Radiative Electroweak Symmetry Breaking Beyond Leading Logarithms

The top-quark Yukawa coupling is too large to permit radiative electroweak symmetry breaking to occur for small values of y, the Higgs self-coupling, to leading-logarithm order. However, a large y solution leading to a viable Higgs mass of approximately 220GeV does exist, and differs from conventional symmetry breaking by an approximately five-fold enhancement of the Higgs self-coupling. This scenario for radiative symmetry breaking is reviewed, and the order-by-order perturbative stability of this scenario is studied within the scalar field theory projection of the standard model in which the Higgs self-coupling y represents the dominant standard-model coupling. Conventional electroweak (EW) symmetry breaking requires the presence of a Higgs scalar-field quadratic term in the Lagrangian. Such a mass term is unnatural if SU(2)×U(1) EW gauge theory is embedded within a grand-unified theory (GUT), since fine-tuning is needed to cancel the unification-scale perturbative corrections generated by this mass term [1] to maintain a Higgs mass empirically bounded not too far from the EW vacuum expectation value (VEV) scale 〈φ〉 = v = 246.2GeV [2]. This fine-tuning problem can be circumvented if the embedding unified theory has a symmetry (e.g. conformal symmetry) which protects these quadratic terms from GUT-scale corrections. Radiative EW symmetry breaking provides such a scenario. Quadratic scalar mass terms are absent, and in the seminal work of Coleman & Weinberg, it is demonstrated that spontaneous symmetry breaking (i.e. the generation of a VEV) occurs via radiative (perturbative) corrections to the conformally-invariant theory [3]. Unlike conventional symmetry breaking where the Higgs mass is an unconstrained parameter, the radiative symmetry breaking mechanism is a self-consistent approach which results in a prediction of both the Higgs mass and its four-point self-coupling after imposition of the external EW scale for the VEV 〈φ〉 = v = 246.2GeV . In the absence of large Yukawa couplings (i.e. Yukawa couplings are dominated by EW gauge couplings), a justifiable assumption at the time of Coleman & Weinberg’s work, the radiative symmetry breaking scenario contains a small-λ solution leading to an O(10GeV) Higgs mass [3], long since ruled out via direct experimental searches. However, the top quark Yukawa coupling is large enough to destabilize this small-λ solution. The Coleman-Weinberg radiative mechanism has thus been revisited in the context of the large top-quark Yukawa coupling, revealing the persistence of a large-λ radiative scenario resulting in a 218GeV Higgs mass for the minimal (single-Higgs-doublet) standard model [4, 5]. Consider the one-loop effective potential Veff = π φS for the Higgs sector, which must satisfy the renormalization group (RG) equation