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 $\lambda$ 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 $\lambda$ to be the dominant coupling constant of the effective potential for the radiatively broken case of electroweak symmetry. We demonstrate the stability of $\lambda$ 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 $\lambda$ are disregarded. We present a full next-to-leading logarithm potential in the three dominant Standard Model coupling constants ($t$-quark-Yukawa, $\alpha_s$, and $\lambda$) from these coupling constants' contribution to two loop $\beta$- and $\gamma$-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 $\alpha_s$ coupling constants to next-to-leading logarithm order, and inclusive of the smaller $SU(2)\times U(1)$ gauge coupling constants to leading logarithm order.