Decay $B_s\to \varphi {\ell }^{+}{\ell }^{-}$ in covariant quark model

Our article is devoted to the study of the rare $B_s\to \varphi {\ell }^{+}{\ell }^{-}$ decay where $\ell =\mu$, $\tau$. We compute the relevant form factors in the framework of the covariant quark model with infrared confinement in the full kinematical momentum transfer region. The calculated form factors are used to evaluate branching fractions and polarization observables in the cascade decay $B\to \varphi (\to K^{+}{K}^{-}){\ell }^{+}{\ell }^{-}$. We compare the obtained results with available experimental data and the results from other theoretical approaches.

Figure 1

Diagrammatic representation of the matrix elements describing $B_s\to \varphi$ transitions. Identification of quarks: $q_1=b$, $q_2=q_3=s$, $w_{13}=m_s/(m_b+m_s)$, and $w_{23}=1/2$.

Figure 2

The $q^2$-dependence of the vector and axial form factors (upper plot) and tensor form factors (lower plot).

Figure 3

Differential branching fraction in ${\mathrm{GeV}}^{-2}$.

Figure 4

Forward-backward asymmetry $A_{\mathrm{FB}}$.

Figure 5

Longitudinal polarization $F_L$.

Figure 6

Clean observables $P_1$ and $P_4^{\prime }$.