Decay constants of the two-pole $D_0^{\ast }(2300)$

Abstract

The nature of the scalar charmed meson $D_0^{\ast }(2300)$ remains one of the most intriguing states in hadron spectroscopy. A prominent interpretation is a two-pole structure generated by the coupled channels $D\pi$, $D\eta$, $D_s\bar{K}$, and $D{\eta }^{\prime }$, in which the lower pole couples mainly to $D\pi$ and the higher pole to $D_s\bar{K}$. Following this picture, we calculate the decay constants of these two poles using the effective Lagrangian approach. The resulting values, $f_{D_0^{\ast }}^{(\mathrm{lower})}=64.6_{-1.0}^{+0.9}\mathrm{MeV}$ and $f_{D_0^{\ast }}^{(\mathrm{higher})}=80.8_{-5.3}^{+9.6}\mathrm{MeV}$, are substantially smaller than those predicted by conventional $c\bar{q}$ excited-state scenarios. This difference suggests that decay constants can serve as a sensitive probe to discriminate between different internal structures of the $D_0^{\ast }(2300)$. As a phenomenological application, we further predict the branching fractions for the Cabibbo-favored decays $B_s\to D_s{D}_0^{\ast }$, ${\Lambda }_b\to {\Lambda }_c{D}_0^{\ast }$, and ${\Xi }_b\to {\Xi }_c{D}_0^{\ast }$ within the factorization approach. These predictions provide crucial tests to validate the two-pole interpretation of the $D_0^{\ast }(2300)$.