Strong Decays of the Orbitally Excited Scalar $D_0^{\ast }$ Mesons

Abstract

We calculate the two-body strong decays of the orbitally excited scalar mesons $D_0^{\ast }(2400)$ and $D_J^{\ast }(3000)$ by using the relativistic Bethe-Salpeter (BS) method. $D_J^{\ast }(3000)$ was observed recently by the LHCb Collaboration, the quantum number of which has not been determined yet. In this paper, we assume that it is the $0^{+}(2P)$ state and obtain the transition amplitude by using the PCAC relation, low-energy theorem and effective Lagrangian method. For the $1P$ state, the total widths of $D_0^{\ast }(2400{)}^0$ and $D_0^{\ast }(2400{)}^{+}$ are 226 MeV and 246 MeV, respectively. With the assumption of $0^{+}(2P)$ state, the widths of $D_J^{\ast }(3000{)}^0$ and $D_J^{\ast }(3000{)}^{+}$ are both about 131 MeV, which is close to the present experimental data. Therefore, $D_J^{\ast }(3000)$ is a strong candidate for the $2^3{P}_0$ state.

Comments: 21 pages, 10 figures