# Does the Standard Model have a Landau pole?

I have seen the statement that the Standard Model has a Landau pole, or at least it its believed that it does at $\sim 10^{34}$ GeV. Has this actually been proven (at least in perturbation theory, as in QED) or what kind of evidence is there to support this?

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I'm not sure if it's the case, and it's possible that the answer is sensitive to measured constants (the Higgs mass, the top mass, alpha-strong). A well-known recent paper that runs relevant SM couplings up to the Planck scale is inspirehep.net/record/1116539 - it hints that the Higgs coupling doesn't blow up but actually almost vanishes at the Planck scale. – Vibert Feb 19 '13 at 15:29
@Vibert: The $\lambda$ result in that paper is interesting, but the $U(1)$ coupling shows no signs of slowing down. I think right now I'd bet that the Standard Model has at least one Landau pole. – user1504 Feb 20 '13 at 13:16

I am not sure whether the standard model has a Landau pole at $10^{34}$ GeV but there are two obstacles to providing a definite answer to the question: (1) perturbation theory is no longer valid when the coupling constants get large, and (2) $10^{34}$ GeV is well beyond the Planck scale, so that ignoring the effects of (quantum) gravity is not valid.
If there is a Landau pole (or failure of a coupling constant to tend to zero at high energy scales) in the standard model, it would appear first in the scalar quartic coupling $\lambda$ -- but the requirement that $\lambda$ and the Yukawa couplings do not blow up before the Planck scale puts useful constraints on particle masses. See, for example,