Decay $X(3872)\to {\pi }^0{\pi }^{+}{\pi }^{-}$ and $S$-wave $D^0{\bar{D}}^0\to {\pi }^{+}{\pi }^{-}$ scattering length

Abstract

The isospin-breaking decay $X(3872)\to (D^{\ast }\bar{D}+{\bar{D}}^{\ast }D)\to {\pi }^{0}D\bar{D}\to {\pi }^0{\pi }^{+}{\pi }^{-}$ is discussed. In its amplitude there is a triangle logarithmic singularity, due to which the dominant contribution to $BR(X(3872)\to {\pi }^0{\pi }^{+}{\pi }^{-})$ comes from the production of the ${\pi }^{+}{\pi }^{-}$ system in a narrow interval of the invariant mass $m_{{\pi }^{+}{\pi }^{-}}$ near the value of $2m_{D^0}\approx 3.73$ GeV. The analysis shows that $BR(X(3872)\to {\pi }^0{\pi }^{+}{\pi }^{-})$ can be expected at the level of $10^{-3}$--$10^{-4}$. This estimate includes, in particular, the assumption that the $S$-wave inelastic scattering length $|α''_{D^0\bar D^0 \toπ^+π^-}|\approx1/(2m_{D^{*+}})\approx0.25\ \mbox{GeV}^{-1}$.

arXiv comment7 pages, 6 figures; v2: journal version; clarifications and references added

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Cited by in corpus (5)

• Triangle singularity in the $B^{-}\to K^{-}{\pi }^{0}X(3872)$ reaction and sensitivity to the $X(3872)$ mass
• Triangle singularity in $B^{-}\to K^{-}X(3872);X\to {\pi }^0{\pi }^{+}{\pi }^{-}$ and the X(3872) mass
• Detecting the pure triangle sigularity effect through the $\psi (2S)\to p\bar{p}\eta /p\bar{p}{\pi }^0$ process
• The role of triangle singularity in isospin breaking process $J/\psi \to \Lambda \bar{\Lambda }\pi$ and the possible evidence of ${\Sigma }^{\ast }({\frac{1}{2}}^{-})$ states
• Constrain the ${\chi }_{cJ}\to D^{(\ast )}{\bar{D}}^{(\ast )}$ effective couplings via the $X(3872)\to {\pi }^0{\chi }_{cJ}$ decays