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.

Comments: 22 pages, 10 figures