Strong decays of excited $2^{+}$ charmed mesons

The new charmed resonance $D_2^{*}(3000)$ was observed by the LHCb Collaboration in $B$ decays. In this paper, by assigning it as four possible excited states of the $2^{+}$ family, we use the instantaneous Bethe-Salpeter method to calculate their Okubo-Zweig-Iizuka-allowed two-body strong decays. The results of $1^3{F}_2$ and $3^3{P}_2$ states deviate from the present experimental observation while $2^3{P}_2$ and $2^3{F}_2$ are in the error range. Our study also reveals that the widths of these states depend strongly on the masses. Due to the large uncertainties and different mass input, variable models get inconsistent conclusions at the moment. The analysis in this work can provide essential assistance for future measurements and investigations.

Figure 1

Feynman diagram of the OZI-allowed two-body strong decay, taking $D_2^{*0}\to D^{+}{\pi }^{-}$ for example. (a) Leading order diagram (b) Approximate diagram.

Figure 2

The dependence of partial widths of channels involving final $D_1(2420)/D_{s1}(2536)$ or $D_1(2430)/D_{s1}(2460)$ mesons on mixing angle ${\theta }_{1P}$. The vertical dashed line indicates the ideal mixing angle ${\theta }_{1P}=\arctan (\sqrt{1/2})\approx 35.3°$. (a) $D_2^{*}(3000{)}^0$ as $2^3{P}_2$ state, (b) $D_2^{*}(3000{)}^0$ as $3^3{P}_2$ state, (c) $D_2^{*}(3000{)}^0$ as $1^3{F}_2$ state, (d) $D_2^{*}(3000{)}^0$ as $2^3{F}_2$ state.

Figure 3

The dependence of partial widths of channels involving final $D_2(2740)$ or $D_2(2780)$ mesons on mixing angle ${\theta }_{1D}$. The vertical dashed line indicates the ideal mixing angle ${\theta }_{1D}=\arctan (\sqrt{2/3})\approx 39.2°$. (a) $D_2^{*}(3000{)}^0$ as $2^3{P}_2$ state, (b) $D_2^{*}(3000{)}^0$ as $3^3{P}_2$ state, (c) $D_2^{*}(3000{)}^0$ as $1^3{F}_2$ state, (d) $D_2^{*}(3000{)}^0$ as $2^3{F}_2$ state.

Figure 4

Some wave functions of $D_2^{*}(3000)$ as different assignments, $D^0$ as $1^1{S}_0$, and $D_0(2550{)}^0$ as $2^1{S}_0$. (a) $D_2^{*}(3000{)}^0$ as $2^3{P}_2$ state (b) $D_2^{*}(3000{)}^0$ as $3^3{P}_2$ state, (c) $D_2^{*}(3000{)}^0$ as $1^3{F}_2$ state, (d) $D_2^{*}(3000{)}^0$ as $2^3{F}_2$ state, (e) $D^0$ as $1^1{S}_0$, (f) $D_0(2550{)}^0$ as $2^1{S}_0$.

Figure 5

Total widths change with the masses of different states for $D_2^{*}$. The vertical and horizontal dashed lines with shades are the present experimental results with errors [3].