Spectrum of higher excitations of $B$ and $D$ mesons in the relativistic potential model

We study the masses and wave functions of heavy-light quark-antiquark system in the relativistic potential model, where we focus on the higher excited states of $B$ and $D$ mesons. The resonances of $D_J(2740)$, $D_J^{*}(2760)$, $D_J^{*}(3000)$, and $D_{sJ}^{*}(2860)$ recently observed in experiments are considered. We find that these four resonances can be identified as the $|1{{}^{1,3}D}_2⟩$, $|1{{}^{3}D}_3⟩$, $|1{{}^{1,3}F}_3⟩$, and $|1{{}^{3}D}_3⟩$ states due to the prediction to the states with $l=2$ and $l=3$ in the potential-model calculation. The masses of $n=2$ excited states are also calculated. All the observed mesons can be accommodated successfully in the potential model.

Figure 1

The radial wave function ${\psi }_{nl}(r)$ of $D$ meson in coordinate space, $l$ from 0 to 4. (a) is for $n=1$, (b) is for $n=2$.