We search for a new light non-Standard Model CP-odd Higgs boson, A0, decaying to tau tau-, mu mu-, and invisible in radiative decays of the Upsilon(2S) and Upsilon(3S). We search for the light scalar particle produced in single-photon decays of the Upsilon(3S) resonance through the process Upsilon(3S) to A0 gamma, A0 to invisible. We also search for evidence of an undetectable Upsilon(1S) decay recoiling against the dipion system. The data samples contain 99x10^6 Upsilon (2S) and 122x106 Upsilon(3S) decays collected by the BABAR detector at the SLAC PEP-II B factory. Show Partial Abstract