Triangle singularity in B− → K−X(3872); X → π0π+π− and the X(3872) mass

Abstract

We evaluate the contribution to the X(3872) width from a triangle mechanism in which the X decays into D∗0D¯0−cc, then the D∗0(D¯∗0) decays into D0π0 (D¯0π0) and the D0D¯0 fuse to produce π+π−. This mechanism produces an asymmetric peak from a triangle singularity in the π+π− invariant mass with a shape very sensitive to the X mass. We evaluate the branching ratios for a reaction where this effect can be seen in the B−→K−π0π+π− reaction and show that the determination of the peak in the invariant mass distribution of π+π− 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∗0D¯0 state is bound or not, measurements like the one suggested here should be most welcome to clarify this issue.