Dependence of the Higgs coupling and the possible onset of new physics

The simple renormalization framework previously discussed by one of us is extended to treat the Higgs potential of the standard model. As an application, we obtain in a straightforward manner the one-loop correction δ(M) in the natural relation h(M) = √12 GμmH2[1 + δ(M)], where mH is the physical mass of the Higgs boson, Gμ the accurately known μ decay coupling constant and h(M) the MS quartic Higgs coupling at mass scale M. The correction δ(M) contains contributions proportional to ξ ≡ mH2/mZ2 and ξ−1 and become large for ξ⪢1 or ξ⪡1. The dependence of h(M) on M and mH is analyzed by combining our one-loop results (which provide initial conditions) and approximate analytic solutions of relevant renormalization group equations. A parameter Mc, which roughly describes the mass scale at which perturbation theory breaks down and the possible onset of new physics, is discussed as a function of mH.