Abstract
The mass spectra of $D$ meson states are calculated in the framework of a relativistic independent quark model. For the present study, we have used the martin like potential for the quark confinement. Our predicted states in S-wave, $2\ ^3S_1$ (2605.86 MeV) and $2\ ^1S_0$ (2521.72 MeV) are in very good agreement with experimental result of $2608\pm{2.4}\pm{2.5}$ MeV and $2539.4\pm{4.5}\pm{6.8}$ MeV respectively reported by BABAR Collaboration. The calculated P-wave $D$ meson states, $1^3P_2$ (2468.22 MeV), $1^3P_1$ (2404.94 MeV), $1^3P_0$ (2315.24 MeV) and $1^1P_1$ (2367.94 MeV) are in close agreement with experimental average (Particle Data Group) values of $2462.6 \pm 0.7 $ MeV, $2427 \pm 26 \pm 25$ MeV, $2318 \pm 29 $ MeV and $2421.3 \pm 0.6 $ MeV respectively. The pseudoscalar decay constant ($f_P$= 202.57 MeV) of $D$ meson obtained using this relativistic formalism is in very good agreement with the experiment as well as with the lattice and other available theoretical predictions. The Cabibbo favoured hadronic decay branching ratios, BR$(D^0\rightarrow K^- \pi^+)$ as $3.835 \%$ and BR $(D^0\rightarrow K^+ \pi^-)$ as $1.069 \times 10^{-4} $ are also in very good agreement with the respective experimental values of $ 3.91 \pm 0.08\%$ and $(1.48\pm 0.07) \times 10^{-4}$ reported by CLEO Collaboration. Our predicted results in leptonic decay widths of $D$ meson are also in better accord with experiment as well as other theoretical results. The mixing parameters of $D^0 - \bar{D}^0$ oscillation, $x_q$ (5.14 $\times 10^{-3}$), $y_q$ (6.02 $\times 10^{-3}$) and $R_M$ (3.13 $\times 10^{-5}$) are in very good agreement with BaBar and Belle Collaboration results.
Highlights
Experiments at LHCb [1] have reported a large number of DJ resonances in the mass range of 2.0 GeV/c2 to 4.0 GeV/c2, of which many belong to natural excited states of the D meson, while quite a number of them belong to unnatural states [1]
The study of the D meson is of special interest as it is a hadron with two open flavours (c, uor d) which restricts its decay via strong interactions
We have studied here the mass spectra and decay properties of the D meson in the framework of the relativistic independent quark model
Summary
Experiments at LHCb [1] have reported a large number of DJ resonances in the mass range of 2.0 GeV/c2 to 4.0 GeV/c2, of which many belong to natural excited states of the D meson, while quite a number of them belong to unnatural states [1]. Though lattice QCD and QCD sum rules are quite successful, their predictions for the excited states of the open flavour mesons in the heavy sector are very few. Recent experimental data on excited D-states are partially inconclusive and require a more detailed analysis involving their decay properties. QCD sum rules are suitable for describing the low q2 region of the form factors; lattice QCD gives good predictions for high q2. As a result these methods do not provide a full picture of the form factors and, more significant, for the relations between the
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