Is [formula omitted] the first radial excitation of [formula omitted

Abstract

We present a quantitative analysis of the DsJ+(2632) observed by SELEX mainly focusing on the assumption that DsJ+(2632) is the first radial excitation of the 1− ground state Ds∗(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(DsJ+→Ds+η)=4.07±0.34 MeV, Γ(DsJ+→D0K+)≃Γ(Γ(DsJ+→D+K0)=8.9±1.2 MeV, and the ratio Γ(DsJ+→D0K+)/Γ(DsJ+→Ds+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 DsJ+(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 DsJ+(2632) is the first radial excitation of the 1− ground state Ds∗(2112). More precise measurements of the relative ratios and the total decay width are urgently required, especially for S–D wave mixing.