  The recent observations of sizable transverse fractions of B-> phi K* are
strongly contrary to the Standard Model expectation. We analyze all possible
new-physics four-quark operators. We find that two classes of new-physics
operators could offer resolutions to the B-> phi K* polarization anomaly. The
(1-\gamma_5)\otimes (1-\gamma_5) and \sigma(1-\gamma_5)\otimes
\sigma(1-\gamma_5) operators in the first class contribute to different
helicity amplitudes as H{00}: H{--}: H{++} ~ O(1/mb):O(1):O(1/mb^2), while the
contributions arising from (1+\gamma_5)\otimes (1+\gamma_5) and
\sigma(1+\gamma_5)\otimes \sigma(1+\gamma_5) operators in the second class to
various helicity amplitudes are given as H{00}: H{--}: H{++} ~
O(1/mb):O(1/mb^2):O(1). For each class of new physics, we find that all new
physics effects can be lumped into a single parameter. Two possible
experimental results of polarization phases, \arg(A_\perp)- \arg(A_\parallel) ~
\pi or 0, originating from the phase ambiguity in data, could be separately
accounted for by our two new-physics scenarios: (i) the first scenario with the
first class new-physics operators, and (ii) the second scenario with the second
class new-physics operators. The consistency between the data and the new
physics analysis, suggests a small new-physics weak phase, together with a
large strong phase. We obtain sizable transversely polarized amplitudes
\Lambda_{\parallel\parallel} + \Lambda_{\perp\perp} = \Lambda_{00}. In the
second scenario, we find \Lambda_{\parallel\parallel} ~ \Lambda_{\perp\perp},
while, in the first scenario, we obtain \Lambda_{\parallel\parallel} ~
\Lambda_{\perp\perp}/2. We discuss the impact of the new-physics weak phase on
observations.
