  We propose two novel methods for testing the standard model using external
photon conversion at a high-luminosity e^+e^- B factory proposed recently. The
first method is to measure the mixing-induced CP-violation parameter
S_{pi^0pi^0} in B^0 --> pi^0 pi^0 decays. The precision of S_{pi^0pi^0} is
estimated to be 0.23 from a Monte Carlo study for a data sample containing 50 x
10^9 BBbar pairs. We demonstrate that this measurement is crucial for reducing
the discrete ambiguity of the Cabibbo-Kobayashi-Maskawa angle phi_2 determined
from the isospin analysis with B --> pi pi decays. The second method is to
measure photon polarization in B^0 --> K^{*0}(--> K^+ pi^-) gamma decays using
the external photon conversion, and combine it with S_{K^{*}gamma} from B^0 -->
K^{*0}(--> K^0_S pi^0) gamma decays. This offers a promising way of determining
the hypothetical right-handed current amplitude and phase beyond the standard
model.
