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

Raquel Molina, Eulogio Oset

Published 2020-02-28Version 1

We evaluate the contribution to the $X(3872)$ width from a triangle mechanism in which the $X$ decays into $D^{*0}\bar{D}^0 -cc$, then the $D^{*0} (\bar{D}^{*0})$ 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 a triangle singularity visible at a precise value of the $\pi^+ \pi^-$ invariant mass, very sensitive to the $X$ mass. The shape of the $M_\mathrm{Inv}(\pi^+ \pi^-)$ distribution is also very sensitive to this 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 the $\pi^+ \pi^-$, which can be done with high precision, 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 $D^{*0} \bar{D}^0$ state is bound or not, measurements like the one suggested here should be most welcome to clarify this issue.