Leptoquark effects on $b \to s \nu \bar{\nu}$ and $B \to K l^+ l^-$ decay processes

We study the rare semileptonic decays of $B$ mesons induced by $b \to s \nu \bar{\nu}$ as well as $b \to s l^+ l^-$ transitions in the scalar leptoquark model where the leptoquarks transform as $(3,2,7/6)$ and $(3,2,1/6)$ under the standard model gauge group. The leptoquark parameter space is constrained using the most recent experimental results on ${\rm Br}(B_s \rightarrow \mu^+ \mu^-)$ and ${\rm Br}(B_d \to X_s \mu^+ \mu^-)$ processes. Considering only the baryon number conserving leptoquark interactions, we estimate the branching ratios for the exclusive $\bar{B} \rightarrow \bar{K}^{(*)} \nu \bar{\nu}$ and inclusive $B \rightarrow X_s \nu \bar{\nu}$ decay processes by using the constraint parameters. We also obtain the low recoil (large lepton invariant mass, i.e., $q^2 \sim m^2_b$) predictions for the angular distribution of $\bar B \rightarrow \bar{K} l^+ l^-$ process and several other observables including the flat term and lepton flavour non-universality factor in this model.