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Nima Arkani-Hamed on the meaning of the 125 GeV Higgs

I've seen parts of some talks at a recent Jerusalem winter school in theoretical physics. For example, the physicist from the title has updated our knowledge about the twistor'n'grassmannian minirevolution. It was interesting to hear that the Yangian is composed of diffeomorphisms.

It's still not clear to me whether I have absorbed the novelties and distinguished the insights that are new for me from those that are actually new for the scientific community.

That's why I will look elsewhere. Let us play another 100-minute video, one that was promoted by JollyJoker. Israel's de facto capital has cordially welcomed a kind of expert that the country of the star of David and especially the holy Al-Quds really loves these days – an Iranian subnuclear physicist. ;-)

OK, he has really been an American physicist these days, and probably more so than many of the self-described American physicists, but one shouldn't reduce the fun of the combination here. Here is what he had to say.

Nima asked all experimenters to leave the room – and once they left, he could talk about them. He said that they were wonderful, especially those that gave the talks at CERN. ;-) The LHC data is spectacular. We're learning a lot. Nima says that the 125 GeV Higgs is a pretty much sure thing and his friends mostly agree.

One thing you can deduce is that Matt Strassler isn't Nima's friend because MS hasn't met anyone who thinks that the Higgs has been discovered. ;-)

The first conclusion is a funeral of technicolor (1977-2011): rest in peace. A 125 GeV Higgs is a triumph of the weak coupling. Nima Arkani-Hamed emphasizes that the picture of the grave with technicolor's bones in it is not a joke; it's a real grave. (My condolences for the closest relatives who loved technicolor to the last moment, e.g. anti-string jihadist Kenneth Lane of BU.) Nima would have been devastated if the strong coupling were the explanation of the electroweak symmetry breaking because the same mechanism appears everywhere – dimensional transmutation, exponential hierarchies, done. But this is our first weakly coupled light scalar. With one strongly-coupled effective theory beneath another one, particle physics would be as boring as condensed matter physics, moreover with a smaller number of more expensive layers.

Someone is arranging things behind the scenes. The Higgs is the most interesting part of the Standard Model; the other particles are details. Nima presents the lightness of the Higgs as the only argument to think we could see new physics at the LHC; not even WIMP dark matter is enough. All other non-Higgs effects have to be suppressed by vastly higher scales.

The best solution would be SUSY; gives gauge coupling unification and dark matter. These are quantitative successes that emerged around 1990, something that other solutions can't really offer. At the beginning, the unification in SUSY was worse. But SUSY theorists were really predicting it should get better than in SM – and it did! SUSY switched to a logarithmic decline.

The Higgs found by the LHC looks pretty much supersymmetric; but it's not a garden-variety SUSY. Nima thinks there is some fine-tuning at the "subleading order". Those words are an introduction to split supersymmetry (Nima, Savas 2004).

Alternatives: pseudo-Goldstone bosons and little Higgs bosons are pretty much dead, too. The latter undershoots the Higgs mass; the old-fashioned composite theories overshoot. Both of them are bad.

Why was there no SUSY at the LHC? Intelligent people shouldn't talk about the "quantitative fine-tuning" behind the little hierarchy problem but rather about qualitative mispredictions of the simplest SUSY. An otherwise cautious Italian physicist promised his student to cut his right ball if SUSY isn't discovered at LEP I. ;-)

By RG flow arguments, colored superpartners are heavier at low energies if they're the same at high energies. The simplest logic implies that the Higgs mass should be matching the heaviest guys such as stop while other superpartners should be even lighter. That's why the Italian wanted to sacrifice his or her organ (I don't want to discriminate against women and claim that they have no right to cut their testicles). But there are no superpartners under the Z mass.

In reality (the more likely one), the stop and the Higgs are close at high energies. However, the Higgs is running and getting light as you go closer to low energies and it stops before reaching zero. The natural expectations have to be replaced by the Neytural ones (suggested by observations).

At the tree level of MSSM, the Higgs is lighter than the Z. SUSY breaking and stops in particular allow us to lift the Higgs mass above the Z mass. This is a more unavoidable bound on the Higgs mass than some model-dependent ways of quantifying the little fine-tuning. We're pushed towards the stop at 5-10 TeV.

A simple way to add extra corrections is the NMSSM (next-to-), with an extra singlet. Its integration out modifies the quartic coupling. However, one runs into a Landau pole near 3 TeV. It is probably a bad idea to mess up with the higgsinos because, as typical things not in complete GUT multiplets, they generically destroy the gauge coupling unification.

If there were an NMSSM-like addition to the Higgs mass, it would naturally be much bigger than 30 GeV or so – hundreds of GeV, and so on. This Z-Higgs proximity suggests that a garden-variety contribution to the Higgs mass isn't really there at all.

The NMSSM-like adjustments to the Higgs came from chiral multiplets and F-terms. One may also try D-terms from some extra U(1) groups. It's only anomaly-free if we have right-hand neutrinos and the masses of neutrinos are Dirac, not Majorana. Nima's favorite U(1) is the separated U(1) in the U(5) embedded into SO(10) in the obvious block way. 125 GeV may be reached; the constraint to avoid the Landau pole of the new U(1) may be successfully imposed.

The U(1) option would be spectacular; it predicts a Z-prime between 1-3 TeV and every particle lighter than that may be made out of it. No MET problems, just a perfect reconstruction of the Z-prime decay products. String theory makes you believe that there could or should be lots of U(1)'s which could make it likely; still, it's not guaranteed by string theory that a U(1) will survive to low energies along with the Standard Model.

After an exchange with David Gross, Nima shows that a solution based on an A-term is even more fine-tuned than the original theory, making the quadratic divergences worse than before. Nima also thinks that the focus point hype is bulšit – well, a bulšity interpretation of valid observations. The observation is that with the universal masses, some totally determined RG running leads the mass to cross the zero near the TeV scale. That's great but one has a big tuning because the scale of SUSY etc. is not related by a theoretical mechanism to the Higgs TeV scale.

I am not sure whether I understand Nima's radical opposition here because we don't know whether the SUSY scale is actually aligned with the Higgs mass, do we? At any rate, he is convinced that the decoupling of scales makes the problem worse, not better. Despite my misunderstanding of some points, it's understandable that focus point SUSY predicts small A-terms so the Higgs should be way lighter than 125 GeV.

Now, the mechanisms to kick the Higgs mass uphill do have consequences; the branching ratios should be non-Standard-Model-like. Nima thinks that the discovery of any deviations of the branching ratios from the SM (by a factor of 1.5-2.0) instantly implies the existence of light scalars (like a down-type Higgs below 230 GeV in a scenario) and a natural theory right behind the corner.

He mentions that he believes that the SM will be measured as SM-like; however, he also hears CMS rumors that they have increased cross sections in vector boson fusion etc.

In the last 10 minutes of the talk, he talks about the alternative view: the weak scale is fine-tuned, after all. The Standard Model up to the Planck scale looks really crazy; but he's going to discuss such things, anyway.

Arkani-Hamed recalls an argument with David Gross who obviously defended the view that (his) QCD isn't fine-tuned. I guess that David Gross means that pure QCD has no dimensionless parameters whatsoever. However, Nima points out that those pure-QCD things are not relevant for nuclear physics' apparent fine-tuning; the latter surely depend on the up-quark and down-quark rest masses (outside pure QCD).

For example, the (triplet) deuteron's binding energy is just an MeV, below the expectations of 100 MeV, due to some cancellations. Even worse, the dineutron (or singlet deuteron) only fails to exist (as a bound state) by 60 keV. Accidents abound. These accidents are reflected in apparent fine-tuning of the 4-nucleon terms in a multinucleon effective theory by Mark Wise and others from the 1990s. Some people in the audience don't get it; I don't know why. I am on Nima's frequency here; however, the observation doesn't imply any anthropic stuff, I think.

Nima got in the right situation to promote split SUSY. It makes most superpartners heavy and some of them are light, in order to preserve gauge coupling unification and a TeV-like WIMP dark matter particle. Great, their scenario follows. The conditions still look too anthropomorphic to me. I don't know why Nature should try to obey exactly these conditions, containing some kind of a "purpose".

Regardless of the detailed "competition rules", Nima sensibly says that the SUSY breaking models have been trying to tell us that scalars should be heavy, like 100 TeV, and fermions should be light, around a TeV. Many model builders wanted to deny these models their freedoms, natural desires, and human rights. What's the consequence of granting them the freedom? Well, a consequence is that 125 GeV becomes reasonable. In their original paper, they stated that it should have been above 120 GeV – which was already risky.

Now, gluinos have to decay via a virtual squarks. Because those are heavy, gluinos should be long-lived – displaced vertices.

A worry is that the higgino and wino weigh 1 and 3 TeV, respectively (in agreement with the "WIMP miracle"). In that case, we won't see any superpartners at the LHC. However, there's some evidence against this nightmare already; it could prefer a heavier Higgs.

Multiple components of dark matter; and later moduli decay would still favor a sub-TeV dark matter particle, not obviously but according to numerical calculations (200-300 GeV wino is perfect).

At this point, some impatient viewers complaint about the duration. Nima claims that he previously gave this 102-minute talk in 30 minutes and he has no idea where the extra factor of pi came from.

In the simplest anomaly-mediated models, let's grant the freedom to the higgsino, too. They will eat a lot (related to the mu-term) and get close to the gravitino mass. Great. A result is that the spectrum is getting a bit squeezed. He shows some examples of models and spectra with extra 5 and 5bar matter; all those acquire G-M masses (BTW, not sure how many balls Giudice has and whether he sent it as food to Argentina, in order to grow new Maldacenas). The gluino is never heavier than 2.5 times the lightest superpartner mass.

Another happy coincidence is that the mass splittings are small, 10%, and they're what dictates the gluino decay which is a reason to think it should be even more long-lived. He clearly believes that the displaced vertices should be seen; so far, they haven't been.

To summarize, a 125 GeV Higgs looks supersymmetric. A question for the near future is whether the parameters are quite natural; or whether a 10^-4 or 10^-6 level tuning should be tolerated in which case one should embrace split SUSY and relatives. Split SUSY is vulnerable and falsifiable – deviations of the Higgs from its SM properties or the discovery of a fermion would immediately falsify split SUSY.

We are waiting, on pins and needles, for the 8 TeV run in 2012.

Other talks

If you click at the Jerusalem link at the top, you may also watch the talks by others – Gross I, Gross II, Nekrasov, Dine, Bern, Spiropulu, Mukhanov, Komargodski, Rabinovici, and... the entropic gravity pseudoscience, too.

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