Escaping the Large Fine-Tuning and Little Hierarchy Problems in the Next to Minimal Supersymmetric Model andh→aaDecays

Abstract

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...

Two-Higgs models for large tan β and heavy second Higgs

“…As an aside we note that recent papers [23][24][25] have considered the possibility that the light Higgs does not decay into the modes that have been sought for at LEP. In those papers there were alternative beyond the minimal supersymmetric model light modes available into which the Higgs can decay.…”

The NMSSM with and a moderate stop mass

“…In the following we report the mass matrices of CP odd and even states, in the basis defined in Eqs. (8,9). We keep the explicit dependence of the matrix elements upon the singlet vev v s .…”

Search for Di-Muon Decays of a Light Scalar Higgs Boson in Radiative Upsilon(1S) Decays

“…For Υ(3S ) dataset AllEvents-Run7-R24bΥ(3S )-OnPeak-Low 1.173 AllEvents-Run7-R24bΥ(3S )-OnPeak-Medium (So far blind) 25.594 AllEvents-Run7-R24bΥ(3S )-OnPeak-High (So far blind)…”

“…The NMSSM adds a singlet chiral superfield (N) to the MSSM [24][25][26] where λ and κ are dimensionless Yukawa couplings, andĤ u andĤ d are up and down types of Higgs superfields. The associated soft terms, which break the supersymmetry explicitly, are…”

“…Such light state of the A 0 is not excluded by the LEP constraints [32], where the CPeven Higgs boson, h, could decay dominantly into a pair of CP-odd scalars [25,29,[33][34][35][36][37].…”