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We present some recent measurements of rare flavor-changing neutral current Bdecays, using data collected with the BABAR detector at the PEP-II e+e-collider at SLAC. First, we search for the rare process B+ -> K+ tau- tau+ andwe do not find evidence for signal. The measured branching fraction is(1.31+0.66-0.61(stat.)+0.35-0.25(sys.)) x 10-3 with an upper limit, at the 90%confidence level, of B(B+ -> K+ tau+ tau-) < 2.25 x 10-3. We then study thelepton forward-backward asymmetry AFB and the longitudinal K* polarization FLin the rare decays B -> K* l+ l-, where l+ l- is either e+ e- or mu+ mu-. Wereport results for both the K*(892)0l+l- and K*(892)+l+l- final states, as wellas their combination K*l+l-, in five disjoint dilepton mass-squared bins.Finally, we measure the time-dependent CP asymmetry in the radiative-penguindecay B0 -> KS0 pi- pi+ gamma. The Kpipi resonant structure is extracted by anamplitude analysis of the m_Kpipi and m_Kpi spectra in B+ -> K+ pi- pi+ gammadecays. We use these results to extract the mixing-induced CP parameters of theprocess B0 -> KS rho gamma from the time-dependent analysis of B0 -> KS0 pi+pi- gamma decays and obtain S = -0.18 pm 0.32(stat.) +0.06 -0.05(syst.).

Measurement of B+ -> K+ tau- tau+, B -> K* l+ l- and B -> K pi+ pi- gamma decays at BABAR