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I know that for the SM we assume that the quartic coupling of the Higgs $\lambda_H>0$ due to vacuum stability, but in principle for $\lambda_H<0$ vacuum stability could still be safe if we have some non-renormalisable interaction (e.g. $\lambda_6 (H^\dagger H)^3$) coming from some large energy scale $\Lambda \gg m_\text{EW}$.

I know that the Higgs sector is not too strongly constraint, but in principle one should get the sign of the $\lambda_H$ coupling by looking at the interference diagrams (one-loop and tree-level to get an odd power of $\lambda_H$) $h\rightarrow b\bar{b}$ decay.

Has some experiment already confirmed such a interference process?

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    $\begingroup$ maybe this proposal includes the above arxiv.org/abs/2004.04240 $\endgroup$
    – anna v
    Jul 2, 2021 at 3:31
  • $\begingroup$ Ideed thanks a lot. So to summarise in this analysis they found from the interference of $gg\rightarrow hh$ (top triangle diagram and box diagram) at 68% C.L. $−0.8<\frac{\lambda_H}{\lambda_{H,\text{SM}}}<6.6$, which could still indicate negative $lambda_H$ although it is not preferred. $\endgroup$
    – krabby patty
    Jul 2, 2021 at 9:15

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