Spectroscopy and flavor changing decays of $B$, $B_s$ mesons in a Dirac formalism

In the framework of the relativistic independent quark model, the mass spectra and decay properties of $B$ and $B_s$ mesons are obtained using a Martin-like potential for the quark confinement. The predicted excited states are in good agreement with the experimental results as well as with the lattice QCD and other theoretical predictions. For instance, the $B_2(5747)$ as $1{{}^{3}P}_2$, $B_1(5721)$ as $1{{}^{3}P}_1$, and $B_0(5732)$ as $1{{}^{3}P}_0$ are identified. The spectroscopic parameters are used to calculate the electromagnetic transitions, pseudoscalar decay constants, hadronic decay widths, and leptonic decay widths. The present result for the decay constant, $f_B(1S)=188.56\mathrm{MeV}$, is in good agreement with recent lattice results (UKQCD Collaboration, Fermilab) and comparable with the experimental value of $(206.7\pm 8.9)$. The pseudoscalar decay constant for the $B_s$ meson obtained here, $f_{B_s}(1S)=240.21\mathrm{MeV}$, is in very good agreement with recent lattice QCD and QCD sum rule predictions. The predicted branching ratio for $B^{+}\to {\tau }^{+}{\nu }_{\tau }$ ($1.354\times {10}^{-4}$) is in accordance with the value, $(1.65\pm 0.34)\times {10}^{-4}$ reported by the Particle Data Group (PDG). The branching ratios of the rare decays $B_s^0\to {\mu }^{+}{\mu }^{-}$ ($(3.1\pm 0.7)\times {10}^{-9}$) and $B^0\to {\mu }^{+}{\mu }^{-}$ ($<6.3\times {10}^{-10}$) as observed by the CMS and LHCb Collaborations very recently are in accordance with our predictions of $3.602\times {10}^{-9}$ and $1.018\times {10}^{-10}$, respectively. The Cabibbo-favored hadronic branching ratios of $B^0\to D^{-}{\pi }^{+}$ ($3.724\times {10}^{-3}$), $B^0\to D^{*-}{\pi }^{+}$ ($3.475\times {10}^{-3}$), and $B_s\to D_s^{-}{\rho }^{+}$ ($3.800\times {10}^{-3}$) are in good agreement with the respective PDG values. The mixing parameters $x_q$, ${\chi }_q$ for $B^0-{\overline{B}}^0$ ($x_d=0.769$, ${\chi }_d=0.1859$) and $B_s-{\overline{B}}_s$ ($x_s=26.41$, ${\chi }_s=0.49929$) are also found to be in excellent agreement with the PDG values of ($0.770\pm 0.008$, $0.1862\pm 0.0023$) and ($26.49\pm 0.29$, $0.499292\pm 0.000016$), respectively.

Figure 1

$B$ meson spectra.

Figure 2

$B_s$ meson spectra.

Figure 3

Feynman diagram for leptonic decay $(M\to l\overline{{\nu }_l})$.

Figure 4

Higher-order flavor-changing neutral current processes for the $B_s^0\to {\mu }^{+}{\mu }^{-}$ decay allowed in the standard model.

Figure 5

$B^0-{\overline{B}}^0$ mixing.

Figure 6

$B_s-{\overline{B}}_s$ mixing.