Theory of charmless hadronic B-decays

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I summarize results and performance of the dynamical theory of charmless hadronic B decays, based on QCD factorization in the heavy quark limit. On the theoretical side, a number of NNLO (alphaₛ²) amplitudes are now available, all showing a well-behaved perturbative expansion. The large observed branching fraction in B0 -> pi0 pi0 remains a challenge, implying either a large inverse moment of the B-meson wave function or a sizable power correction (or unexpected new physics). B-factory/Belle2 analyses of B -> gamma l nu may shed light on this. On the other hand, the new Belle and LHCb measurements of ACP(pi+ pi-) bring the experimental result closer to QCDF predictions, similar to what is found in B -> pi K decays, while Sₚipi gives a competitive gamma-determination. I remind the reader that for vector-vector final states, a theoretical treatment of the full set of helicity amplitudes has existed and met with some success since the B-factory era, and applies equally to LHCb measurements of e.g. Bₛ -> phi phi.