Non-leptonic B decays into charmless final states offer an important laboratory to study CP violation and the dynamics of strong interactions. Particularly interesting are B 0 s → K − K + and B 0 d → π − π + decays, which are related by the U -spin symmetry of strong interactions, and allow for the extraction of CP-violating phases and tests of the Standard Model. The theoretical precision is limited by U -spin-breaking corrections and innovative methods are needed in view of the impressive future experimental precision expected in the era of Belle II and the LHCb upgrade. We have recently proposed a novel method to determine the B 0decays are a new ingredient and the theoretical situation is very favourable. We discuss this strategy in detail, with a focus on penguin contributions as well as exchange and penguin-annihilation topologies which can be probed by a variety of non-leptonic B decays into charmless final states. We show that a theoretical precision as high as O(0.5 • ) for φ s can be attained in the future, thereby offering unprecedented prospects for the search for new sources of CP violation. 7 Prospects of the new strategy 42 8 Conclusions 462 Decay amplitudes and CP asymmetries
TopologiesThe non-leptonic decay B 0 d → π − π + , characterized by ab →ūud transition, is governed by the decay topologies depicted in figure 1. The decay amplitude is dominated by contributions from the tree (T ) and penguin (P ) topologies, but also receives contributions from exchange (E) and penguin-annihilation (P A) topologies. In the SM, we have [4]2.1) which is only sensitive to non-factorizable U -spin-breaking corrections because the factorizable contributions cancel in these ratios of amplitudes. Contrary, the U -spin relation C = C (2.10) is affected by both factorizable and non-factorizable U -spin-breaking effects. JHEP03(2017)055 Current [21, 32] Upgrade [3]A dir CP (B d → π − π + ) −0.31 ± 0.05 −0.31 ± 0.008A mix CP (B d → π − π + ) 0.66 ± 0.06 0.66 ± 0.008A dir CP (B s → K − K + ) 0.14 ± 0.11 0.087 ± 0.008A mix CP (B s → K − K + ) −0.30 ± 0.13 −0.19 ± 0.008 1 To be conservative, we consider only the largest uncertainty for K in eq. (2.28).