Results obtained by various experiments show that the $D_{ s0}^{ \ast}(2317)$ and $D_{ s1}(2460)$ mesons are very narrow states located below the $DK$ and $D^{ \ast}K$ thresholds, respectively. This is markedly in contrast with the expectations of naive quark models and heavy quark symmetry. Motivated by a recent lattice study 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 $D^{ (\ast)}K$ 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. 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, from light to heavy. We observe that the coupling of the $0^{ +}$ $(1^{ +})$ meson sector to the $DK$ $(D^{ \ast}K)$ threshold is the key feature to simultaneously lower the masses of the corresponding $D_{ s0}^{ \ast}(2317)$ and $D_{ s1}(2460)$ states predicted by the naive quark model and describe the $D_{ s1}(2536)$ meson as the $1^{ +}$ state of the $j_{ q}^{ P}=3/2^{ +}$ doublet predicted by heavy quark symmetry, reproducing its strong decay properties. Our calculation allows to introduce the coupling with the $D$-wave $D^{ \ast}K$ channel and the computation of the probabilities associated with the different Fock components of the physical state.
Categories: hep-ph hep-ex hep-lat nucl-th