125 GeV Higgs Boson From Gauge-Higgs Unification: A Snowmass white paper

In certain five dimensional gauge theories compactified on the orbifold $S^1/Z_2$ the Standard Model Higgs doublet is identified with the zero mode of the fifth component of the gauge field. This gauge-Higgs unification scenario is realized at high energies, and the Standard Model as an effective theory below the compactification scale satisfies the boundary condition that the Higgs quartic coupling vanishes at the compactification scale (gauge-Higgs condition). This is because at energies above the compactification scale, the five dimensional gauge invariance is restored and the Higgs potential vanishes as a consequence. We consider scenario where top quark Yukawa and weak gauge coupling unification can be realized and identify the compactification scale as one at which this two coupling couplings have the same value. Taking into account the experimental uncertainties in measurements of the top quark mass and the QCD coupling constant, the Higgs mass prediction of 119-126 GeV from the gauge-Higgs unification scenario is consistent with the experimentally measured value of 125-126 GeV. More precise measurements of the top quark mass and the QCD coupling constant are crucial to reduce the interval of the Higgs mass prediction and thereby test the feasibility of the gauge-Higgs unification scenario.