Wednesday 25 May 2016

particle physics - Is the Standard model an effective field theory (EFT)?


I've seen both positive and negative answers to this question, though most part of the community seem to agree it can be said it is an EFT up to the electroweak scale. My question is: What are the main arguments from each side? References are welcome too.




Answer



Well, the Standard Model is definitely an effective field theory description of physical reality since it neglects both gravity and neutrino masses.


It's also an effective QFT in the sense that there's a sensible definition of it on the lattice. (Not trivial, because there are chiral fermions.)


But I think what you're really asking is: Does the specific QFT we currently call the Standard Model have a continuum limit? That's an open question in theoretical physics. I think most theorists lean towards "no", because hypercharge and quartic Higgs couplings have beta functions with the wrong sign in the perturbative regime. Absent a miracle, this means that those sectors have Landau poles, making it impossible to find a continuum limit with interactions in the IR. (A Landau pole means that if you adjust the lattice coupling as you refine the lattice in order to keep the long-distance physics fixed, you'll see the lattice coupling run off towards infinity at a finite lattice scale.)


But this isn't proof: the perturbative approximation becomes unreliable as one approaches the region where the Landau pole would happen. Numerical computation with lattice $\phi^4$ theory also suggests that there's a Landau pole. However, those calculations aren't under analytic control; we don't know that we're not missing something.


On the other hand, I don't know of any compelling evidence that the Standard Model might not have a Landau pole.


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