Study of the rare semileptonic decays $B_d^0\to K^{*}{l}^{+}{l}^{-}$ in scalar leptoquark model

We study the effect of scalar leptoquarks on the exclusive rare $B$-meson decays ${\overline{B}}_d^0\to {\overline{K}}^{*0}(\to K^{-}{\pi }^{+})l^{+}{l}^{-}$ in the full kinematically accessible physical region. We work out the constraints on leptoquark parameter space using the measured branching ratio of the $B_s\to {\mu }^{+}{\mu }^{-}$ process by the CMS and LHCb collaborations. We compute the branching ratio, forward-backward asymmetry, and isospin asymmetry distribution using the constrained parameter space. We also look into various form-factor-independent and $CP$-violating observables in the scalar leptoquark model.

Figure 1

Box diagram for $B_s-{\overline{B}}_s$ mixing phenomenon in the leptoquark model.

Figure 2

The allowed parameter space for the leptoquark couplings in the $|{\lambda }^{32}{\lambda }^{22}/M_S|$ vs ${\varphi }^{NP}$ plane obtained from the mass difference between $B_s$-meson mass eigenstates ($\mathrm{\Delta }{M}_s$). The left panel corresponds to bounds on $X(3,2,7/6)$, and the right panel is for $X(3,2,1/6)$ couplings.

Figure 3

The variation of branching ratios of $\overline{B}\to {\overline{K}}^{*}{\mu }^{+}{\mu }^{-}$ (left panel) and $\overline{B}\to {\overline{K}}^{*}{e}^{+}{e}^{-}$ (right panel) with low $q^2$ in the standard model and in leptoquark mode. The green bands are due to the leptoquark contributions, and the gray bands represent the theoretical uncertainties from the input parameters in the SM. The plots in the top panel are for $X(3,2,7/6)$, and those in the bottom panel are for $X(3,2,1/6)$.

Figure 4

Variation of longitudinal and transverse $K^{*}$ polarization fractions in the low-$q^2$ region. The plots in the top panel are for $X(3,2,7/6)$, and those in the bottom panel are for $X(3,2,1/6)$.

Figure 5

The variation of forward-backward asymmetry for $X(3,2,7/6)$ (left panel) and for $X(3,2,1/6)$ (right panel) with $q^2$.

Figure 6

The variation of transverse asymmetry parameters $A_T^{(3)}$, $A_T^{(4)}$, $A_{\mathrm{Im}}$, and the $K^{*}$ polarization factor with $q^2$ in high recoil for $X(3,2,7/6)$ LQ.

Figure 7

The variation of the observables $P_{1,2,3}$ and $P_{4,5,6}^{\prime }$ with $q^2$ for $X(3,2,7/6)$ LQ.

Figure 8

The variation of isospin asymmetry for $X(3,2,7/6)$ (left panel) and for $X(3,2,1/6)$ (right panel) with $q^2$.

Figure 9

The variation of the branching ratio for $\overline{B}\to {\overline{K}}^{*}{l}^{+}{l}^{-}$ with high $q^2$ for $X(3,2,7/6)$ LQ.

Figure 10

The variation of forward-backward asymmetry, isospin asymmetry, and longitudinal and transverse polarization fractions with high $q^2$ for $X(3,2,7/6)$ LQ.

Figure 11

Variation of the observables $P_2$, and $A_T^{(4)}$ for $X(3,2,7/6)$ LQ.