We demonstrate that the NMSSM can have small fine-tuning and modest light stop mass while still evading all experimental constraints. For small tan β (large tan β), the relevant scenarios are such that there is always (often) a SM-like Higgs boson that decays to two lighter -possibly much lighter -pseudoscalar Higgses.In the CP-conserving Minimal Supersymmetric Model (MSSM), large soft-supersymmetry-breaking mass parameters are required in order that the one-loop corrections to the tree-level prediction for the lightest Higgs boson (m h ≤ m Z ) increase m h sufficiently to avoid conflict with lower bounds from LEP data. The large size of these soft-SUSY breaking masses compared to the weak scale, the natural scale where supersymmetry is expected, is termed the little-hierarchy problem. This hierarchy implies that a substantial amount of fine-tuning of the MSSM soft-SUSY breaking parameters is needed. The severity of these problems has led to a variety of alternative approaches. For instance, little Higgs models [1] can be less fine tuned. Or, one can argue that large fine-tuning is not so bad, as in "split-supersymmetry" [2]. In this letter, we show that the Next to Minimal Supersymmetric Model (NMSSM [3]) can avoid or at least ameliorate the fine-tuning and little hierarchy problems. In addition, we find that parameter choices that are consistent with all LEP constraints and that yield small fine-tuning at small tan β (large tan β) are nearly always (often) such that there is a relatively light SM-like CP-even Higgs boson that decays into two light, perhaps very light, pseudoscalars. Such decays dramatically complicate the Tevatron and LHC searches for Higgs bosons.The NMSSM is very attractive in its own right. It provides a very elegant solution to the µ problem of the MSSM via the introduction of a singlet superfield S. For the simplest possible scale invariant form of the superpotential, the scalar component of S naturally acquires a vacuum expectation value of the order of the SUSY breaking scale, giving rise to a value of µ of order the electroweak scale. The NMSSM is the simplest supersymmetric extension of the standard model in which the electroweak scale originates from the SUSY breaking scale only. A possible cosmological domain wall problem [4] can be avoided by introducing suitable nonrenormalizable operators [5] that do not generate dangerously large singlet tadpole diagrams [6]. Hence, the phenomenology of the NMSSM deserves to be studied at least as fully and precisely as that of the MSSM.Radiative corrections to the Higgs masses have been computed [7,8,9,10] The extent to which there is a no-lose theorem for NMSSM Higgs discovery at the LHC has arisen as an important topic [13,17,18,19,20]. In particular, it has been found that the Higgs to Higgs pair decay modes can render inadequate the usual MSSM Higgs search modes that give rise to a no-lose theorem for MSSM Higgs discovery at the LHC. And, it is by no means proven that the Higgs to Higgs pair modes are directly observable at the LHC, althou...

We use t, b, tau Yukawa unification to constrain supersymmetry parameter space. We find a narrow region survives for mu>0 (suggested by b-->sgamma and the anomalous magnetic moment of the muon) with A0 approximately -1.9m(16), m(10) approximately 1.4m(16), m(16) approximately 1200-3000 GeV and muM(1/2) approximately 100-500 GeV. Demanding Yukawa unification thus makes definite predictions for Higgs and sparticle masses.

Completely natural electroweak symmetry breaking is easily achieved in supersymmetric models if there is a SM-like Higgs boson, h, with m h < ∼ 100 GeV. In the minimal supersymmetric model, such an h decays mainly to bb 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 → aa, with Br(h → aa) > 0.7, and if ma < 2m b , then the LEP constraints are satisfied. In this letter, we show that in the next-tominimal 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(Υ → γa) that dedicated runs at present (and future) B factories can explore.Low energy supersymmetry remains one of the most attractive solutions to the naturalness / hierarchy problem of the Standard Model (SM). However, the minimal supersymmetric model (MSSM), containing exactly two Higgs doublets, suffers from the "µ problem" and requires rather special parameter choices in order that the light Higgs mass is above LEP limits without electroweak symmetry breaking being "fine-tuned", i.e. highly sensitive to supersymmetry-breaking parameters chosen at the grand-unification scale. Both problems are easily solved by adding Higgs (super) fields to the MSSM. For generic SUSY parameters well-below the TeV scale, finetuning is absent [1] and a SM-like h is predicted with m h < ∼ 100 GeV. Such an h can avoid LEP limits on the tightly constrained e + e − → Z +b ′ s channel if Br(h → bb) is small by virtue of large Br(h → aa), where a is a new light (typically CP-odd) Higgs boson, and m a < 2m b so that a → bb is forbidden [2]. The perfect place to search for such an a is in Upsilon decays, Υ → γa. The simplest MSSM extension, the next-to-minimal supersymmetric model (NMSSM), naturally predicts that the lightest h and a, h 1 and a 1 , have all the right features [1,2,3,4,5]. In this letter, we show that large Br(h 1 → a 1 a 1 ) implies, at fixed m a1 , a lower bound on Br(Υ → γa 1 ) (from now on, Υ is the 1S resonance unless otherwise stated) that is typically within reach of present and future B factories.In the NMSSM, a light a 1 with substantial Br(h 1 → a 1 a 1 ) is a very natural possibility for m Z -scale soft parameters developed by renormalization group running starting from U (1) R symmetric GUT-scale soft parameters [5]. (See also [6,7] for discussions of the light a 1 scenario.) The fine-tuning-preferred m h1 ∼ 100 GeV (for tan β > ∼ f ew) gives perfect consistency with precision electroweak data and the reduced Br(h 1 → bb) ∼ 0.09 − 0.15 explains the ∼ 2.3σ excess at LEP in the Zbb channel at M bb ∼ 100 GeV. The motivation for this scenario is thus very strong.Hadron collider probes of the NMSSM Higgs sector are problematical. The h 1 → a 1 a 1 → 4τ (2m τ < m a1 < 2m b ) or 4 jets (m a1 < 2m τ ) signal is a very difficult one at the Tevatron and very possibly at the LHC [8,9,10,11]. Higgs discovery or, at the very least, certification of a marginal LHC Higgs signal will requi...

We construct a minimal supersymmetric SO(10) grand unified model in 5 dimensions. The extra dimension is compactified on an S 1 /(Z 2 ϫZ 2 Ј) orbifold which has two inequivalent fixed points. These are flat 4-dimensional Minkowski spaces: the visible and the hidden branes. By orbifolding, the gauge symmetry on the hidden brane is reduced down to the Pati-Salam gauge symmetry SU(4)ϫSU(2) L ϫSU(2) R . On the visible brane the SO(10) is broken by the ordinary Higgs mechanism down to SU(5). The resulting 4-dimensional theory has the standard model gauge symmetry ͓the intersection of SU(5) and SU(4) ϫSU(2) L ϫSU(2) R ͔ and the massless spectrum consists of the MSSM gauge fields and two Higgs doublets. The matter fields are assumed to live on the visible brane. We discuss gauge coupling unification in our 5-dimensional model in terms of corrections to the conventional 4-dimensional unification. Supersymmetry is broken on the hidden brane ͑where mass terms for gauginos and a term are generated͒ and communicated to squarks and sleptons via gaugino mediation. We also discuss a possibility of linking the supersymmetry breaking on the hidden brane to the Higgs mechanism responsible for partial breaking of the gauge symmetry on the visible brane via the shining mechanism. Finally, there are no operators of dimension 5 leading to proton decay. Proton decay through dimension 6 operators is enhanced compared to conventional GUTs and can be seen in current or next generation proton decay experiments.

In simple SO(10) SUSY GUTs the top, bottom and tau Yukawa couplings unify at the GUT scale. A naive renormalization group analysis, neglecting weak scale threshold corrections, leads to moderate agreement with the low energy data. However it is known that intrinsically large threshold corrections proportional to tan β ∼ m t (M Z )/m b (M Z ) ∼ 50 can nullify these t, b, τ mass predictions. In this paper we turn the argument around. Instead of predicting fermion masses, we use the constraint of Yukawa unification and the observed values M t , m b (m b ), M τ to constrain SUSY parameter space. We find a narrow region survives for µ > 0 with µ, M 1/2 << m 16 , A 0 ≈ −1.9 m 16 and m 16 > 1200 GeV. Demanding Yukawa unification thus makes definite predictions for Higgs and sparticle masses. In particular we find a light higgs with mass m 0 h = 114 ± 5 ± 3 GeV and a light stop with (mt 1 ) M IN ∼ 450 GeV and mt 1 << mb 1 . In addition, we find a light chargino and a neutralino LSP. It is also significant that in this region of parameter space the SUSY contribution to the muon anomalous magnetic moment a SU SY µ < 16 × 10 −10 .1 Note, recent theoretical reevaluations of the standard model contribution are now closer to experiment with a N EW µ = 25.6 (16) × 10 −10 [12].

We study scenarios in the minimal and next-to minimal supersymmetric models in which the lightest CP-even Higgs boson can have mass below the 114 GeV standard model LEP limit by virtue of reduced ZZ coupling due to substantial mixing among the Higgs bosons. We pay particular attention to the size of corrections from superpartners needed for these scenarios to be viable and point to boundary conditions at large scales which lead to these scenarios while at the same time keeping electroweak fine tuning modest in size. We find that naturalness of electroweak symmetry breaking in the mixed-Higgs scenarios of both models points to the same region of soft supersymmetry breaking terms, namely those leading to large mixing in the stop sector at the electroweak scale, especially if we also require that the lightest CP-even Higgs explains the Higgs-like LEP events at ∼ 98 GeV.

We examine the LEP limits for the Zh → Z + b's final state and find that the excess of observed events for m h ∼ 100 GeV correlates well with there being an m h ∼ 100 GeV Higgs boson with SMlike ZZh coupling that decays partly via h → bb+τ + τ − [with B(h → bb) ∼ 0.08] but dominantly via h → aa [with B(h → aa) ∼ 0.9], where ma < 2m b so that a → τ + τ − (or light quarks and gluons) decays are dominant. Scenarios of precisely this type arise in the Next-to-Minimal Supersymmetric Model for parameter choices yielding the lowest possible fine-tuning.

The deviation of the measured value of the muon anomalous magnetic moment from the standard model prediction can be completely explained by mixing of the muon with extra vectorlike leptons, L and E, near the electroweak scale. This mixing simultaneously contributes to the muon mass. We show that the correlation between contributions to the muon mass and muon g-2 is controlled by the mass of the neutrino originating from the doublet L. Positive correlation, simultaneously explaining both measured values, requires this mass below 200 GeV. The decay rate of the Higgs boson to muon pairs is modified and, in the region of the parameter space that can explain the muon anomalous magnetic moment within one standard deviation, it ranges from 0.5 to 24 times the standard model prediction. In the same scenario, h → γγ can be enhanced or lowered by ∼50% from the standard model prediction. The explanation of the muon g-2 anomaly and predictions for h → γγ are not correlated since these are controlled by independent parameters. This scenario can be embedded in a model with three complete vectorlike families featuring gauge coupling unification, sufficiently stable proton, and the Higgs quartic coupling remaining positive all the way to the grand unification scale.