Pionic transitions of the spin-2 partner of X (3872) to ₂₉

We investigated the pionic transitions between the X₂ spin-2 partner of the X (3872) and ₂₁, ₂ using a nonrelativistic effective field theory. The X₂ is assumed to be a bound state of the D^* and D^* mesons and to decay through several kinds of loops, including the bubble, triangle and box loops. Within the present model, the widths for the single-pion decays X₂⁰₂₉ are predicted to be about 3--30 keV. For the dipion decays, the widths are a few keVs. These widths yield a branching fraction of 10^-3--10^-2. The ratio R₂₀= (X₂^+^-₂₉) / (X₂⁰⁰₂₉) 1. 6, which is a bit smaller than the expected value of 2, and R₂₁= (X₂₂₂) / (X₂₂₁) 0. 85. These ratios are nearly independent of the X₂ mass and the coupling constants, which might be a good quantity for the experiments. Moreover, the invariant mass spectra of the ⁰₂₉ final state for the dipion processes are presented, showing a cusp structure at the D D^* threshold enhanced and narrowed by the nearby triangle singularity.