New constraints on a light CP-odd Higgs boson and related NMSSM Ideal Higgs Scenarios

Recent BaBar limits on $\br(\Upsilon(3S)\to \gam a\to \gam \tau^+\tau^-)$ and $\br(\Upsilon(3S)\to \gam a\to \gam \mu^+\mu^-)$ provide increased constraints on the $a b\anti b$ coupling of a CP-odd Higgs boson, $a$, with $m_a<M_{\Upsilon(3S)}$. We extract these limits from the BaBar data and compare to the limits previously obtained using other data sets, especially the CLEO-III $\br(\Upsilon(1S)\to \gam\to\tau^+\tau^-)$ limits. Comparisons are made to predictions in the context of "ideal"-Higgs NMSSM scenarios, in which the lightest CP-even Higgs boson, $h_1$, can have mass below $105\gev$ (as preferred by precision electroweak data) and yet can escape old LEP limits by virtue of decays to a pair of the lightest CP-odd Higgs bosons, $h_1\to a_1a_1$, with $m_{a_1}<2m_B$. Most such scenarios with $m_{a_1}<2m_\tau$ are eliminated, but the bulk of the $m_{a_1}>7.5\gev$ scenarios, which are theoretically the most favored, survive. We also outline the impact of preliminary ALEPH LEP results in the $e^+e^-\to Z+4\tau$ channel. For $\tan\beta\geq 3$, only NMSSM ideal Higgs scenarios with $m_{h_1}\sim 105\gev$ (the upper limit of "ideal") and $m_{a_1}$ close to $2m_B $ satisfy the preliminary ALEPH limits. For $\tan\beta\lsim 2$, the ALEPH results pick out the most theoretically preferred NMSSM scenarios which are those with $m_{a_1}$ close to $2m_B$ and $m_{h_1}\sim 90\gev-100\gev$.