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Doubly protected Higgs is naturally natural

Nathaniel Craig (now Rutgers) and Kiel Howe (Stanford) released an interesting preprint

Doubling down on naturalness with a supersymmetric twin Higgs
which provides a very nice explicit example why one should never be too ambitious when deducing consequences of naturalness – why "small unnaturalness" is never a problem or a problem that may be solved by a better model.

They consider an extension of the Minimal Supersymmetric Standard Model which protects the Higgs boson by two protection mechanisms. One of them is the supersymmetry, in the usual sense, and the other protection mechanism is (in their particular case) the twin Higgs mechanism.




Supersymmetry has been discussed on this blog frequently – although just a small fraction of the 391 TRF blog entries with the word "supersymmetry" say something really nontrivial about SUSY.




However, as far as I know, I haven't discussed the "twin Higgs models". They are an alternative approach that may explain the lightness of the observed Higgs boson – and as these authors argue in their new paper, this approach may be particularly powerful when it is combined with SUSY.

Many people who are told about the \(E_8\times E_8\) heterotic string theory (or Hořava-Witten heterotic M-theory) models describing the real Universe like to propose that the "other \(E_8\) group" could have the same fate as "our \(E_8\)" and it could also be broken to the Standard Model group etc. The states charged under the "other Standard Model group" would represent a shadowy dark sector (you may visualize it as the opposite side of the Hořava-Witten desk-shaped world) that interacts with us weakly (gravitationally plus by some weak interactions) and that is otherwise "analogous" (if not "identical") to the particles we know. Just to be sure, the normal assumption is that the fate of the other \(E_8\) is different and it may remain unbroken while its gauginos ignite the supersymmetry breaking through their condensate.

So they take two copies of the MSSM and assume a complete \(\ZZ_2\) symmetry for them, at least for the Higgs potential terms. Accidentally, this \(\ZZ_2\) is sufficient to guarantee the full \(U(4)\) symmetry – with the usual "additive" embedding of \(U(2)\times U(2)\) of both "Standard Models" – for all perturbative terms in the potential. Such a situation is known as an "accidental symmetry", in this case \(U(4)\).

At the end, the symmetry is broken by other phenomena and the Goldstone theorem guarantees massless or – because the symmetry isn't really exact – light scalar bosons. The observed \(125.6\GeV\) Higgs boson from the LHC is an example of such light scalar bosons. The two worlds are not completely decoupled in their models, however. A chiral superfield \(S\) interacts with both worlds via the \(SS\) superpotential.

The degree of fine-tuning is very small in their model even if the top squarks lie above \(3\TeV\). The Higgsinos are recommended to be around \(1\TeV\) which – I note – happens to agree with the estimate of the nearly pure Higgsino LSP in an unconstrained MSSM where the mass was computed as a best fit. I guess that the normal MSSM may still be embedded into the doubled one so the two papers aren't quite incompatible and one could say that there's "diverse evidence" to think that the LSP is a Higgsino and near \(1\TeV\).

Of course, I am not promising you that a model like that has to be right. It's just interesting and intriguing to know about this "spot" which is more likely than some generic points of the parameter space.



I would like to mention one more paper, one by Norma Susana Mankoč Borštnik of Slovenia (that's one female name, not two or four),
Spin-charge-family theory is explaining appearance of families of quarks and leptons, of Higgs and Yukawa couplings,
that almost claims to have "a theory of everything" unifying the spectrum of the Standard Model including several families into a single representation. The main idea of the "spin-charge-family unification" isn't too different from the wrong claims made by Garrett Lisi and all people on the same frequency. Well, Borštnik's picture is less obviously wrong because she doesn't claim to include gravity – this is what is really impossible to get from similar naive models.

At any rate, all the lepton and quark fields of all generations are claimed to arise from a single chiral 64-dimensional spinor in 13+1 dimensions. You embed \(SO(3,1)\) to \(SO(13,1)\) in the obvious additive way and the remaining \(SO(10)\) dimensions are "enough" to give you some additional degeneracy.

While it's not "immediately wrong", I think that much of my criticism against Garrett Lisi's and similar papers still holds. In particular, the \(SO(13,1)\) symmetry isn't really exact or unbroken because that would require all the 13+1 dimensions to be uncompactified. So the symmetry has to be broken – morally by a compactification – and because she assumes that the representation theory for the spinors works just like in a flat 13+1-dimensional space, it looks like a toroidal compactification. But that would give us a bad, non-chiral theory. So the \(SO(13,1)\) has to be broken explicitly, in a different way than the normal compactification, but then I don't understand the rules of the game. Why is she trusting this large symmetry to pick the spectrum if the symmetry is broken and cannot be trusted for most other questions?

I would like one of these attempts to be right but as far as I can say, all of them are wrong because they're using "extra dimensions" – something that is imposed upon us by string/M-theory – but without all the careful analyses of subtleties that string/M-theory demands along with the extra dimensions at the same moment.

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