$D_{s0}^{\ast }(2317)$ and $DK$ scattering in $B$ decays from BaBar and LHCb data

Abstract

We study the experimental $DK$ invariant mass spectra of the reactions $B^{+}\to {\bar{D}}^0{D}^0{K}^{+}$, $B^0\to D^{-}{D}^0{K}^{+}$ (measured by the BaBar Collaboration) and $B_s\to {\pi }^{+}{\bar{D}}^0{K}^{-}$ (measured by the LHCb Collaboration), where an enhancement right above the threshold is seen. We show that this enhancement is due to the presence of $D_{s0}^{\ast }(2317)$, which is a $DK$ bound state in the $I(J^P)=0(0^{+})$ sector. We employ a unitarized amplitude with an interaction potential fixed by heavy meson chiral perturbation theory. We obtain a mass $M_{D_{s0}^{\ast }}=2315_{-17}^{+12}{}_{-5}^{+10}\text{MeV}$, and we also show, by means of the Weinberg compositeness condition, that the $DK$ component in the wave function of this state is $P_{DK}=70_{-6}^{+4}{}_{-8}^{+4}\%$, where the first (second) error is statistical (systematic).