  We search for a new light non-Standard Model CP-odd Higgs boson, $A^0$,
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 $\Upsilon(3S) \to \gamma A^0, A^0 \to$ invisible. We also search for
evidence of an undetectable $\Upsilon(1S)$ decay recoiling against the dipion
system. The data samples contain $99 \times 10^6 \Upsilon(2S)$ and $122 \times
10^6 \Upsilon(3S)$ decays collected by the \babar\ detector at the SLAC PEP-II
$B$ factory.
