Optimal Renormalization-Group Improvement of Two Radiatively-Broken Gauge Theories

Abstract

In the absence of a tree-level scalar-field mass, renormalization-group (RG) methods permit the explicit summation of leading-logarithm contributions to all orders of the perturbative series for the effective-potential functions utilized in radiative symmetry breaking. For scalar-field electrodynamics, such a summation of leading logarithm contributions leads to upper bounds on the magnitudes of both gauge and scalar-field coupling constants, and suggests the possibility of an additional phase of spontaneous symmetry breaking characterized by a scalar-field mass comparable to that of the theory's gauge boson. For radiatively-broken electroweak symmetry, the all-orders summation of leading logarithm terms involving the dominant three couplings (quartic scalar-field, t-quark Yukawa, and QCD) contributing to standard-model radiative corrections leads to an RG-improved potential characterized by a 216 GeV Higgs boson mass. Upon incorporation of electroweak gauge couplants we find that the predicted Higgs mass increases to 218 GeV. The potential is also characterized by a quartic scalar-field coupling over five times larger than that anticipated for an equivalent Higgs mass obtained via conventional spontaneous symmetry breaking, leading to a concomitant enhancement of processes (such as $W^+ W^- \to ZZ$) sensitive to this coupling. Moreover, if the QCD coupling constant is taken to be sufficiently strong, the tree potential's local minimum at $\phi = 0$ is shown to be restored for the summation of leading logarithm corrections. Thus if QCD exhibits a two-phase structure similar to that of $N = 1$ supersymmetric Yang-Mills theory, the weaker asymptotically-free phase of QCD may be selected by the large logarithm behaviour of the RG-improved effective potential for radiatively broken electroweak symmetry.