  The small P wave compoment of $B\to J/\psi K^*$ measured by CLEO makes it
practical to measure $\sin2\beta$ using $B^0\to J/\psi K^{*0}\to J/\psi K_S
\pi^0$, independent from $B^0\to J/\psi K_S$. Because these modes are color
suppressed, new physics enhanced color dipole $bsg$ coupling, as hinted from
the persistent ${\cal B}_{s.l.}$ and $n_C$ problems as well as the newly
observed large semi-inclusive $B\to \eta^\prime + X_s$ decay, may have
significant impact. We show that it may lead to a difference in the $\sin
2\beta$ measurements between $B^0\to J/\psi K_S$ and $J/\psi K_S \pi^0$
measureable at the B Factories in the near future.
