Testing the Standard Model and searching for New Physics with B_d to π π and B_s to K K decays

We propose to perform a combined analysis of $B \to \pi\pi$ 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.