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 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 \(B^- \rightarrow K^- \pi ^0 \pi ^+ \pi ^-\) 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 \(D^{*0} {\bar{D}}^0\) state is bound or not, measurements like the one suggested here should be most welcome to clarify this issue.

中文翻译：

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$$ B ^-\ rightarrow K ^ -X（3872）; X \ rightarrow \ pi ^ 0 \ pi ^ + \ pi ^-$$ B-→K-X（3872）; X→π0π+π-和X（3872）质量

我们评估到的贡献X（3872）从一个三角形机构宽度，其中X衰变为\（d ^ {* 0} {\酒吧{d}} ^ 0 -cc \） ，则\（d ^ { * 0}（{\ bar {D}} ^ {* 0}）\）衰减为\（D ^ 0 \ pi ^ 0 \）（\（{\ bar {D}} ^ 0 \ pi ^ 0 \））和\（D ^ 0 {\ bar {D}} ^ 0 \）保险丝产生\（\ pi ^ + \ pi ^-\）。这种机制会根据\（\ pi ^ + \ pi ^-\）不变质量中的三角形奇点产生不对称峰，其形状对X质量非常敏感。我们评估反应的支化率，在\（B ^-\ rightarrow K ^-\ pi ^ 0 \ pi ^ + \ pi ^-\）中可以看到这种效果反应并表明确定X（质量）只需确定\（\ pi ^ + \ pi ^-\）的不变质量分布中的峰。考虑到X质量的当前不确定性，这些不确定性不允许知道\（D ^ {* 0} {\ bar {D}} ^ 0 \）状态是否受约束，应采用此处建议的测量方法非常欢迎您澄清此问题。