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

We evaluate the contribution to the X(3872) width from a triangle mechanism in which the X decays into D0D0-cc, then the D0(D0) decays into D0 pi 0 (D0 pi 0) and the D0D0 fuse to produce pi+pi-. This mechanism produces an asymmetric peak from a triangle singularity in the pi+pi- 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-pi 0 pi+pi- reaction and show that the determination of the peak in the invariant mass distribution of pi +pi - 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 D0D0 state is bound or not, measurements like the one suggested here should be most welcome to clarify this issue.