CP Violating Phase Difference between $B\to J/\psi K_S$ and $J/\psi K_S \pi^0$ from New Physics

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.