Do precision electroweak constraints guarantee \epem collider discovery of at least one Higgs boson of a type-II two-Higgs-doublet model?

The manner in which the parameters of a two-Higgs-doublet model can be chosen so that no Higgs boson is discovered at a \sqrt{s}\leq 800\gev \epem collider, while maintaining consistency with current precision electroweak measurements, is described. The importance of a Giga-$Z$ factory and higher collider energies for such a scenario is emphasized.Comment: 6 pages, 3 figure

The NMSSM Close to the R-symmetry Limit and Naturalness in h→aah \to aa Decays for m_a<2\mb

Dominant decay of a SM-like Higgs boson into particles beyond those contained in the minimal supersymmetric standard model has been identified as a natural scenario to avoid fine tuning in electroweak symmetry breaking while satisfying all LEP limits. In the simplest such extension, the next-to-minimal supersymmetric model, the lightest CP-even Higgs boson can decay into two pseudoscalars. In the scenario with least fine tuning the lightest CP-even Higgs boson has mass of order 100 GeV. In order to escape LEP limits it must decay to a pair of the lightest CP-odd Higgs bosons with Br(h -> aa)>.7 and m_a \tau^+ \tau^- or light quarks and gluons). The mass of the lightest CP-odd Higgs boson is controlled by the soft-trilinear couplings, A_\lambda(m_Z) and A_\kappa(m_Z). We identify the region of parameter space where this situation occurs and discuss how natural this scenario is. It turns out that in order to achieve m_a < 2 m_b with A_\lambda(m_Z), A_\kappa(m_Z) of order the typical radiative corrections, the required tuning of trilinear couplings need not be larger than 5-10 %. Further, the necessity for this tuning can be eliminated in specific SUSY breaking scenarios. Quite interestingly, Br(h -> aa) is typically above 70 % in this region of parameter space and thus an appropriately large value requires no additional tuning.Comment: 33 pages, 25 figure

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 the new ALEPH LEP results in the \epem\to Z+4\tau channel. For $\tan\beta\geq 3$, only NMSSM ideal Higgs scenarios with m_{h_1}\gsim 98\gev and $m_{a_1}$ close to $2m_B$ satisfy the ALEPH limits. For \tan\beta\lsim 2, the ALEPH limits are easily satisfied for 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.Comment: 24 pages, 25 figures, paper updated to incorporate final ALEPH limits in Z+4\tau channel

Probing NMSSM Scenarios with Minimal Fine-Tuning by Searching for Decays of the Upsilon to a Light CP-Odd Higgs Boson

Completely natural electroweak symmetry breaking is easily achieved in supersymmetric models if there is a SM-like Higgs boson, $h$, with m_h\lsim 100\gev. In the minimal supersymmetric model, such an $h$ decays mainly to b\anti b and is ruled out by LEP constraints. However, if the MSSM Higgs sector is expanded so that $h$ decays mainly to still lighter Higgs bosons, e.g. $h\to aa$, with $BR(h\to aa)>0.7$, and if $m_a<2m_b$, then the LEP constraints are satisfied. In this letter, we show that in the next-to-minimal supersymmetric model the above $h$ and $a$ properties (for the lightest CP-even and CP-odd Higgs bosons, respectively) imply a lower bound on BR(\Upsilon\to \gam a) that dedicated runs at present (and future) $B$ factories can explore.Comment: 4 pages, 2 figure