  We show that in a decay of the form B_d or B_s-> P_1 P_2 gamma (where P_1 and
P_2 are pseudoscalar mesons), through a flavor changing dipole transition, time
dependent oscillations can reveal the presence of physics beyond the Standard
Model. If P_1 and P_2 are CP eigenstates (e.g. as in B_d -> K_S pi0 gamma), the
oscillation is independent of the resonance structure. Thus data from
resonances as well as from nonresonant decays can be included. This may
significantly enhance the sensitivity to new physics of the method. If P_1 is a
charged particle, and P_2 its anti-particle (e.g. as in B_d -> pi+ pi- gamma),
one has the additional advantage that both the magnitude and the weak phase of
any new physics contribution can be determined from a study of the angular
distribution. These signals offer excellent ways to detect new physics because
they are suppressed in the Standard Model. We also show that the potential
contamination of these signals originating from the Standard Model annihilation
diagram gives rise to photons with, to a very good approximation, the same
helicity as the dominant penguin graph and thus causes no serious difficulty.
