

The possible role of the triangle mechanism in the $B^{-}$ decay into $D^{\ast 0}{\pi }^{-}{\pi }^0\eta$ and $D^{\ast 0}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ is investigated. In this process, the triangle singularity appears from the decay of $B^{-}$ into $D^{\ast 0}{K}^{-}{K}^{\ast 0}$ followed by the decay of $K^{\ast 0}$ 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 ${\bar{K}}^{\ast }K\bar{K}$ loop generates a peak around 1420 MeV in the invariant mass of ${\pi }^{-}{a}_0$ or ${\pi }^{-}{f}_0$, and gives sizable branching fractions $Br(B^{-}\to D^{\ast 0}{\pi }^{-}{a}_0;a_0\to {\pi }^0\eta )=1.66\times 10^{-6}$ and $Br(B^{-}\to D^{\ast 0}{\pi }^{-}{f}_0;f_0\to {\pi }^{+}{\pi }^{-})=2.82\times 10^{-6}$.

arXiv comment10 pages, 7 figures

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