B→ϕK∗, Bd0→ϕKS and new physics

We consider the New-Physics (NP) solution to the polarization puzzle in B→ϕK∗ decays. We note that any such solution must reproduce the data in Bd0→ϕKS, where there are disagreements with the standard model in CP-asymmetry measurements. We examine 10 NP operators, of S/P, V/A and T variety. We find that, as long as Bd0→ϕKS exhibits large CP-violating effects, no single operator can explain the observations in both B→ϕK∗ and Bd0→ϕKS. For 2-NP-operator solutions, there are four possibilities, all of S/P type, which are presently allowed. We discuss ways of distinguishing among these solutions in the future. Models which contain only V/A operators, such as those with supersymmetry or extra Z′ bosons, cannot explain both Bd0→ϕKS and B→ϕK∗ data. On the other hand, the two-Higgs-doublet model, which has only S/P operators, is favored.