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I read that "essentially everything in the Standard Model impacts the running of every physical constant in the Standard Model. So, if there is even a single particle missing from the Standard Model, the beta function for the running of the Higgs vev will be wrong, and at close to the GUT scale, it will be maximally wrong."

How about dark matter? If a subsector of dark matter is say self interacting, can it also impact the running of physical constant in the Standard Model? Why or why not?

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If dark matter is a new kind of particle or field, then yes, it should affect the running of Standard Model couplings. However, the amount may be exceedingly small.

Since dark matter evidently couples to gravity, and gravity couples to everything, then there can be loop inside of a diagram used to compute a beta function where, say, a Standard Model particle creates a pair of gravitons that annihilate into a dark matter particle (this is just to give you an idea, I'm not saying that specific interaction will actually happen or is the most important). However, at energies below the Planck scale, coupling of the Standard Model particles to gravity are extremely weak, so this kind of contribution to a beta function would be extremely small and impossible to measure in practice at realistic collider energies.

If dark matter directly couples to Standard Model particles (which is not guaranteed), then this interaction would also affect the running couplings. However, we already know from collider, astrophysical, and direct detection experiments that the interaction between dark matter and Standard Model particles must be very small, so again this is going to be hard to detect.

However, precision measurements of loop effects is certainly a valid method to look for physics beyond the standard model, eg https://physics.aps.org/articles/v15/32

So, looking for dark matter by probing beta functions at high precision is probably a long shot, but scientifically it is a reasonable thing to look for.

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  • $\begingroup$ If say dark matter only couples to matter at high energies or in a phase transition. Will the running coupling also shows up only at that same high energy or would it also show up at low energy? $\endgroup$
    – Jtl
    Commented May 27 at 0:48
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    $\begingroup$ @Jtl I am not aware of a coupling that only exists at high energies or in a phase transition -- in the examples I know of, if a coupling at all then it always exists in some form. But supposing you could make such a coupling, loop contributions are off shell, so there will presumably be some part of the integral that has the kinematics you need to make the interaction exist, so the contribution will be nonzero. In other words, you have particles of arbitrarily high energy running in loops (hence UV divergences). But, the contribution will be small, if the energies needed are large. $\endgroup$
    – Andrew
    Commented May 27 at 1:39
  • $\begingroup$ Isnt it in the GUT argument. They say the running constant all coincide at the point for electroweak and strong force? So why cant it be interpretated the coupling constant depends on temperature? $\endgroup$
    – Jtl
    Commented May 27 at 1:51
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    $\begingroup$ @Jtl I agree with these statements: 1. Coupling constants depend on energy. 2. You can interpret 1 as meaning coupling constants depend on temperature. 3. The GUT argument is that if you run the standard model (or MSSM) couplings to high energies, they converge on a scale called the GUT scale. However, I do not agree with the statement that a coupling "only exists" at high energies, meaning it is zero below some energy cutoff. ("Do not agree" in this case, meaning I don't know any examples that behave like that). $\endgroup$
    – Andrew
    Commented May 27 at 2:32
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    $\begingroup$ @Jtl The Higgs VEV goes to zero at high energies but not the Yukawa couplings (couplings between the Higgs field and fermions) nor the gauge interactions. $\endgroup$
    – Andrew
    Commented May 27 at 3:26

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