Mass spectroscopy and strong decays of excited open charm $${D}_{J}$$ mesons using relativistic Dirac formalism

The mass spectra for the heavy-light $$(c{\bar{q}}) ;$$ ( c q ¯ ) ; $$q = u$$ q = u or d charmed mesons are computed based on a relativistic framework. The low-lying 1 P states are found to be in an excellent agreement with the PDG reported values. Using the computed mass spectra and following effective Lagrangian approach based on heavy quark and chiral symmetry, the OZI allowed two body strong decays are computed. The computed decay rates, ratios and branching fractions allow us to identify the proper spin-parity assignments of the newly observed charm states. Accordingly, we could identify $$D_J(2560)$$ D J ( 2560 ) as $$2^1S_0$$ 2 1 S 0 , $$D_J^*(2680)$$ D J ∗ ( 2680 ) as $$2^3S_1$$ 2 3 S 1 , $$D_J(2740)$$ D J ( 2740 ) as $$1^3D_2$$ 1 3 D 2 , $$D_J^*(2760)$$ D J ∗ ( 2760 ) as $$1^3D_3$$ 1 3 D 3 , $$D^*_J(3000)$$ D J ∗ ( 3000 ) as $$2^3P_0$$ 2 3 P 0 , $$D_J(3000)$$ D J ( 3000 ) as $$2^1P_1$$ 2 1 P 1 and $$D^*_2(3000)$$ D 2 ∗ ( 3000 ) as $$1^3F_2$$ 1 3 F 2 open charm states. The effective coupling constants, $$g_T$$ g T , $$\tilde{g_H}$$ g H ~ , $$g_Y$$ g Y , $$\tilde{g_S}$$ g S ~ and $$g_Z$$ g Z extracted from the present study are found to be in accordance with the reported values. These coupling constants would be useful in further investigations. We found $$D^{*+} \pi ^-$$ D ∗ + π - as a favorable channel for the experimental search of the missing $$1^1F_3$$ 1 1 F 3 state.