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We search for a light Higgs boson, $A^0$, in the radiative decay$\Upsilon(3S)\to\gamma A^0$, $A^0\to\tau^+\tau^-$, $\tau^+\to e^+\nu_e\bar{\nu}_{\tau}$ or $\tau^+\to \mu^+ \nu_{\mu} \bar{\nu}_{\tau}$. The datasample contains 122 million $\Upsilon(3S)$ events recorded with the \babardetector. We find no evidence for a narrow structure in the studied$\tau^+\tau^-$ invariant mass region of $4.03<m_{\tau^+\tau^-}<10.10$ \gevcc.We exclude at the 90% confidence level (C.L.) a low mass Higgs decaying to$\tau^+\tau^-$ with a product branching fraction ${\cal{B}}(\Upsilon(3S)\to\gamma A^0)\times {\cal {B}}(A^0\to\tau^+\tau^-)$$>(1.5-16)\times 10^{-5}$ across the $m_{\tau^+\tau^-}$ range. We also set a90% C.L. upper limit on the $\tau^+\tau^-$-decay of the $\eta_b$ at${\mathcal{B}}(\eta_b\to \tau^+\tau^-)<8%$.

Search for a low-mass Higgs boson in Y(3S)-->gamma A^0, A^0-->tau^+tau^- at BABAR