6533b86dfe1ef96bd12ca7cd

RESEARCH PRODUCT

Triangle singularity in the B−→K−π0X(3872) reaction and sensitivity to the X(3872) mass

subject

description

We have done a study of the ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}X(3872)$ reaction by means of a triangle mechanism via the chain of reactions: ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{D}^{*0}{\overline{D}}^{*0}$; ${D}^{*0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{D}^{0}$; ${D}^{0}{\overline{D}}^{*0}\ensuremath{\rightarrow}X(3872)$. We show that this mechanism generates a triangle singularity in the ${\ensuremath{\pi}}^{0}X(3872)$ 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 ${\ensuremath{\pi}}^{0}X$ line shape.