Electromagnetic decays of X (3823) as the ψ2 (1 D 3 2) state and its radial excited states

We study the electromagnetic (EM) decays of X(3823) as the ψ2(1D32) state by using the relativistic Bethe-Salpeter method. Our results are Γ[X(3823)→χc0γ]=1.2 keV, Γ[X(3823)→χc1γ]=265 keV, Γ[X(3823)→χc2γ]=57 keV, and Γ[X(3823)→ηcγ]=1.3 keV. The ratio B[X(3823)→χc2γ]/B[X(3823)→χc1γ]=0.22, agrees with the experimental data. Similarly, the EM decay widths of ψ2(n3D2), n=2, 3, are predicted, and we find the dominant decays channels are ψ2(nD32)→χc1(nP)γ, where n=1, 2, 3. The wave function include different partial waves, which means the relativistic effects are considered. We also study the contributions of different partial waves.