Understanding the charmed states recently observed by the LHCb and BaBar Collaborations in the quark model

Comparing the expected spectroscopy in the relativistic quark model and the predicted strong decays in the ${}^3{P}_0$ model employing the realistic wave functions from the relativistic quark model with the measured properties of the LHCb and BABAR charmed states, we find that the masses and strong decays of these charmed states can be reasonably explained in the conventional $q\overline{q}$ picture, and therefore suggest that the $D(2550)/D_J(2580)$, $D^{*}(2600)/D_J^{*}(2650)$, $D(2750)/D_J(2740)$, $D^{*}(2760)/D_J^{*}(2760)$, $D_J(3000)$, and $D_J^{*}(3000)$ can be identified as the $D(2^1{S}_0)$, $D(2^3{S}_1)$, $D_2^{\prime }(1D)$, $D(1^3{D}_3)$, $D(3^1{S}_0)$, and $D(1^3{F}_4)$, respectively.

Figure 1

The charmed meson spectrum. The solid lines are the GI quark model predictions and the shaded regions are the expected mass ranges from some other relativistic quark models [23, 24, 25]. The observed charmed states are also shown. The N and UN denote natural parity and unnatural parity, respectively.

Figure 2

Total decay width of $D_J(2740)/D(2750)$ as the $D_2(1D)$ and $D_2^{\prime }(1D)$ versus the mixing angle. The blue dashed line with a green band denotes the LHCb and BABAR experimental average. The vertical red solid line corresponds to the mixing angle ${\theta }_{1D}=-38.2^{\circ }$ obtained in Sec. 2.

Figure 3

Total widths of the $D_1(2P)$, $D_1^{\prime }(2P)$, $D_3(1F)$, and $D_3^{\prime }(1F)$ versus the mixing angle. The vertical red solid line corresponds to the mixing angle obtained in Sec. 2: ${\theta }_{2P}=-29.4^{\circ }$ and ${\theta }_{1F}=-39.5^{\circ }$.