  We analyze the possibility of observing new physics effects in the $b \to d$
penguin amplitudes. For this purpose, we consider the decay mode $B \to K^0
\bar K^0 $, which has only $b \to d$ penguin contributions. Using the QCD
factorization approach, we find very tiny CP violating effects in the standard
model for this process. Furthermore, we show that the minimal supersymmetric
standard model with $LR$ mass insertion and R-parity violating supersymmetric
model can provide substantial CP violation effects. Observation of sizable CP
violation in this mode would be a clear signal of new physics.
