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

TL;DR

This paper calculates the mass spectra, decay constants, and decay properties of D mesons using a relativistic Dirac formalism with a Martin-like potential, showing good agreement with experimental data and previous theoretical models.

Contribution

The study introduces a relativistic Dirac formalism with a Martin-like potential to accurately predict D meson spectra and decay properties, aligning well with experimental results.

Findings

Predicted D meson masses match experimental values within a few MeV.

Calculated decay constants and branching ratios agree with experimental and lattice results.

Results support the validity of the relativistic Dirac approach for heavy-light meson studies.

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.