We show that in a decay of the form $B_d$ or $B_s\to P_1{P}_2\gamma$ (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 $B_d\to K_S{\pi }^0\gamma$), then to leading order in the effective Hamiltonian, 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 antiparticle (e.g. as in $B_d\to {\pi }^{+}{\pi }^{-}\gamma$), 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. The formalism which applies to the case where $P_1$ and $P_2$ are $C$ eigenstates also further generalizes to the case of final states containing multiple $C$ eigenstates and a photon. This suggests several additional channels to search for new physics, such as $K_S{\eta }^{\prime }(\eta )\gamma$, $\varphi K_S\gamma$ etc. We also emphasize that the contribution of nondipole interactions can be monitored by the dependence of the mixing-induced $CP$ asymmetry of nonresonant modes on the Dalitz variables. Furthermore, using a number of different final states can also provide important information on the contribution from nondipole effects.

• Received 17 December 2004

DOI:https://doi.org/10.1103/PhysRevD.71.076003