Electroweak-Higgs unification and the Higgs boson mass

We propose an alternative unification scenario where the Higgs self-coupling (lambda) is determined by imposing its unification with the electroweak gauge couplings. An attractive feature of models within this scenario is the possibility to determine the Higgs boson mass by evolving lambda from the electroweak Higgs unification scale M-GH down to the electroweak scale. The unification condition for the gauge (g(1), g(2)) and Higgs couplings is written as g(1) = g(2) = f(lambda), where g(1) = k(Y)(1/2)gy, k(Y) being the normalization constant. Two variants for the unification condition are discussed; scenario I is defined through the linear relation: g(1) = g(2) = k(H)lambda(M-GH), while scenario II assumes a quadratic relation: g(1) = g(2) = k(H)lambda(M-GH). Fixing k(H) = O(1) and the standard normalization (k(Y) = 5/3), we obtain a Higgs boson mass value m(H) similar or equal to 190 GeV, with similar results for other normalizations such as k(Y) = 7/4 and 3/2. However, the unification scale MGH depends on the value of k(Y), going from 1.8 x 10(12) GeV up to 4.9 x 10(14) GeV for 7/4 > k(Y) > 3/2. Possible tests of this idea at a future linear collider and its application for determining the Higgs spectrum in the two-Higgs doublet model are also discussed. We also elaborate on these unification scenarios within the context of a six-dimensional SU(3)(c) x SU(3)(w) Gauge-Higgs unified model, where the Higgs boson arises as the extra-dimensional components of the 6D gauge fields.