Minimal Nonminimal Supersymmetric Standard Model

We review the basic field-theoretic and phenomenological features of the recently introduced Minimal Nonminimal Supersymmetric Standard Model (MNSSM). The introduced model is the simplest and most economic version among the proposed nonminimal supersymmetric models, in which the so-called μ-problem can be successfully addressed. As opposed to the MSSM and the frequently-discussed NMSSM, the MNSSM can naturally predict the existence of a light charged Higgs boson with a mass smaller than 100 GeV. Such a possible realization of the Higgs sector can be soon be tested at the upgraded Run II phase of the Tevatron collider. It is known that Minimal Supersymmetric Standard Model (MSSM) suffers from the so called μ-problem. The superpotential of the MSSM contains a bilinear term −μĤ1Ĥ2 involving the two Higgs-doublet superfields Ĥ1 and Ĥ2, known as the μ-term. Naive implementation of the μ-parameter within supergravity theories would lead to a μ value of the order of the Planck scale MP. However, for a successful Higgs mechanism at the electroweak scale, the μ-parameter is actually required to be many orders of magnitude smaller of order MSUSY. Many scenarios, all based on extensions of the MSSM, have been proposed in the existing literature [1] to provide a natural explanation for the origin of the μ-term. Recently, a minimal extension of the MSSM has been presented [2, 3, 4, 5], called the Minimal Nonminimal Supersymmetric Standard Model (MNSSM) [3, 5], in which the μproblem can be successfully addressed in a rather minimal way. In the MNSSM the μparameter is promoted to a chiral singlet superfield Ŝ, and all linear, quadratic and cubic operators involving only Ŝ are absent from the renormalizable superpotential; Ŝ enters through the single term λ Ŝ Ĥ1Ĥ2: W ren MNSSM = W̃MSSM + λ Ŝ Ĥ T 1 iτ2 Ĥ2 , (1) where W̃MSSM is the superpotential of the MSSM without the presence of the μ term. The crucial difference between the MNSSM and the frequently-discussed Next-to-Minimal Supersymmetric Standard Model (NMSSM) [6] lies in the fact that the cubic term 1 3 κ Ŝ does not appear in the renormalizable superpotential of the former. The key point in the construction of the renormalizable MNSSM superpotential is that the simple form (1) may be enforced by discrete R-symmetries, such as ZR 5 [2, 3, 4, 5] and ZR 7 [3, 5]. These discrete R-symmetries, however, must be extended to the gravity-induced non-renormalizable superpotential and Kähler potential terms as well. To communicate † Talk given at the conference “Beyond the Desert 2002,” 2–7 June 2002, Oulu, Finland Minimal Nonminimal Supersymmetric Standard Model 2 the breaking of supersymmetry (SUSY), we consider the scenario of N = 1 supergravity spontaneously broken by a set of hidden-sector fields at an intermediate scale. Within this framework of SUSY-breaking, we have then been able to show [3] that the above Rsymmetries are sufficient to postpone the appearance of the potentially dangerous tadpole [7, 8] tS S at a loop level n higher than 5, where tS ∼ 1 (16π2)n MP M 2 SUSY . (2) From this last expression, one can estimate that the size of the tadpole parameter tS is in the right ballpark, i.e. |tS| < ∼ 1–10 TeV for n = 6, 7, such that the gauge hierarchy does not get destabilized. To be specific, the tadpole tS S together with the soft SUSY-breaking mass term mSS ∗S ∼ M SUSYSS lead to a vacuum expectation value (VEV) for S, 〈S〉 = 1 2vS , of order MSUSY ∼ 1 TeV. The latter gives rise to a μ-parameter at the required electroweak scale, i.e. μ = − 1 √ 2 λvS ∼ MSUSY . (3) Thus, a natural explanation for the origin of the μ-parameter can be obtained. Finally, since the effective tadpole term tS S explicitly breaks the continuous Peccei–Quinn symmetry governing the remaining renormalizable Lagrangian of the MNSSM, the theory naturally avoids the presence of a phenomenologically excluded weak-scale axion. In addition to the tadpole tS of the physical scalar S, an effective tadpole for its auxiliary component FS is generated [8]. However, depending on the underlying mechanism of SUSY breaking, the effective tadpole proportional to FS could in principle be absent from the model. Such a reduction of the renormalizable operators does not thwart the renormalizability of the theory. The resulting renormalizable low-energy scenario has one parameter less than the frequently-discussed NMSSM with the cubic singlet-superfield term κ 3 Ŝ present; it therefore represents the most economic, renormalizable version among the non-minimal supersymmetric models proposed in the literature. As opposed to the NMSSM, the MNSSM satisfies the tree-level mass sum rule [3]: M H1 + M 2 H2 + M H3 = M 2 Z + M 2 A1 + M A2 , (4) where H1,2,3 and A1,2 are the three CP-even and two CP-odd Higgs fields, respectively. The tree-level mass sum rule (4) is very analogous to the corresponding one of the MSSM [9], where the two heavier Higgs states H3 and A2 are absent in the latter. This striking analogy to the MSSM allows us to advocate that the Higgs sector of the MNSSM differs indeed minimally from the one of the MSSM, i.e. the introduced model truly constitutes the minimal supersymmetric extension of the MSSM. In the NMSSM, the violation of the mass sum rule (4) can become much larger than the one induced by the one-loop stop/top effects, especially for relatively large values of |κ|, |μ| and |Aκ|. In the non-minimal supersymmetric standard models, the upper bound on the lightest CP-even Higgs-boson mass MH1 has a tree-level dependence on the coupling λ [6, 10, 3, 4], i.e. M 2(0) H1 ≤ M Z ( cos 2β + 2 λ g2 w + g ′2 sin 2β ) , (5) where the angle β is defined by means of tanβ = v2/v1, the ratio of the VEVs of the two Higgs doublets. Since in the MNSSM λ can take its maximum allowed value naturally corresponding to the NMSSM with κ = 0 [10], the value of MH1 is predicted to be the highest. In particular, a renormalization-group-improved analysis [5] of the effective MNSSM Higgs potential leads to the upper bound: MH1 < ∼ 145 GeV, for large stop mixing (see also Fig. 1). Minimal Nonminimal Supersymmetric Standard Model 3 60 80 100 120 140 160 -500 -400 -300 -200 -100 0 100 200 300 400 500 μ [ GeV ] M H 1 [ G eV ] (a) tanβ = 2, λ = 0.65, λ tS / μ = 1 TeV 2 μ [ GeV ] M H 1 [ G eV ] tanβ = 2, λ = 0.65, λ tS / μ = 0.04 TeV 2 (b) 60 80 100 120 140 160 -800 -600 -400 -200 0 200 400 600 800 Figure 1. Numerical values for MH1 versus μ in the MNSSM with m 2 12 = 0, for MH+ = 0.1 (solid), 0.3 (dashed), 0.7 (dotted) and 1 (dash-dotted) TeV. Consequently, such a scenario can only be decisively tested by the upgraded Run II phase of the Tevatron collider at Fermilab and by the Large Hadron Collider (LHC) at CERN. The MNSSM can comfortably predict viable scenarios, where the mass of the charged Higgs boson H is in the range: 80 GeV < MH+ < ∼ 3 TeV, for phenomenologically relevant values of |μ| > ∼ 100 GeV [11]. In fact, as can be seen from Fig. 2, there is an absolute upper Minimal Nonminimal Supersymmetric Standard Model 4 MH+ [ GeV ] m ax (M H 1 ) [ G eV ] λ tS / μ = 0.04 TeV 2 λ tS / μ = 1 TeV 2 tanβ = 2, λ = 0.65 80 90 100 110 120 130 140 150 160 0 50