Consequences of Leading-Logarithm Summation for the Radiative Breakdown of Standard-Model Electroweak Symmetry

In the empirically sensible limit in which QCD, t-quark Yukawa, and scalar-fieldinteraction coupling constants dominate all other Standard-Model coupling constants, we sum all leading-logarithm terms within the perturbative expansion for the effective potential that contribute to the extraction of the Higgs boson mass via radiative electroweak symmetry breaking. A Higgs boson mass of 216 GeV emerges from such terms, as well as a scalar-field-interaction coupling constant substantially larger than that anticipated from conventional spontaneous symmetry breaking. The sum of the effective potential’s leading logarithms is shown to exhibit a local minimum in the limit φ → 0 if the QCD coupling constant is sufficiently strong, suggesting (in a multiphase scenario) that electroweak physics may provide the mechanism for choosing the asymptotically-free phase of QCD. 1. RADIATIVE ELECTROWEAK SYMMETRY BREAKING Radiative symmetry breaking, in which a vacuum expectation value arises from radiative corrections to a potential with no quadratic mass term, was first addressed in a classic paper by S. Coleman and E. Weinberg [1]. Unlike conventional symmetry breaking, in which an arbitrary but negative mass term leads to a correspondingly arbitrary Higgs boson mass, the radiative scenario for electroweak symmetry breaking necessarily predicts the Higgs boson mass as well as the magnitude of the quartic scalar-field interaction coupling constant λ . Unfortunately, the first such predictions preceded the discovery of the top-quark, whose large Yukawa coupling dominates all one-loop radiative effects. Indeed, the large magnitude of this coupling constant destroys not only the applicability of Coleman and Weinberg’s prediction for the Higgs mass (which is far below present empirical lower bounds), but also the use of a purely one-loop potential to make any such predictions via radiative symmetry breaking [2]. The only hope for the program of radiative symmetry breaking for electroweak physics is to include radiative effects past one-loop order. In the present work, we demonstrate how renormalization-group methods permit one to extract all contributing leading-logarithm contributions to the Higgs boson mass, as well as some surprising results from the summation of leading logarithms in the zero field limit. 2. LEADING LOGARITHMS AND THE HIGGS BOSON MASS The dominant couplants of the single-Higgs-doublet standard model are the t-quark Yukawa couplant ( x ≡ g2 t (v)/4π2 = 2m2 t /(2πv)2 = 0.0253 ) , the QCD gauge couplant