The starting point to our discussion is the ”B → Kπ puzzle”. We show, that although the ”puzzle” can be resolved by a more detailed analysis, there is a more fundamental question that needs to be addressed: Is New Physics necessary to describe the experimentally observed asymmetries and branch- ing fractions of the B → P P decays? We perform a phenomenological anal- ysis based on fits of an model-independent New Physics parameterisation and obtain exclusion χ2 plots of the two ad-hoc parameters (magnitude and a weak phase) sensitive to New Physics. The results show that the Standard Model expectation value lies within 2σ with respect to the global minimum but the overall picture is not well constrained by the existing data. Our re- sults are mostly sensitive to the time-dependent asymmetry and branching fraction of the B 0 → K 0 π 0 decay. New experimental outcomes are highly expected and results of this analysis provide strong hints for improvement of precision in current experiments LHCb and Belle II.