  An angular analysis for B decays into two vector mesons gives parameters
sensitive to new physics. They are the decay amplitudes of the three helicity
states, the asymmetry in triple product, and the CP violating phase. The
measurements of these quantities are performed for $B^0 \to J/\psi K^{*0}$
decays in a data sample with 253 fb$^{-1}$ taken by the Belle detector in the
KEKB asymmetric $e^+e^-$ collider. With the time-integrated angular analysis,
the decay amplitudes' moduli and phase angles are measured to be
$|A_0|^2=0.585\pm 0.012 \pm 0.09$, $|A_{\parallel}|^2=0.233\pm 0.013\pm 0.008$,
$|A_\perp|^2=0.181\pm 0.012\pm 0.008$, $\arg(A_\parallel)=2.888\pm 0.090\pm
0.008$ radians, and $\arg(A_\perp)=0.239\pm 0.064\pm 0.010$ radians. The
difference between $\arg(A_\parallel)$ and $\arg(A_\perp)$ is $2.649\pm0.110$
radians, which is shifted from $\pi$ by more than $4\sigma$; this can be
interpreted as evidence for the existence of the final state interaction. The
amplitude values are used in triple product correlations to obtainasymmetries
of $A_T^{(1)}=0.101\pm 0.033\pm 0.007$ and $A_T^{(2)}=-0.102\pm 0.032\pm 0.003$
for $B^0$ meson decays, and $\bar{A}_T^{(1)}=0.056\pm 0.030\pm 0.006$ and
$\bar{A}_T^{(2)} = -0.091\pm 0.028\pm 0.003$ for $\bar{B^0}$ meson decays. The
time dependent angular analysis gives the measurements of CP violating
parameters $\sin 2\phi_1$ and $\cos 2\phi_1$ to be $0.30 \pm 0.32 \pm 0.02$ and
$-0.31 \pm 0.91 \pm 0.10$, respectively. The value of $\cos 2\phi_1$ is $-0.56
\pm 0.86 \pm 0.11$ if $\sin 2\phi_1$ is fixed at the world average value
(0.731).
