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 (m_W), the Kaluza-Klein mass scale (M_{KK}), and the Higgs boson mass (m_H) being derived. It is shown that M_{KK}/m_W = (2 pi kR)^{1/2} (pi/theta_W) and m_H /m_W = 0.054 kR (pi/theta_W), where k^2, R, and theta_W are the curvature and size of the extra-dimensional space and the Wilson line phase determined dynamically. For typical values kR = 12 and theta_W = (0.2 to 0.4) pi, one finds that M_{KK} = (1.7 to 3.5) TeV, k = (1.3 to 2.6) x 10^{19} GeV, and m_H = (131 to 262) GeV