Natural Μ-term with Peccei-quinn Symmetry

The generalized Higgs mass term NH1H2 of the supersymmetric standard model is used to implement the Peccei-Quinn Symmetry to solve the strongCP problem. Then supersymmetry breaking can generate the Higgs mass parameter μ of order m3/2 through soft-breaking parameters. This kind of extension contains extra light fields of the axion supermultiplet whose dominant coupling may come from the supersymmetric axion-Higgs-Higgs coupling. We present a working example and discuss the cosmological implications of the model. ∗Email address: [email protected] The supersymmetric Higgs mass term μH1H2 in the minimal supersymmetric standard model (MSSM) brings a problem of naturalness, so called the μ-problem [1]. The μ-term together with soft supersymmetry breaking terms drive electroweak symmetry breaking. Therefore both the parameter μ and soft-breaking parameters are required to be at or slightly above the electroweak scale. The scale of soft-breaking parameters (characterized by the gravitino mass m3/2) can be understood from the hidden-sector supersymmetry breaking mechanism [2]. The question is why the μ-parameter is so small compared to the other scale in the theory, e.g., the Planck scale MP l. The μ-term may well be generated dynamically due to supersymmetry breaking. One conventional way to explain the origin of the μ-term is to include a singlet N under the standard model (SM) gauge group and introduce a term NH1H2 [3]. Then one can arrange for the vacuum expectation value (VEV) of N to get the proper value. In this case one generically expects the presence of extra light singlets. Very recently it has been demonstrated that introducing an U(1) gauge group can achieve the generation of the μ-term without producing light singlets [4]. This approach can make N as heavy as MP l but calls for some light colored fields in order to cancel the anomaly. In this letter we stress that the generation of the μ-term can be made much more appealing if one uses the Peccei-Quinn (PQ) Symmetry [5] instead of any other global or local symmetry. Obviously one can combine the μ-problem and the strong-CP problem [6] in this way. If one wants to understand the strong-CP problem in terms of the PQ mechanism, it is quite natural to assign the presence of the term hNH1H2 to the PQ symmetry. Then one has to arrange certain Higgs superpotential providing PQ symmetry breaking at the invisible scale MPQ ∼ 10 10 − 10 GeV. In this case 〈N〉 ∼ MPQ implies extreme fine-tuning of h. But it is not necessary for N to have such a large VEV as is commonly believed. If the VEV of N vanishes in the supersymmetric limit, soft supersymmetry breaking may induce nonvanishing VEV which is expected to be of order m3/2. The PQ symmetry is broken by some other fields which couple to N . In the first attempt to relate the dynamical generation of the μ-term to the strong-CP problem, a non-renormalizable term like S2H1H2/MP l was used [1]. For this to provide the proper value of μ, the PQ scale (〈S〉 ∼ MPQ) is necessarily of the same order as the hidden sector supersymmetry breaking scale which is indeed inside the above-mentioned