= Higgs self-coupling Landau-pole bound
{c}
{title2=$\mu_L=\mu_0\exp[1/(2b\alpha_H(\mu_0))]$}
In the self-coupling-dominated approximation $d\alpha_H/d\ln\mu^2=b\alpha_H^2$, $b>0$, the <running coupling> reaches a perturbative <Landau pole> at the displayed scale. With the conventional <Higgs potential>, $m_H^2=2\lambda_Hv^2$ and one can normalize $\alpha_H=\lambda_H/(4\pi)$. A larger <Higgs boson> mass therefore decreases the logarithmic interval before the self-coupling becomes strong. Requiring perturbative validity up to a fixed high cutoff gives an upper Higgs-mass bound in this approximation. The full <Standard Model> beta function also contains gauge and <Yukawa couplings>; its sign is not universally positive. A perturbative pole is not a theorem excluding every nonperturbative ultraviolet completion.
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