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O-6 - The Higgs quartic coupling and its beta function both nearly vanish at the Planck scale

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Properties6
type
observation
id
O-6
statement
The best-fit Higgs quartic coupling at the Planck scale is small and negative - lambda(M_Pl) = -0.0129 + 0.0028(Mh - 125.5 GeV) +- 0.0047_Mt +- 0.0018_as +- 0.0028_th - with exact vanishing excluded at 2 sigma; its beta function vanishes at ~3x10^17 GeV, so the measured SM parameters put the Higgs potential remarkably close to the critical boundary between the stability and metastability phases.
source
S-20 - Degrassi et al. 2012, Higgs mass and vacuum stability in the Standard Model at NNLO
locator
§4.1, eq. (64), fig. 6; §5
link_state
linked

lambda(M_Pl) = 0 would require Mt about 2 GeV below its measured central value (Mt below ~171 GeV). The near-vanishing of both lambda and beta_lambda at M_Pl is the quantitative sense in which the SM vacuum is near-critical.

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