Estimate of the $S$-wave $D^{\ast }K$ scattering length in the isospin-0 channel from Belle and LHCb data

It is shown that the Belle and LHCb data on the interference of the amplitudes of the $S$ and $D$ partial waves in the decays $D_{s1}(2536{)}^{+}\to D^{\ast +}{K}_S^0$ and $D_{s1}(2536{)}^{-}\to {\bar{D}}^{\ast 0}{K}^{-}$ allow us to obtain an estimate of the $S$-wave $D^{\ast }K$ scattering length in the channel with isospin $I=0$: $\mathrm{\mid }{a}_{D^{\ast }K}^{(0)}\mathrm{\mid }=(0.94\pm 0.06)$ fm. The possibility of explaining the found value by the contribution of the $D_{s1}(2460)$ resonance is discussed. The decay of $B_{s1}(5830)\to B^{\ast }\bar{K}$ is also briefly discussed.