Testing the Standard Model and searching for New Physics with $B_d \to ππ$ and $B_s \to K K$ decays

We propose to perform a combined analysis of $B \to ππ$ and $B_s \to K^+ K^-$ modes, in the framework of a global CKM fit. The method optimizes the constraining power of these decays and allows to derive constraints on NP contributions to penguin amplitudes or on the $B_s$ mixing phase. We illustrate these capabilities with a simplified analysis using the recent measurements by the LHCb Collaboration, neglecting correlations with other SM observables.

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