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 $D_{ s1}(2536 )^+\to D^{ *+}K^0_S$ and $D_{ s1}(2536)^-\to\bar D^{ *0}K^-$ allow us to obtain an estimate of the $S$-wave $D^*K$ scattering length in the channel with isospin $I=0$: $|a^{ (0)}_{ D^*K}|=(0.94\pm0.06)$ fm. The possibility of explaining the found value by the contribution of the $D_{ s1}(2460)$ resonance is discussed. The decay of $B_{ s1}(5830)\to B^*\bar K$ is also briefly discussed.
Categories: hep-ph hep-ex nucl-ex nucl-th