Mass spectra and decay properties of $D$ Meson in a relativistic Dirac formalism

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, $2{}^3{S}_1$ (2605.86 MeV) and $2{}^1{S}_0$ (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, $1^3{P}_2$ (2468.22 MeV), $1^3{P}_1$ (2404.94 MeV), $1^3{P}_0$ (2315.24 MeV) and $1^1{P}_1$ (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$(D^0\to K^{-}{\pi }^{+})$ as $3.835\%$ and BR $(D^0\to K^{+}{\pi }^{-})$ 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.

26 Pages, 10 Tables, 3 figures,. arXiv admin note: substantial text overlap with arXiv:1402.4227; text overlap with arXiv:hep-ex/0606040 by other authors

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• Improved search for D^0 mixing using semileptonic decays at Belle
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• Tetraquark states in the bottom sector and the status of the $Y_b$(10890) state
• Bottomonium spectroscopy motivated by general features of pNRQCD
• Masses of tetraquark states in the hidden charm sector above $D-D^{\ast }$ threshold