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: $B^{-}\to K^{-}{D}^{*0}{\overline{D}}^{*0}$; $D^{*0}\to {\pi }^0{D}^0$; $D^0{\overline{D}}^{*0}\to X(3872)$. 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 $D^0{\overline{D}}^{*0}$ threshold may be extracted from the asymmetry of the ${\pi }^{0}X$ line shape.

• Received 14 February 2020
• Accepted 28 February 2020

DOI:https://doi.org/10.1103/PhysRevD.101.054030

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society