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A semi-relativistic potential model is adopted to calculate the mass spectraof charmed and charmed-strange meson states up to the $2D$ excitations.Thestrong decay properties are further analyzed with a chiral quark model by usingthe numerical wave functions obtained from the potential model. By using thestrong decay amplitudes extracted from the chiral quark model, we alsosystematically study the coupled-channel effects on the bare masses of the$1P$-wave states, since the masses of $D^*_{s0}(2317)$ and $D_{s1}(2460)$cannot be explained with bare $1P$-wave states within the potential model.Based on our good descriptions of the mass and decay properties for thelow-lying well-established states, we give a quark model classification for thehigh mass resonances observed in recent years. In the $D$-meson family,$D_0(2550)$ can be classified as the radially excited state $D(2^1S_0)$;$D_3^*(2750)$ and $D_2(2740)$ can be classified as the second orbitalexcitations $D(1^3D_3)$ and $D(1D'_2)$, respectively; $D_J^*(3000)$ may be acandidate of $D(1^3F_4)$ or $D(2^3P_2)$; while $D_J(3000)$ may favor the highmass mixed state $D(2P'_1)$; however, there still exist puzzles forunderstanding the natures of $D_1^*(2600)$ and $D_1^*(2760)$, whose decayproperties cannot be well explained with either pure $D(2^3S_1)$ and$D(1^3D_1)$ states or their mixing. In the $D_s$-meson family, $D_{s3}^*(2860)$favors the $D_s(1^3D_3)$ assignment; $D_{s1}^*(2700)$ and $D_{s1}^*(2860)$ mayfavor the mixed states $|(SD)_1\rangle_L$ and $|(SD)_1\rangle_H$ via the$2^3S_1$-$1^3D_1$ mixing, respectively; $D_{sJ}(3040)$ may favor $D_s(2P_1)$ or$D_s(2P_1')$, or corresponds to a structure contributed by both $D_s(2P_1)$ and$D_s(2P_1')$.

Mass spectra and strong decays of charmed and charmed-strange mesons