Recent results on rare B decays with BaBar

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Flavor Changing Neutral Current transitions b→sl+l− and b→sγ provide an excellent laboratory for the search for physics beyond the Standard Model.Standard Model tests are performed through measurements of the lepton forward-backward asymmetry AFB and the longitudinal K* polarization FL in the decay B→K⁎l+l−, and the search for the rare decay B+→K+τ+τ−.From the study of the Kπ+π− system in B radiative-penguin decays, the time-dependent CP asymmetry in the decay B0→KS0π+π−γ is measured, together with the branching fractions of B+→K+π−π+γ and B0→K0π−π+γ.