Scalar leptoquarks and the rare $B$ meson decays

We study some rare decays of $B$ mesons involving the quark-level transition $b\to q{l}^{+}{l}^{-}(q=d,s)$ in the scalar leptoquark model. We constrain the leptoquark parameter space using the recently measured branching ratios of $B_{s,d}\to {\mu }^{+}{\mu }^{-}$ processes. Using such parameters, we obtain the branching ratios, direct $CP$-violation parameters, and isospin asymmetries in the $B\to K{\mu }^{+}{\mu }^{-}$ and $B\to \pi {\mu }^{+}{\mu }^{-}$ processes. We also obtain the branching ratios for some lepton-flavor-violating decays $B\to l_i^{+}{l}_j^{-}$. We find that the various anomalies associated with the isospin asymmetries of the $B\to K{\mu }^{+}{\mu }^{-}$ process can be explained in the scalar leptoquark model.

Figure 1

The allowed regions in the $r-{\varphi }^{\mathrm{NP}}$ parameter space obtained from $\mathrm{BR}(B_d\to {\mu }^{+}{\mu }^{-})$ (left panel) and $\mathrm{BR}(B_s\to {\mu }^{+}{\mu }^{-})$ (right panel).

Figure 2

The allowed regions in $C_{10}^{\mathrm{NP}}-{\varphi }^{\mathrm{NP}}$ parameter space (left panel) and $C_9^{\prime \mathrm{NP}}-C_{10}^{\prime \mathrm{NP}}$ (right panel) obtained from $\mathrm{BR}(B\to X_s{e}^{+}{e}^{-})$, where the green (red) region corresponds to high-$q^2$ (low-$q^2$) limits.

Figure 3

The variation of branching ratios with $q^2$ for the decay processes $B^0\to K^0{\mu }^{+}{\mu }^{-}$ (left panel) and $B^{+}\to K^{+}{\mu }^{+}{\mu }^{-}$ (right panel) in the standard model and in the leptoquark model. The red band for the leptoquark model is obtained using the allowed leptoquark parameter space. The $q^2$-averaged (binwise) $1\sigma$ experimental results are shown by black plots, where the horizontal (vertical) line denotes the bin width ($1\sigma$ error).

Figure 4

The variation of isospin asymmetry (left panel) for $B\to K\mu \mu$ and of $R_K$ (right panel) with $q^2$.

Figure 5

The differential branching ratios for ${\overline{B}}^0\to {\pi }^0{\mu }^{+}{\mu }^{-}$ (left panel) and $B^{-}\to {\pi }^{-}{\mu }^{+}{\mu }^{-}$ (right panel) in the SM and the leptoquark model.

Figure 6

Variation of $A_{CP}(q^2)$ for $B^0({\overline{B}}^0)\to {\pi }^0{\mu }^{+}{\mu }^{-}$ (left panel) and $B^{\pm }\to {\pi }^{\pm }{\mu }^{+}{\mu }^{-}$ (right panel).

Figure 7

The variation of isospin asymmetry for the $B\to \pi {\mu }^{+}{\mu }^{-}$ process and $R_{+}(q^2)$ in both the SM and the LQ model.