Radiative decays of the spin-2 partner of X(3872)

Abstract

It has been generally expected that the X(3872) has a spin-2 partner, X2, with quantum numbers JPC=2++. In the hadronic molecular model, its mass was predicted to be below the D⁎D¯⁎ threshold, and the new structure reported in the γψ(2S) invariant mass distribution by the Belle Collaboration with mass M=(4014.3±4.0±1.5) MeV and decay width Γ=(4±11±6) MeV, with a global significance of 2.8 σ, is a nice candidate for it. We consider the radiative decay widths for the X2→γψ with ψ=J/ψ,ψ(2S) treating the X2 as a D⁎D¯⁎ shallow bound state, and estimate the events of X2 in two-photon collisions that can be collected in the γJ/ψ→γℓ+ℓ− (ℓ=e,μ) final states at Belle. Based on the upper limit for the ratio of decay widths of X(3872)→γψ(2S) and X(3872)→γJ/ψ measured by BESIII, we predict the similar ratio Γ(X2→γψ(2S))/Γ(X2→γJ/ψ) to be smaller than 1.0. We suggest searching for the X2 signal in the γJ/ψ invariant mass distribution via two-photon fusions. The results will lead to insights into both the X(3872) and the new structure observed by Belle.