$D_{s}$ mesons with $DK$ and $D^{*}K$ scattering near threshold

$D_s$ mesons are studied in three quantum channels ($J^P=0^+$, $1^+$ and $2^+$), where experiments have identified the very narrow $D_{s0}^*(2317)$, $D_{s1}(2460)$ and narrow $D_{s1}(2536)$, $D_{s2}^*(2573)$. We explore the effect of nearby $DK$ and $D^*K$ thresholds on the subthreshold states using lattice QCD. Our simulation is done on two very different ensembles of gauge configurations (2 or 2+1 dynamical quarks, Pion mass of 266 or 156 MeV, lattice size $16^3\times 32$ or $32^3\times 64$). In addition to $\bar{q}q$ operators we also include meson-meson interpolators in the correlation functions. This clarifies the identification of the states above and below the scattering thresholds. The ensemble with $m_\pi \simeq 156~$MeV renders the $D_{s1}(2460)$ as a strong interaction bound state 44(10)MeV below $D^*K$ threshold, which is in agreement with the experiment. The $D_{s0}^*(2317)$ is found 37(17)MeV below $DK$ threshold, close to experiment value of 45MeV. The narrow resonances $D_{s1}(2536)$ and $D_{s2}^*(2573)$ are also found close to the experimental masses.