Exotic Doubly Charmed Ds0*(2317)D and Ds1*(2460)D* Molecules

Abstract

The $D_{s0}^{\ast }(2317)D$ and $D_{s1}^{\ast }(2460)D^{\ast }$ heavy meson systems can exchange a kaon that is emitted in S-wave owing to the opposite intrinsic parity of the $D_{s0}^{\ast }$($D_{s1}^{\ast }$) and $D$($D^{\ast }$) mesons. As a consequence of the mass difference of the $D_{s0}^{\ast }$($D_{s1}^{\ast }$) and $D$($D^{\ast }$) mesons, the range of the kaon exchange potential will be significantly longer than expected, corresponding to an effective mass of about $200\mathrm{MeV}$. The potential will be very strong: the strength of the interaction is proportional to $(m_{D_{s0}}-m_D{)}^2/f_{\ddot{I}}{€}^2$ and $(m_{D_{s1}}-m_{D^{\ast }}{)}^2/f_{\ddot{I}}{€}^2$. This combination of range and strength almost guarantees the existence of $D_{s0}^{\ast }(2317)D$ and $D_{s1}^{\ast }(2460)D^{\ast }$ bound states with $J^P=0^{-}$ and $J^P=0^{-},2^{-}$ respectively. Concrete calculations indicate a binding energy of $5-15\mathrm{MeV}$ independently of $J^P$. The $D_{s0}^{\ast }(2317)D$ and $D_{s1}^{\ast }(2460)D^{\ast }$ molecules have manifestly exotic flavour quantum numbers: $C=2$, $S=1$ and $I=1/2$. We expect the existence of bottom counterparts composed of the $B{B}_{s0}$ and $B^{\ast }{B}_{s1}^{\ast }$ mesons, which will be more bound and have a richer spectrum that might include a shallow P-wave state and an excited S-wave state.

6 Pages, 1 Figure