We discuss NMSSM scenarios in which the lightest Higgs boson $h_1$ is consistent with the small LEP excess at about 98 GeV in $e^+e^- to Zh$ with $hto banti b$ and the heavier Higgs boson $h_2$ has the primary features of the LHC Higgs-like signals a
t 125 GeV, including an enhanced $gammagamma$ rate. Verification or falsification of the 98 GeV $h_1$ may be possible at the LHC during the 14 TeV run. The detection of the other NMSSM Higgs bosons at the LHC and future colliders is also discussed, as well as dark matter properties of the scenario under consideration.
We develop diagnostic tools that would provide incontrovertible evidence for the presence of more than one Higgs boson near 125 GeV in the LHC data.
We examine GUT-scale NMSSM scenarios in which {it both} $h_1$ and $h_2$ lie in the 123 -- 128 GeV mass range. Very substantially enhanced $gammagamma$ and other rates are possible. Broadened mass peaks are natural.
We explore the parameter choices in the five-dimensional Randall-Sundrum model with the inclusion of Higgs-radion mixing that can describe current LHC hints for one or more Higgs boson signals.
We assess the extent to which various constrain
We show that a $Wjj$ excess in Tevatron data could be explained in the context of the standard non-supersymmetric two-Higgs-doublet model for appropriately chosen parameters. Correlated signals in the $gammagamma$ and $W^+ W^- b anti b$ final states
are predicted and are on the verge of being detectable. The proposed model is most attractive if the cross section for the $Wjj$ excess is $lsim 1-2pb$.
We consider the impact of a 4th generation on Higgs to $gammagamma$ and $WW,ZZ$ signals and demonstrate that the Tevatron and LHC have essentially eliminated the possibility of a 4th generation if the Higgs is SM-like and has mass below 200 GeV. We a
lso show that the absence of enhanced Higgs signals in current data sets in the $gammagamma$ and $WW,ZZ$ final states can strongly constrain the possibility of a 4th generation in two-Higgs-doublet models of type II, including the MSSM.
We examine the extent to which it is possible to realize the NMSSM ideal Higgs models espoused in several papers by Gunion et al in the context of partially universal GUT scale boundary conditions. To this end we use the powerful methodology of neste
d sampling. We pay particular attention to whether ideal-Higgs-like points not only pass LEP constraints but are also acceptable in terms of the numerous constraints now available, including those from the Tevatron and $B$-factory data, $(g-2)_mu$ and the relic density $Omega h^2$. In general for this particular methodology and range of parameters chosen, very few points corresponding to said previous studies were found, and those that were found were at best $2sigma$ away from the preferred relic density value. Instead, there exist a class of points, which combine a mostly singlet-like Higgs with a mostly singlino-like neutralino coannihilating with the lightest stau, that are able to effectively pass all implemented constraints in the region $80<m_h<100$. It seems that the spin-independent direct detection cross section acts as a key discriminator between ideal Higgs points and the hard to detect singlino-like points.
Recent data from CoGeNT and DAMA are roughly consistent with a very light dark matter particle with $msim 4-10gev$ and spin-independent cross section of order $sigma_{SI} sim (1-3)times 10^{-4}pb$. An important question is whether these observations
are compatible with supersymmetric models obeying $Omega h^2sim 0.11$ without violating existing collider constraints and precision measurements. In this talk, I review the fact the the Minimal Supersymmetric Model allows insufficient flexibility to achieve such compatibility, basically because of the highly constrained nature of the MSSM Higgs sector in relation to LEP limits on Higgs bosons. I then outline the manner in which the more flexible Higgs sectors of the Next-to-Minimal Supersymmetric Model and an Extended Next-to-Minimal Supersymmetric Model allow large $sigma_{SI}$ and $Omega h^2sim 0.11$ at low LSP mass without violating LEP, Tevatron, BaBar and other experimental limits. The relationship of the required Higgs sectors to the NMSSM ideal-Higgs scenarios is discussed.
We assess the extent to which the NMSSM can allow for light dark matter in the $2gevlsim mcnonelsim 12gev$ mass range with correct relic density and large spin-independent direct-detection cross section, $sigsi$, in the range suggested by cogent and
DAMA. For standard assumptions regarding nucleon $s$-quark content and cosmological relic density, $rho$, we find that the NMSSM falls short by a factor of about 10 to 15 (3 to 5) without (with) significant violation of the current $(g-2)_mu$ constraints.
