Charmed-strange mesons revisited: Mass spectra and strong decays

Inspired by the present experimental status of charmed-strange mesons, we perform a systematic study of the charmed-strange meson family in which we calculate the mass spectra of the charmed-strange meson family by taking a screening effect into account in the Godfrey-Isgur model and investigate the corresponding strong decays via the quark pair creation model. These phenomenological analyses of charmed-strange mesons not only shed light on the features of the observed charmed-strange states, but also provide important information on future experimental search for the missing higher radial and orbital excitations in the charmed-strange meson family, which will be a valuable task in LHCb, the forthcoming Belle II, and PANDA.

Figure 1

The $r$ dependence of ${\tilde{V}}^{\text{scr}}(r)$, $V(r)=br$, and $\tilde{V}(r)=\int d^3{\mathit{r}}^{\prime }{\rho }_{12}(\mathit{r}-{\mathit{r}}^{\prime })b{r}^{\prime }$. Here, we take two values $\mu =0.02\mathrm{GeV}$ and $\mu =0.05\mathrm{GeV}$ to show ${\tilde{V}}^{\text{scr}}(r)$. Other parameters involved in ${\tilde{V}}^{\text{scr}}(r)$, $V(r)=br$, and $\tilde{V}(r)$ are $m_s=1.628\mathrm{GeV}$, $m_c=0.419\mathrm{GeV}$, ${\sigma }_0=1.80\mathrm{GeV}$, and $s=1.55$ in the expression of ${\sigma }_{12}$. See Table II in [2].

Figure 2

Mass spectrum of charmed-strange mesons (in units of MeV). Here, the blue lines stand for the results obtained by the GI model [2, 86], while the red lines show the modified GI model with $\mu =0.02\mathrm{GeV}$. The black rectangles denote the experimental data taken from PDG [1]. The corresponding ${}^{2S+1}{L}_J$ quantum numbers are listed in the abscissa. In addition, when there exists a mixture of $n{}^1{L}_L$ and $n{}^3{L}_L$ states, we use another notation $L_L$.

Figure 3

The $D_{s0}^{*}(2317)\to D_s{\pi }^0$ (left panel) and $D_{s1}(2460)\to D_s^{*}{\pi }^0$ (right panel) decays through the $\eta -{\pi }^0$ mixing.

Figure 4

The mixing angle ${\theta }_{1P}$ dependence of a decay width $D_{s1}(2536)\to D^{*}K$.

Figure 5

The ${\theta }_{SD}$ dependence of the calculated partial and total decay widths and ratio $\mathrm{\Gamma }(D^{*}K)/\mathrm{\Gamma }(DK)$. The vertical band corresponds to the common range of ${\theta }_{SD}$, where our results can be matched with the experimental widths and ratio [28].

Figure 6

The ${\theta }_{SD}$ dependence of the decay widths and ratio $\mathrm{\Gamma }(D^{*}K)/\mathrm{\Gamma }(DK)$ of $D_{s1}^{*}(2860)$. The vertical band corresponds to the common range of ${\theta }_{SD}$, where our results can be matched with the experimental width and ratio of $D_{s1}^{*}(2700)$ [28].

Figure 7

The ${\theta }_{1D}$ dependence of the partial decay widths and the total decay width of $D_s(1D(2^{-}))$ (left panel) and $D_s(1D^{\prime }(2^{-}))$ (right panel). The vertical dashed lines correspond to the mixing angle ${\theta }_{1D}=-50.8^{\circ }$