Implications for new physics from B¯0→π0π0 and B¯0→K¯0K0

We have analyzed the B¯0→π0π0 puzzle in three kinds of models beyond the standard model (SM). It is shown that the minimal flavor violation (MFV) models, the minimal supersymmetric standard model (MSSM), and the two Higgs doublet models (2HDM) I and II cannot give an explanation of the B¯0→π0π0 puzzle within 1σ experimental bounds and the model III 2HDM can explain the puzzle without a conflict with other experimental measurements. If the constraint on C8g from b→sg is not imposed, for all kinds of insertions considered there are regions of parameter space, where the scalar quark mass is larger (much larger) than the gluino mass in the case of LR or RL (LL or RR), in which the puzzle can be resolved within 1σ experimental bounds.