Triangle singularity in $B^{-}\to K^{-}X(3872);X\to {\pi }^0{\pi }^{+}{\pi }^{-}$ and the X(3872) mass

Abstract

We evaluate the contribution to the $X(3872)$ width from a triangle mechanism in which the $X$ decays into $D^{\ast 0}{\bar{D}}^0-cc$, then the $D^{\ast 0}({\bar{D}}^{\ast 0})$ decays into $D^0{\pi }^0$ (${\bar{D}}^0{\pi }^0$) and the $D^0{\bar{D}}^0$ fuse to produce ${\pi }^{+}{\pi }^{-}$. This mechanism produces an asymmetric peak from a triangle singularity in the ${\pi }^{+}{\pi }^{-}$ invariant mass with a shape very sensitive to the $X$ mass. We evaluate the branching ratios for a reaction where this effect can be seen in the $B^{-}\to K^{-}{\pi }^0{\pi }^{+}{\pi }^{-}$ reaction and show that the determination of the peak in the invariant mass distribution of ${\pi }^{+}{\pi }^{-}$ is all that is needed to determine the $X$ mass. Given the present uncertainties in the $X$ mass, which do not allow to know whether the $D^{\ast 0}{\bar{D}}^0$ state is bound or not, measurements like the one suggested here should be most welcome to clarify this issue.

10 pages,10 figures

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• Heating triangle singularities in heavy ion collisions
• Detecting the pure triangle sigularity effect through the $\psi (2S)\to p\bar{p}\eta /p\bar{p}{\pi }^0$ process
• The role of triangle singularity in isospin breaking process $J/\psi \to \Lambda \bar{\Lambda }\pi$ and the possible evidence of ${\Sigma }^{\ast }({\frac{1}{2}}^{-})$ states
• On the precise measurement of the $X(3872)$ mass and its counting rate
• $\Lambda (1405)$ mediated triangle singularity in the $K^{-}d\to p{\Sigma }^{-}$ reaction
• The role of triangle singularity in the decay process $D^0\to {\pi }^{+}{\pi }^{-}{f}_0(980),f_0\to {\pi }^{+}{\pi }^{-}$
• Box Singularity Conditions in Box Diagrams of Decay Processes