Window For Higgs Boson Mass From Gauge-Higgs Unification

We consider six dimensional gauge models compactified on the orbifold T /ZN (N = 2, 3, 4, 6) such that the Standard Model (SM) Higgs doublet arises from the extra-dimensional components of the gauge field. For Λ ≤ 10 GeV, where Λ denotes the compactification scale, we obtain 114.4 GeV ≤ mH ≤ 164 GeV for the SM Higgs boson mass. We also consider gaugeHiggs-top and gauge-Higgs-bottom Yukawa unification which respectively yield mH = 131 +4 −5 GeV and mH = 150 +2 −2 GeV for a top quark pole mass Mt = 170.9 +1.8 −1.8 GeV. As a special case we recover the result mH ≤ 132 GeV previously obtained for five dimensional models. 1 On a leave of absence from: Andronikashvili Institute of Physics, GAS, 380077 Tbilisi, Georgia. E-mail: [email protected] 2 E-mail: [email protected] 3 E-mail: [email protected] In a recent paper [1], hereafter called I, we investigated five dimensional (5D) gauge models compactified on the orbifold S/Z2 in which the zero mode of the fifth component of the gauge field could be identified with the SM Higgs doublet H . The five dimensional gauge invariance requires that the Higgs quartic coupling vanish at tree level. By imposing this condition at the compactification scale Λ [2], the SM Higgs boson mass was estimated using two-loop renormalization group equations (RGE). For 10 GeV≤ Λ ≤ 10 GeV, and for a top quark pole mass of 170.9± 1.8 GeV [3], the mass is in the range 114.4 GeV ≤ mH ≤ 132 GeV. [In I the upper bound was found to be 129 GeV. A more careful treatment here of the top quark pole mass yields the slightly larger value of 132 GeV.] In the SM with the standard particle content, the SU(2) gauge coupling and the top quark Yukawa coupling have the same magnitude at scales of order 10 GeV. If the latter scale is identified with Λ, one obtains mH = 117 ± 4 GeV [1]. It is amusing to note that the Higgs boson mass predictions in this 5D model have a great deal of overlap with the minimal supersymmetric Standard Model (MSSM) prediction for the mass of the lightest CP-even Higgs boson. The uncertainty in the Higgs mass predictions are largely due to the experimental uncertainty in the determination of the top quark mass. In this paper we extend our earlier results in I by considering 6D gauge-Higgs unification (GHU) models compactified on the orbifold T /ZN , with N = 2, 3, 4 and 6. For N = 2, two SU(2) doublets appear under appropriate boundary conditions as the zero modes of the extra-dimensional components of the gauge field [4]. Since our goal here is to predict the mass of the SM Higgs boson H , we will assume that a suitable linear combination of these two doublets corresponds to H , while the orthogonal combination acquires mass of order Λ. The six dimensional gauge invariance determines the quartic tree level coupling of H in terms of the SU(2) gauge coupling and tanβ, where tanβ is defined, as usual, as the ratio of the vacuum expectation value of the two Higgs doublets. With this value of the quartic coupling as the boundary condition at a given scale Λ, and for a given tanβ, the Higgs boson mass is estimated using two-loop RGEs. We find 114.4 GeV≤ mH ≤ 164 GeV, for Λ ≤ 10 GeV, with 0 ≤ tan β < ∞. Compactification on T /ZN orbifolds with N = 3, 4, 6 leaves only a single Higgs doublet [5], as desired. The Higgs mass for these cases is realized in the limit tanβ = 0 or ∞. We also discuss gauge-Higgs-Yukawa unification for which a more precise prediction for mH is found. Thus, mH = 131 GeV (150 GeV) with top (bottom) quark unification for a top quark pole mass Mt = 170.9 GeV. Finally, for tan β = 1, we recover our earlier result for mH(≤132 GeV) obtained in I with 5D gauge-Higgs unification. We begin with a very brief review of the basic structure of 6D GHU models. As a simple example, consider a SU(3) GHU model compactified on the orbifold T /ZN (N = 2, 3, 4, 6) [4, 5]. Note that at least one additional U(1) factor is needed to recover the 4D electroweak