Higgs Boson Mass From Gauge-Higgs Unification

In certain five dimensional gauge theories the Standard Model Higgs doublet is identified, after compactification on the orbifold S/Z2, with the zero mode of the fifth component of the gauge field. An effective potential for the Higgs field is generated via quantum corrections, triggered by the breaking of the underlying gauge symmetry through boundary conditions. The quartic Higgs coupling can be estimated at low energies by employing the boundary condition that it vanishes at the compactification scale Λ, as required by five dimensional gauge invariance. For Λ & 10 − 10 GeV, the Standard Model Higgs boson mass is found to be mH = 125± 4 GeV, corresponding to a top quark pole mass Mt = 170.9± 1.8 GeV. A more complete (gaugeHiggs-Yukawa) unification can be realized for Λ ∼ 10 GeV, which happens to be the scale at which the SU(2) weak coupling and the top quark Yukawa coupling have the same value. For this case, mH = 117± 4 GeV. 1 E-mail: [email protected] 2 E-mail: [email protected] 3 E-mail: [email protected] It seems reasonable to hope that the Standard Model (SM) Higgs boson will likely be found in the near future, most likely at the LHC. The discovery should reveal a great deal about the origin of electroweak breaking and the mechanism responsible for generating the quark and charged lepton masses. A precise measurement of the Higgs mass mH should help distinguish between various competing theoretical ideas. One could argue, for example, that the MSSM would be one of the favored schemes if mH turns out to be close to its current experimental lower limit of 114.4 GeV [1]. However, values of mH around 125 GeV or larger, would suggest a much more serious consideration of other competing ideas. For instance, in a class of higher dimensional supersymmetric orbifold models in which the 4D N=1 supersymmetry is broken at MGUT, the Higgs mass mH = 145(±19) GeV [2]. The SM gauge couplings in these models are unified at MGUT by employing a non-canonical U(1)Y . An important extension of these ideas implements gauge and Yukawa coupling unification at MGUT [3]. For instance, with gauge-top quark Yukawa coupling unification and with SUSY broken at MGUT, the SM Higgs boson mass turns out to be 135± 6 GeV [3]. Somewhat larger values for the Higgs mass, 144± 4 GeV, are found with gauge-bottom quark Yukawa coupling unification [3]. In this letter we attempt to estimate mH by employing the idea of gauge-Higgs unification (GHU) which has attracted a fair amount of recent attention [4]-[12]. We consider, in particular, 5D models compactified on an orbifold S/Z2, such that the zero mode of the fifth component of the bulk gauge field can be identified with the SM Higgs doublet. The so-called ”gauge-Higgs” condition , to be explained shortly, enables us to estimate the SM Higgs mass mH . Using two-loop renormalization group equations (RGEs), we find that mH exceeds the LEP2 lower bound if the compactification scale Λ & 10 GeV. The weak SU(2) gauge coupling and the top Yukawa coupling have the same magnitude at scales close to 10 GeV. If the latter is identified with the compactification scale, the Higgs mass mH is predicted to be 117 ± 4 GeV. Finally, following [2, 3], if Λ is identified with the SM gauge coupling unification scale of order 4× 10 GeV which is possible with non-canonical U(1)Y , mH = 125± 4 GeV. We consider 5D Gauge-Higgs Unification (GHU) model with the fifth dimension compactified on the orbifold S/Z2 which yields a chiral ”low energy” theory in four dimensions. In GHU models, the 5D bulk gauge symmetry is broken down to the SM by imposing suitable boundary conditions. The SM Higgs doublet emerges as a zero-mode of the fifth component of the higher dimensional gauge field. The higher dimensional gauge symmetry prevents the appearance of a tree level scalar potential. However, since the bulk gauge symmetry is broken by the boundary condition, a quartic Higgs potential is induced through quantum correction. In particular, at one-loop level, the effective Higgs potential has been found to be finite [6]. This finiteness can be interpreted as a remnant of the higher dimensional gauge invariance and its