Decay X(3872) → π~0π~+ π~? and S-wave D~0D~ 0 → π~+ π~? scattering length

摘要

The isospin-breaking decay X(3872) → (D~*D~- + D~* D) → π~0DD → π~0π~+π~? is discussed. In its amplitude there is a triangle logarithmic singularity, due to which the dominant contribution to BR(X(3872) → π~0π~+π~?) comes from the production of the π~+π~? system in a narrow interval of the invariant mass m_(π~+π~?) near the value of 2_(m_(D~0)) ≈ 3.73 GeV. The analysis shows that BR(X(3872) → π~0π~+π~?) 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~0D~0→π~+π~?) | ≈ 1/(2mD_(*+) ≈ 0.25 GeV~(?1).