Matching conditions and Higgs boson mass upper bounds reexamined

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 ${\mu }_{0,t}\simeq m_t$ and ${\mu }_{0,H}\simeq \max \{m_t{,M}_H\}$. Using these results, the two-loop Higgs boson mass upper bounds are reanalyzed. Previous results for $\Lambda \approx$ few TeV are found to be too stringent, and a recent update is found to be wrong. For $\Lambda {=10\mathrm{}}^{19}$ GeV we find $M_H<180\mathrm{}\pm 4\pm 5$ GeV, the first error indicating the theoretical uncertainty and the second error reflecting the experimental uncertainty due to $m_t=175\mathrm{}\pm 6$ 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 $\Lambda {=10\mathrm{}}^{19}$ GeV if $m_t=175\mathrm{}$ 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.