$D_{s0}^{*}(2317)^+$ in the decay of $B_c$ into $J/\psi DK$

In this paper we study the relationship between the $D_{s0}^{*}(2317)^+$ resonance and the decay of the $B_c$ meson into $J/\psi DK$. In this process, the $B_c$ meson decays first into $J/\psi$ and the quark pair $c\bar{s}$, and then the quark pair hadronizes into $DK$ or $D_s\eta$ components, which undergo final state interaction. This final state interaction, generating the $D_{s0}^{*}(2317)^+$ resonance, is described by the chiral unitary approach. With the parameters which allow us to match the pole position of the $D_{s0}^{*}(2317)^+$, we obtain the $DK$ invariant mass distribution of the decay $B_c\to J/\psi DK$, and also the rate for $B_c\to J/\psi D_{s0}^{*}(2317)$. The ratio of these two magnitude is then predicted.