Lepton Polarization Asymmetry in $B\to K^{(*)} l^+l^-$

Abstract

We investigate the longitudinal lepton polarization asymmetry in the exclusive processes $B\to K l^+l^-$ and $B\to K^* l^+l^-$. We include both short and long-distance contributions to the asymmetry in our discussions. We find that average values of the polarization asymmetries of the muon and tau for $B\to K^{(*)}\mu^+\mu^-$ and $B\to K^{(*)}\tau^+\tau^-$ are $-0.8\ (-0.7)$ and $-0.2\ (-0.5)$, respectively.