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

Manan Shah; Bhavin Patel; P. C. Vinodkumar

doi:10.1140/epjc/s10052-016-3875-5

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2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2016) 76: 36
https://doi.org/10.1140/epjc/s10052-016-3875-5

Regular Article - Theoretical Physics

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

Manan Shah¹^,2^*, Bhavin Patel² and P. C. Vinodkumar¹

¹ Department of Physics, Sardar Patel University, Vallabh Vidyanagar, 388 120, India
² P D Patel Institute of Applied Sciences, CHARUSAT, Changa, 388 421, India

^* e-mail: mnshah09@gmail.com

Received: 16 August 2015
Accepted: 26 December 2015
Published online: 22 January 2016

Abstract

For the present study, we have used the Martin-like potential for the quark confinement. Our predicted states in the S-wave, $2\ ^3S_1$ (2605.86 MeV) and $2\ ^1S_0$ (2521.72 MeV), are in very good agreement with experimental results of $2608\pm 2.4 \pm 2.5$ MeV and $2539.4\pm 4.5\pm 6.8$ MeV, respectively, reported by the BABAR Collaboration. The calculated P-wave D meson states, $$1^3P_2$$ (2462.50 MeV), $$1^3P_1$$ (2407.56 MeV), $$1^3P_0$$ (2373.82 MeV) and $$1^1P_1$$ (2423.28 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 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 $(D^0\rightarrow K^- \pi ^+)$ of $4.071\,\%$ and BR $(D^0\rightarrow K^+ \pi ^-)$ of $1.135 \times 10^{-4}$ , 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. The mixing parameters of the $$D^0 $$ – $\bar{D}^0$ 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.