Astrology & Alchemy in the SM

[selfAdjoint]

"Astrology & Alchemy" in the SM

Peter Woit links to this terrific little paper on the arxiv:


http://arxiv.org/PS_cache/hep-ph/pdf/0609/0609274.pdf

hep-ph/0609274

The Standard Model: Alchemy and Astrology
Authors: Joseph D. Lykken
Comments: 12 pages, 0 figures, review talk from "Physics at LHC", Krakow, 3-8 July 2006
Report-no: FERMILAB-CONF-06-347-T
An brief unconventional review of Standard Model physics, containing no plots.

For starters, just consider this little couple of paragraphs on the Higgs boson:

Because we have forbidden higher dimension operators by hand, the
Standard Model has no explicit cutoff dependence. However, if the Higgs
self-coupling is too large – corresponding to a physical Higgs boson mass
greater than about 180 GeV – then the SM generates its own ultraviolet
cutoff $$\Lambda_{LP}$$ . This is because λ runs logarithmically with energy scale, and if λ is large enough at the electroweak scale the sign of the effect is to increase λ at higher energies. At some energy scale $$\Lambda_{LP}$$ the coupling hits a Landau pole and the electroweak sector of the Standard Model breaks down.

If the Higgs self-coupling at the electroweak scale is too small – corre-
sponding to a physical Higgs boson mass less than about 130 GeV – then
the running goes the other way, and at some high energy scale the sign of
this quartic coupling goes negative. At best, this destabilizes the vacuum;
at worst, theories with this kind of disease are unphysical. One could at-
tempt to compensate by invoking dimension 6 Higgs self–couplings, but this would violate one of our defining theoretical inputs.

 

[Haelfix]

Yep, this is why field theory cannot be the last word on the subject, at least not field theories that aren't asymptotically free. No matter what you write down (this applies to GUTs and any sort of other thing you can think off), you invariably run into problems like Landau poles at some scale and so forth.

Ergo the final theory of everything has to go beyond effective field theory, or at the very least to be capable of generating an infinite cascade of field theories (or descriptions) all valid at specific and individual points in the phase space such that it fills out the entire space.