Higgs boson mass and electroweak-gravity hierarchy from dynamical gauge-Higgs unification in the warped spacetime

Dynamical electroweak symmetry breaking by the Hosotani mechanism in the Randall-Sundrum warped spacetime is examined, relations among the W-boson mass (mW), the Kaluza-Klein mass scale (MKK), and the Higgs boson mass (mH) being derived. It is shown that MKK/mW∼(2πkR)1/2(π/θW) and mH/mW∼0.058kR(π/θW), where k2, R, and θW are the curvature and size of the extra-dimensional space and the Wilson line phase determined dynamically. For typical values kR=12 and θW=(0.2-0.4)π, one finds that MKK=1.7-3.5TeV, k=(1.3-2.6)×1019GeV, and mH=140-280GeV.