Canceling Quadratic Divergences in a Class of Two-Higgs-Doublet Models

The Newton-Wu conditions for the cancellation of quadratic divergences in a class of two-Higgs-doublet models are analyzed as to how they may be satisfied with a typical extension of the Standard Model of particle interactions. In the Standard Model (SM) of particle interactions, there is one physical scalar Higgs boson H . Its mass may be constrained by the requirement that the one quadratic divergence of the theory be canceled among its gauge, Yukawa, and quartic scalar couplings [1], i.e. 3 2 M W + 3 4 M Z + 3 4 m2H = ∑ f Nfm 2 f , (1) where the sum is over all SM fermions with Nf its number of color degrees of freedom, i.e. Nf = 3 for quarks and Nf = 1 for leptons. The above has been written in terms of masses because all SM couplings are related to masses through the one vacuum expectation value (VEV) of the theory. Given that mt = 174 GeV and all other fermion masses are negligible compared to it, the prediction is then mH = 316 GeV. In the two-Higgs-doublet extension of the SM, there are 4 quadratic divergences and they are functions again of the gauge, Yukawa, and quartic scalar couplings. They have been calculated previously by Newton and Wu [2]. However, since there are now more possible quartic scalar couplings than masses, and the Yukawa terms are not uniquely determined (because of the different possible choices of which fermion couples to which scalar), the 4 conditions vary according to what specific two-Higgs-doublet extension is assumed. In this note, the following Higgs potential for two doublets Φ1,2 = (φ + 1,2, φ 0 1,2) is considered: V = μ21Φ † 1Φ1 + μ 2 2Φ † 2Φ2 + μ 2 12(Φ † 1Φ2 + Φ † 2Φ1) + 1 2 λ1(Φ † 1Φ1) 2 + 1 2 λ2(Φ † 2Φ2) 2 +λ3(Φ † 1Φ1)(Φ † 2Φ2) + λ4(Φ † 1Φ2)(Φ † 2Φ1) + 1 2 λ5(Φ † 1Φ2) 2 + 1 2 λ∗5(Φ † 2Φ1) . (2) This is the most general form of V under the assumption that a discrete odd-even symmetry (Φ1 is odd and Φ2 is even or vice versa) exists which is broken only by soft terms (μ 2 12). The utility of such a formulation in model building is widely recognized [3]. The same odd-even symmetry restricts the Yukawa couplings of the SM fermions of each type to be associated with either Φ1 or Φ2, but not both. Under these assumptions, the 4 Newton-Wu conditions