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

Abstract

We have done a study of the $B^{-}\to K^{-}{\pi }^{0}X(3872)$ reaction by means of a triangle mechanism via the chain of reactions: $B^{-}\to K^{-}{D}^{\ast 0}{\bar{D}}^{\ast 0}$; $D^{\ast 0}\to {\pi }^0{D}^0$; $D^0{\bar{D}}^{\ast 0}\to X(3872)$. We show that this mechanism generates a triangle singularity in the ${\pi }^{0}X(3872)$ invariant mass for a very narrow window of the $X(3872)$ mass, around the present measured values, and show that the peak positions and the shape of the mass distributions are sensitive to the $X(3872)$ mass, such that a measurement of the reaction can serve to improve on the present values of this mass. In particular, we point out that the $X(3872)$ mass relative to the $D^0{\bar{D}}^{\ast 0}$ threshold may be extracted from the asymmetry of the ${\pi }^{0}X$ line shape.

arXiv comment22 pages, 10 figures

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• $T_{cc}^{+}$ decays: Differential spectra and two-body final states
• Triangle Singularity in the Production of $T_{cc}^{+}$(3875) and a Soft Pion
• Charm-meson Triangle Singularity in $e^{+}{e}^{-}$ Annihilation into $D^{\ast 0}{\bar{D}}^0+\gamma$
• Triangle singularity in $B^{-}\to K^{-}X(3872);X\to {\pi }^0{\pi }^{+}{\pi }^{-}$ and the X(3872) mass
• Galilean-Invariant XEFT at Next-to-Leading Order
• Triangle singularity appearing as an $X(3872)$-like peak in $B\to (J/\psi {\pi }^{+}{\pi }^{-})K\pi$
• Possible precise measurements of the $X(3872)$ mass with the $e^{+}{e}^{-}\to {\pi }^0\gamma X(3872)$ and $p\bar{p}\to \gamma X(3872)$ reactions
• Role of the triangle mechanism in the ${\Lambda }_b\to {\Lambda }_c{\pi }^{-}{f}_0(980)$ reaction
• Triangle singularity in $B^0\to {\pi }^{-}{K}^{+}X(3872)$ via the $D_{s1}\bar{D}{D}^{\ast }$ loop and possible precise measurement of the $X(3872)$ mass
• 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
• The role of triangle singularity in the decay process $D^0\to {\pi }^{+}{\pi }^{-}{f}_0(980),f_0\to {\pi }^{+}{\pi }^{-}$
• Photoproduction of the $X(3872)$ beyond vector meson dominance: the open-charm coupled-channel mechanism
• Production of the $X(3872)$ state via the $B^0\to K^{\ast 0}X(3872)$ decay
• Box Singularity Conditions in Box Diagrams of Decay Processes
• Proposal to detect a moving triangle singularity in $\psi (2S)\to {\pi }^{+}{\pi }^{-}{K}^{+}{K}^{-}$ process