Is D_sJ⁺(2632) the first radial excitation of D _s*(2112)?

We present a quantitative analysis of the D_sJ⁺(2632) observed by SELEX mainly focusing on the assumption that D_sJ ⁺(2632) is the first radial excitation of the 1^- ground state D_s*(2112). By solving the instantaneous Bethe-Salpeter equation, we obtain the mass 2658±15 MeV for the first excited state, which is about 26 MeV heavier than the experimental value 2632±1.7 MeV. By means of PCAC and low-energy theorem we calculate the transition matrix elements and obtain the decay widths: Γ(D_sJ⁺→ D_s⁺η)=4.07±0.34 MeV, Γ(D _sJ⁺→D⁰K⁺) ≃Γ(Γ(D_sJ⁺→D⁺K ⁰)=8.9±1.2 MeV, and the ratio Γ(D_sJ ⁺→D⁰K⁺)/Γ(D_sJ ⁺→D_s⁺η)=2.2±0.2 as well. This ratio is quite different from the SELEX data 0.14±0.06. The summed decay width of those three channels is approximately 21.7 MeV, already larger than the observed bound for the full width (≤17 MeV). Furthermore, assuming D _sJ⁺(2632) is 1^- state, we also explore the possibility of S-D wave mixing to explain the SELEX observation. Based on our analysis, we suspect that it is too early to conclude that D_sJ ⁺(2632) is the first radial excitation of the 1^- ground state D_s*(2112). More precise measurements of the relative ratios and the total decay width are urgently required, especially for S-D wave mixing.