Results obtained by various experiments show that the $D_{s0}^{\ast}(2317)$ and $D_{s1}(2460)$ mesons are very narrow states located, respectively, below the $DK$ and $D^{\ast}K$ thresholds. This has led much attention because it is markedly in contrast with the expectations from naive quark models and heavy quark symmetry [1]. Early lattice QCD studies found $D_{s0}^{\ast}$ and $D_{s1}$ energy levels in line with quark model expectations (see, for instance, Ref. [2]).

Motivated by a recent lattice study [3, 4] which addresses the mass shifts of the $c\bar{s}$ ground states with quantum numbers $J^{P}=0^{+}$ ($D_{s0}^{\ast}(2317)$) and $J^{P}=1^{+}$ ($D_{s1}(2460)$) due to their coupling with $S$-wave $DK$ and $D^{\ast}K$ thresholds, we perform a similar analysis within a nonrelativistic constituent quark model in which quark-antiquark and meson-meson degrees of freedom are incorporated. The quark model has been applied to a wide range of hadronic observables and thus the model parameters are completely constrained (see references [5, 6] for reviews). The coupling between quark-antiquark and meson-meson Fock components is done using a $^{3}P_{0}$ model in which its only free parameter $\gamma$ has been elucidated performing a global fit to the decay widths of mesons that belong to different quark sectors [7].

We observe that the $S$-wave coupling of the $0^{+}$ $(1^{+})$ meson sector to the $DK$ $(D^{\ast}K)$ threshold is a key feature in lowering the masses of the corresponding $D_{s0}^{\ast}(2317)$ and $D_{s1}(2460)$ states predicted by the naive quark model, but also in describing the $D_{s1}(2536)$ meson as the $1^{+}$ state of the $j_{q}^{P}=3/2^{+}$ doublet predicted by heavy quark symmetry and thus reproducing its strong decay properties. Two features of our formalism cannot be address nowadays by lattice computations: the coupling of the $D$-wave $D^{\ast}K$ threshold in the $J^{P}=1^{+}$ channel and the computation of the probabilities associated with different Fock components in the physical state.

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[2] G.S. Bali Phys. Rev. D68, 071501 (2003)

[3] D. Mohler et al., Phys. Rev. Lett. 111, 222001 (2013)

[4] C.B. Lang et al., Phys. Rev. D90, 034510 (2014)

[5] A. Valcarce et al., Rept. Prog. Phys. 68, 965 (2005)

[6] J. Segovia et al., Int. J. Mod. Phys. E22 1330026 (2013)

[7] J. Segovia, D.R. Entem and F. Fernandez, Phys. Lett. B715, 322 (2012)