  Recent time-dependent CP asymmetry measurements in the $B_d \to J/\psi K_S$
channel by the BaBar and Belle Collaborations yield somewhat lower values of
$\sin 2\beta$ compared to the one obtained from the standard model fit. If the
inconsistency between these numbers persists with more statistics, this will
signal new physics contaminating the $B_d \to J/\psi K_S$ channel, thus
disturbing the extraction of $\beta$. We show that the R-parity-violating
interactions in supersymmetric theories can provide extra new phases which play
a role in significantly reducing the above CP asymmetry, thus explaining why
BaBar and Belle report lower values of $\sin 2\beta$. The same couplings also
affect the $B_d \to \phi K_S$ decay rate and asymmetry, explain the $B \to
\eta' K$ anomaly, and predict nonzero CP asymmetry in dominant $B_s$ decays.
The scenario will be tested in the ongoing and upcoming B factories.
