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I have always thought that the Higgs sector, which is $\phi^4$ theory in essence, is not asymptotically free.

However, I ran into the following statement from this paper:

The standard model is, in fact, not asymptotically free because of the perturbative Landau pole singularity in the U(1) gauge sector. Still, all other gauge couplings as well as the dominant top-Yukawa coupling and the Higgs self-coupling decrease towards higher energies.

This gives me the impression that the Higgs sector is asymptotically free.

Do I misunderstand something? Could anyone please clarify for me?

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  • $\begingroup$ It is not asymptotically free, hard to say why that paper claims it is. Did you check other sources? $\endgroup$
    – AccidentalFourierTransform
    Commented May 11 at 15:12
  • $\begingroup$ @AccidentalFourierTransform My understanding is that Higgs sector is not AF. However, a non-Abelian gauge theory having not-too-many matter fields can be AF. $\endgroup$
    – Keith
    Commented May 24 at 16:45
  • $\begingroup$ @AccidentalFourierTransform However, it seems that the $U(1)$ gauge sector cannot be salvaged from the Landau pole even if other non-Abelian gauge fields are present. Do I understand correctly? $\endgroup$
    – Keith
    Commented May 24 at 16:46
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    $\begingroup$ yes indeed. ${}{}$ $\endgroup$
    – AccidentalFourierTransform
    Commented Jun 21 at 15:40

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