Stability of subsequent-to-leading-logarithm corrections to the effective potential for radiative electroweak symmetry breaking

Abstract

We demonstrate the stability under subsequent-to-leading logarithm corrections of the quartic scalar-field coupling constant λ and the running Higgs boson mass obtained from the (initially massless) effective potential for radiatively broken electroweak symmetry in the single-Higgs-doublet Standard Model. Such subsequent-to-leading logarithm contributions are systematically extracted from the renormalization group equation considered beyond one-loop order. We show λ to be the dominant coupling constant of the effective potential for the radiatively broken case of electroweak symmetry. We demonstrate the stability of λ and the running Higgs boson mass through five orders of successively subleading logarithmic corrections to the scalar-field-theory projection of the effective potential for which all coupling constants except the dominant coupling constant λ are disregarded. We present a full next-to-leading logarithm potential in the three dominant Standard Model coupling constants ( t-quark-Yukawa, α s , and λ) from these coupling constants' contribution to two loop β- and γ-functions. Finally, we demonstrate the manifest order-by-order stability of the physical Higgs boson mass in the 220 – 231 GeV range. In particular, we obtain a 231 GeV physical Higgs boson mass inclusive of the t-quark-Yukawa and α s coupling constants to next-to-leading logarithm order, and inclusive of the smaller SU ( 2 ) × U ( 1 ) gauge coupling constants to leading logarithm order.