D meson spectroscopy and their decay properties using Martin potential in a relativistic Dirac formalism

For the present study, we have used the Martin-like potential for the quark confinement. Our predicted states in the S-wave, 2\ ³S₁ (2605.86 MeV) and 2\ ¹S₀ (2521.72 MeV), are in very good agreement with experimental results of 2608± 2.4 ± 2.5 MeV and 2539.4± 4.5± 6.8 MeV, respectively, reported by the BABAR Collaboration. The calculated P-wave D meson states, 1³P₂ (2462.50 MeV), 1³P₁ (2407.56 MeV), 1³P₀ (2373.82 MeV) and 1¹P₁ (2423.28 MeV), are in close agreement with experimental average (Particle Data Group) values of 2462.6 ± 0.7 MeV, 2427 ± 26 ± 25 MeV, 2318 ± 29 MeV and 2421.3 ± 0.6 MeV, respectively. The pseudoscalar decay constant ( fP = 202.57 MeV) of the D meson is in very good agreement with the experiment as well as with the lattice predictions. The Cabibbo favoured nonleptonic decay branching ratios, BR (D⁰→ K⁻ π ⁺) of $$4.071\,%$$ and BR (D⁰→ K⁺ π ⁻) of 1.135 × 10⁻⁴ , are also in very good agreement with the respective experimental values of 3.91 ± 0.08\,% and (1.48± 0.07) × 10⁻⁴ reported by CLEO Collaboration. The mixing parameters of the D⁰ – D̄⁰ oscillation, xq (5.14 × 10⁻³ ), yq (6.02 × 10⁻³ ) and RM (3.13 × 10⁻⁵ ), are in very good agreement with BaBar and Belle Collaboration results.