Abstract
Low-energy data, combined with renormalization group (RG) equations, can predict new physics at far higher energy scales. In this paper, we consider the possibility that the measured Higgs boson mass and top quark mass hint at a five-dimensional gauge-Higgs unification (5D GHU) model at a scale above TeV. We note that the vanishing of the Higgs quartic coupling and the proximity of the top quark Yukawa coupling and weak gauge coupling at high scales, inferred from the experimental data, are in harmony with 5D GHU, because in 5D GHU models the Higgs quartic coupling is forbidden by the 5D gauge symmetry and the Yukawa couplings and the weak gauge coupling originate from a common 5D gauge coupling. Based on the above insight, we propose a 5D GHU model where the Standard Model fermions are embedded in 5D fermions in a way to tightly relate the top Yukawa coupling with the weak gauge coupling. Also, the model predicts the presence of vector-like fermions (other than the Kaluza-Klein modes), which can affect the RG evolutions of the 4D theory and reconcile the scale of vanishing Higgs quartic coupling and that of equality of the top Yukawa and weak gauge couplings, thereby achieving a successful matching of the 4D theory with 5D GHU. We predict the vector-like fermion mass and the compactification scale of 5D GHU from the conditions for the successful matching.
Highlights
In the Standard Model (SM), the Higgs quartic coupling exhibits an interesting property that it vanishes at an energy scale below the Planck scale along renormalization group (RG) evolutions
Another interpretation [2,3,4,5] is that the SM is matched, around the scale of vanishing Higgs quartic coupling, with a model of gauge-Higgs unification [6,7,8,9,10,11]1 in five dimensions (5D GHU), where the SM Higgs field is identified with the fifthdimensional component of a gauge field whose quartic coupling is forbidden by the 5D gauge symmetry
Motivated by the above insights, we propose a model in which the scale where the Higgs quartic coupling vanishes is reconciled with the scale where the top quark Yukawa coupling equals the weak gauge coupling, and this common scale is interpreted as the scale where 5D GHU emerges
Summary
In the Standard Model (SM), the Higgs quartic coupling exhibits an interesting property that it vanishes at an energy scale below the Planck scale along renormalization group (RG) evolutions. This property is usually interpreted as implying metastability of our vacuum [1] as the Higgs quartic coupling turns negative above that scale. The top quark Yukawa coupling and the weak gauge coupling show an interesting feature that they become equal at the energy scale of Oð108Þ GeV This suggests that the two couplings may have a common origin in some new physics above that scale. Small Yukawa couplings other than the top quark Yukawa coupling are reproduced by introducing 4D vectorlike fermions at an orbifold fixed point that mix with the massless modes of 5D fermions. The above structure materializes the idea that the Yukawa couplings and the
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