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

Abstract

We have done a study of the B-→K-π0X(3872) reaction by means of a triangle mechanism via the chain of reactions: B-→K-D∗0D∗0; D∗0→π0D0; D0D∗0→X(3872). We show that this mechanism generates a triangle singularity in the π0X(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 D0D∗0 threshold may be extracted from the asymmetry of the π0X line shape.