Exclusive Semileptonic Rare Decays $B \to K^{(*)} l^+ l^-$ in a SUSY SO(10) GUT

In the SUSY SO(10) GUT context, we study the exclusive processes $B \to K^{(*)} l^+l^-(l=\mu,\tau)$. Using the Wilson coefficients of relevant operators including the new operators $Q_{1,2}^{(\prime)}$ which are induced by neutral Higgs boson (NHB) penguins, we evaluate some possible observables associated with these processes like, the invariant mass spectrum (IMS), lepton pair forward backward asymmetry (FBA), lepton polarization asymmetries etc. In this model the contributions from Wilson coefficients $C_{Q_{1,2}}^\prime$, among new contributions, are dominant. Our results show that the NHB effects are sensitive to the FBA, $dL/d\hat{s}$, and $dT/d\hat{s}$ of $B \to K^{(*)} \tau^+ \tau^-$ decay, which are expected to be measured in B factories, and the average of the normal polarization $dN/d\hat{s}$ can reach several percent for $B \to K \mu^+ \mu^-$ and it is 0.05 or so for $B\to K \tau^+\tau^-$, which could be measured in the future super B factories and provide a useful information to probe new physics and discriminate different models.