ar X iv : h ep - p h / 02 11 10 2 v 1 7 N ov 2 00 2 The MSSM without μ term

We propose a supersymmetric extension of the standard model which does not have a “μ” supersymmetric Higgs mass parameter. The matter content of the MSSM is extended with three additional chiral superfields: one singlet, an SU(2) triplet and a color octet, and an approximate U(1)R symmetry naturally guarantees that tanβ is large, explaining the top/bottom quark mass hierarchy. Unlike in the MSSM, there are significant upper bounds on the masses of superpartners, including an upper bound of 114 GeV on the mass of the lightest chargino. However the MSSM bound on the lightest Higgs mass does not apply. 1 The 6 μSSM and its low energy spectrum In the Minimal Supersymmetric Model (MSSM) there is a supersymmetric Higgs mass parameter, “μ”, which must be of order of the electroweak scale for successful phenomenology. The difficulty of generating the correct mass scale for this supersymmetric mass parameter is the so called “μ problem”. This problem is more severe in gauge mediated supersymmetry breaking (GMSB) models, since it is quite difficult in gauge mediation to induce a μ parameter which is naturally related to supersymmetry breaking, without inducing an excessively large Bμ parameter [1]. We consider an alternative solution to the μ problem, by building a viable model which does not have a μ parameter. In order to obtain a spectrum of superpartner masses experimentally acceptable without μ we have to add some matter content to the MSSM. This model, which we call the “μ-less Supersymmetric Standard Model” (6 μSSM), has an approximate U(1)R symmetry which guarantees naturally large tan β, explaining the top/bottom quark mass hierarchy, and suppresses dangerous supersymmetric contributions to anomalous magnetic moments, b → sγ, and proton decay. The 6 μSSM can naturally arise from either gauge or gravity mediation [2], if the supersymmetry breaking sector respects an approximate U(1)R symmetry. Such an approximate symmetry can easily arise by accident, as a consequence of the absence of gauge singlet chiral superfields with F−terms in the supersymmetry breaking or mediation sector. We start with the principle that all mass terms arise directly either from electroweak symmetry breaking or from supersymmetry breaking. We therefore do not allow a supersymmetric μ term or any supersymmetric mass term. The MSSM without a μ term would have charginos lighter than the W boson, which should have been found at LEP II, so we have to extend the theory. In the exact U(1)R symmetric limit there are no supersymmetry breaking Majorana gaugino masses, so in order to give the gauginos Dirac masses we add three chiral superfields, namely a color octet O, a triplet under the SU(2) gauge group, T and a singlet S. These adjoint matter multiplets could have an extra dimensional origin, since extra dimensional theories in 70 80 90 100 110 120 130 140 80 100 120 140 160 180 200 Figure 1: Lighter chargino masses for hT = 1, tan β = 60 and m̃2 =5 GeV. which gauge bosons live in the bulk and chiral matter fields live on a three brane typically have additional matter fields in the adjoint representation when described four dimensionally, unless the extra dimension is orbifolded. The adjoint fields might be N = 2 superpartners of the gauge fields [3]. We now turn to a discussion of the spectrum of the 6 μSSM, from the bottom up. The charge assignments of some of the components of Higgs and electroweak gauge fields under the unbroken U(1)R are: ΨH1 ΨH2 Ψ ± T H1 H2 λ ± 1 -1 -1 2 0 1 (1) Thus we can add the superpotential coupling