Gauge Unification and the Supersymmetric Light Higgs Mass

Abstract

We consider general supersymmetric models with (a) arbitrary matter content and (b) gauge coupling unification near the string scale ϳ10 17 GeV, and derive the absolute upper limit on the mass of the lightest Higgs boson. For models without Higgs couplings to extra SU(2) triplets the bound is about 155 GeV. The bound is maximized for models with such triplets and can be as high as 205 GeV, significantly larger than previous estimates partly due to a normalization error.[ S0031-9007(98) In this context, the sector of the theory responsible for electroweak symmetry breaking has a special status. While all superpartners of the known SM particles can be made heavy by simply rising soft SUSY-breaking mass parameters in the model, the Higgs sector necessarily contains a physical Higgs scalar whose mass does not depend sensitively on the details of soft masses but is fixed by the scale of electroweak symmetry breaking. This important fact follows simply from the spontaneous breaking of the electroweak gauge symmetry [3,4] and it is not specific to supersymmetric models. More precisely, the general statement is that some Higgs boson must exist whose mass squared satisfies m 2 h # ly 2 , where y is the electroweak scale (y 174.1 GeV) and l is the dimensionless quartic coupling of some Higgs state in the model. In other words, the mass of the light Higgs can be made heavy only at the expense of making the coupling l very strong. The role of supersymmetry is to fix l in some models. For example, in the minimal supersymmetric standard model (MSSM), which includes two Higgs doublets,to give masses to quarks and leptons, l is related to the SU͑2͒ L 3 U͑1͒ Y gauge couplings (g and g 0 , respectively) and the following (tree-level) bound on the mass of the lightest Higgs boson holdswhere tan b ͗H 0 2 ͗͘͞H 0 1 ͘. This represents a very stringent prediction which, as is well known, gets significantly relaxed when radiative corrections to l are included [5][6][7]. These corrections depend logarithmically on the soft masses and push the upper mass limit for the lightest Higgs boson of the MSSM up to 125 GeV (for a top-quark mass M t 175 GeV and M SUSY , 1 TeV). The fact that l is calculable in terms of gauge couplings in the MSSM is due to supersymmetry and to the fact that the superpotential does not contain cubic terms of the form W h X XH i H j (with i, j 1, 2) as no X field exists with the appropriate quantum numbers to form a gauge-invariant object. In extended models, the presence of such fields and couplings modifies the quartic Higgs self-interactions, which can ultimately have an impact on the tree-level upper bound on m 2 h , which receives corrections proportional to h 2 X y 2 . The Yukawa coupling h X is unknown but asymptotically nonfree, and so it can be bounded from above if it is further required to remain in the perturbative regime up to some large energy scale [where grand unified theory (GUT), string, or Planck physics takes over].As there is no reason to believe that low-energy supersymmetry is realized in Natur...

NSUSY fits

“…This can happen through new sectors coupled to the Higgs in such a way that they add at tree-level new supersymmetric F -term or D term (or even susy-breaking) contributions to the Higgs quartic even in the Higgs decoupling limit (see [111][112][113][114][115][116][117][118][119][120][121][122][123][124][125][126] for an incomplete list of studies on this). A very moderate tree-level upward shift of this quartic, which can be interpreted as a threshold correction at the SUSY scale, would have a direct and very important impact on increasing the predicted Higgs mass and reducing the associated finetuning.…”

μB-driven electroweak symmetry breaking

“…We find that the potential takes the same form as the MSSM potential except that there is a new quartic term, |λH u H d | 2 . Since the S scalar is relatively heavy, it effectively appears at the scale v that a "non-supersymmetric" quartic coupling has been added to the supersymmetric Higgs potential [22].…”

The soft supersymmetry-breaking Lagrangian: theory and applications

“…Assuming only perturbative unification, the Higgs mass could be as heavy as 205 GeV in more general frameworks than the MSSM or NMSSM (i.e. with additional nonsinglet Higgs representations) [849,850]. Given the constraints placed on the MSSM parameter space from the current LEP Higgs mass bounds, there is certainly a strong motivation to consider models such as the NMSSM which have extended Higgs sectors.…”