Matching conditions and Higgs boson mass upper bounds reexamined

Abstract

Matching conditions relate couplings to particle masses. We discuss the importance of one-loop matching conditions in the Higgs boson and top quark sector as well as the choice of the matching scale. We argue for matching scales ${\ensuremath{\mu}}_{0,t}\ensuremath{\simeq}{m}_{t}$ and ${\ensuremath{\mu}}_{0,H}\ensuremath{\simeq}\mathrm{max}{{m}_{t}{,M}_{H}}$. Using these results, the two-loop Higgs boson mass upper bounds are reanalyzed. Previous results for $\ensuremath{\Lambda}\ensuremath{\approx}$ few TeV are found to be too stringent, and a recent update is found to be wrong. For $\ensuremath{\Lambda}{=10}^{19}$ GeV we find ${M}_{H}<180\ifmmode\pm\else\textpm\fi{}4\ifmmode\pm\else\textpm\fi{}5$ GeV, the first error indicating the theoretical uncertainty and the second error reflecting the experimental uncertainty due to ${m}_{t}=175\ifmmode\pm\else\textpm\fi{}6$ GeV. Hence a Higgs boson mass of about 160--170 GeV certainly satisfies both upper and lower Higgs boson mass bounds for cutoff scales up to $\ensuremath{\Lambda}{=10}^{19}$ GeV if ${m}_{t}=175$ GeV. For such Higgs boson and top quark masses the renormalization group behavior of the minimal standard model does not require new physics to set in before the Planck scale.