Triangle singularity in (B^-ightarrow K^-X(3872);Xightarrow pi ^0pi ^+pi ^-) and the X(3872) mass

摘要

We evaluate the contribution to the X(3872) width from a triangle mechanism in which the X decays into $$D^{*0}{ar{D}}^0 -cc$$ D ? 0 D ˉ 0 - c c , then the $$D^{*0} ({ar{D}}^{*0})$$ D ? 0 ( D ˉ ? 0 ) decays into $$D^0 pi ^0$$ D 0 π 0 ( $${ar{D}}^0 pi ^0$$ D ˉ 0 π 0 ) and the $$D^0 {ar{D}}^0$$ D 0 D ˉ 0 fuse to produce $$pi ^+ pi ^-$$ π + π - . This mechanism produces an asymmetric peak from a triangle singularity in the $$pi ^+ pi ^-$$ 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 $$B^- ightarrow K^- pi ^0 pi ^+ pi ^-$$ B - → K - π 0 π + π - reaction and show that the determination of the peak in the invariant mass distribution of $$pi ^+ pi ^-$$ 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 $$D^{*0} {ar{D}}^0$$ D ? 0 D ˉ 0 state is bound or not, measurements like the one suggested here should be most welcome to clarify this issue.