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Arkani-Hamed: “Dark Forces, Smoking Guns, and Lepton Jets at the LHC” December 11, 2008

Posted by dorigo in news, physics, science.
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As we’ve been waiting for the LHC to turn on and turn the world upside down, some interesting data has been coming out of astrophysics, and a lot of striking new signals could show up. This motivates theoretical investigations on the origins of dark matter and related issues, particularly in the field of Supersymmetry.

Nima said he wanted to tell the story from the top-down approach: what all the
anomalies were, what motivated his and his colleagues’ work. But instead, he offered a parable as a starter.

Imagine there are creatures made of dark matter: ok, dark matter does not clump, but anyway, leaving disbelief aside, let’s imagine there are these dark astrophysicists, who work hard, make measurements, and eventually see that 4% of the universe dark to them, they can’t explain the matter budget of the universe. So they try to figure out what’s missing. A theorist comes out with a good idea: a single neutral fermion. This is quite economical, and this theory surely receives a lot of subscribers. But another theorist envisions that there is a totally unknown gauge theory, with a broken SU(2)xU(1) group, three generations of fermions, the whole shebang… It seems crazy, but this guy has the right answer!

So, we really do not know what’s in the dark sector. It could be more interesting than just a single neutral particle. Since this is going to be a top-down discussion, let us imagine the next most complicated thing you might imagine: Dark matter could be charged. If the gauge symmetry was exact, there would be some degenerate gauge bosons. How does this stuff have contact with the standard model ?

Let us take a mass of a TeV: everything is normal about it, and the coupling that stuff from this dark U(1) group can have is a kinetic mixing between our SM ones and these new gauge fields, a term of the form 1/2 \epsilon F_{\mu \nu}^{dark} F^{\mu \nu} in the Lagrangian density.

In general, any particle at any mass scale will induce a loop mixing through their hypercharge above the weak scale. All SM particles get a tiny charge under the new U(1)’. The coupling can be written as kinetic mixing term, and it will be proportional to their electric charge. The size of the coupling could be in the 10^-3, 10^-4 range.

This construct would mess up our picture of dark matter, and a lot about our
cosmology. But if there are higgses under this sector, we have the usual problem of hierarchy. We know the simplest solution to the hierarchy is SUSY. So we imagine to supersymmetrize the whole thing. There is then a MSSM in our sector, and a whole SUSY dark sector. Then there is a tiny kinetic mixing between the two. If the mixing is 10^-3, from the breaking of symmetry at a mass scale of about 100 GeV, the breaking induced in the DM world would be of radiative origin, through loop diagrams, at a few GeV mass scale.

So the gauge interaction in the DM sector is broken at the Gev scale. A bunch
of vectors, and other particles, right next door. Particles would couple
to SM ones proportionally to charge at levels of 10^-3 – 10^-4. This is dangerous since the suppression is not large. The best limits to such a scenario come from e+e- factories. It is really interesting to go back and look at these things in BaBar and other experiments: existing data on tape. We might discover something there!

All the cosmological inputs have difficulty with the standard WIMP scenario. DAMA, Pamela, Atic are recently evidenced anomalies that do not fit with our
simplest-minded picture. But they get framed nicely in our picture instead.

The scale of these new particles is more or less fixed at the GeV region. This has an impact in every way that you look at DM. As for the spectrum of the theory, there is a splitting in masses, given by the coupling constant \alpha in the DM sector times the mass in the DM sector: a scale of the order \alpha M.  It is radiative. There are thus MeV-like splittings between the states. And there are new bosons with GeV masses that couple to them. These vectors couple off-diagonally to the DM. This is a crucial fact, sinply because if you have N states, their gauge interaction is a subpart of a rotation between them. The only possible interaction that these particles can have with the vector is off-diagonal. That gives a cross section comparable to the weak scale.

The particles annihilate into the new vectors, which eventually have to decay. They would be stable, but there is a non-zero coupling to our world, so what do they decay into ? Not to proton-antiproton pairs, but electrons, or muon pairs. These features are things that are hard to get with ordinary WIMPS.

And there is something else to expect: these particles move slowly, have long range interaction, geometric cross sections, and they may go into excited states. Their splitting is of the order of the MeV, which is not different from the kinetic energy in the galaxy. So with the big geometric cross section they have, you expect them not to annihilate but excite. They decay back by emitting e+e- pairs. So that’s a source of low-energy e- and e+: that explains an integral excess in these particles from cosmic rays.

If they hit a nucleus, the nucleus has a charge, the vector is light, and thus the cross section is comparable to Z and H exchange. So the collision is not elastic, it changes the nature of the particle. This changes the analysis you would do, and it is possible for DAMA to be consistent with the other experiments.

Of course, the picture drawn above is not the most minimal possible thing, to
imagine that dark matter is charged and has gauge interactions is a quite far-fetched thing in fact. But it can give you a correlated explanation to the cosmological inputs.

Now, why does this have the potential of making life so good at the LHC ? Because we can actually probe this sector sitting next door, particularly in the SUSY picture. In fact, SUSY fits nicely in the picture, while being motivated elsewhere.

This new “hidden” sector has been studied by Strassler and friends in Hidden valley models. It is the leading way by means of which you can have a gauge sector talking to our standard model.

The particular sort of hidden valley model we have discussed is motivated if you take the hints from astrophysics seriously. Now what does it do to the LHC ? GeV particles unseen for thirty years….  But that is because we have to pay a price, the tiny mixing.

Now, what happens with SUSY is nice: if you produce superpartners you will always go into this sector. The reason is simple: normally particles decay into the LSP, which is stable. But now it cannot be stable any longer, because the coupling will give a mixing between gaugino in our sector and photino in their sector. Thus, the LSP will decay to lighter particle in the other sector, producing other particles. These particles are light, so they come out very boosted. They make a Higgs boson in the other sector, which decays to a W pair, and finally ends up with the lightest vector in the other sector: it ends up as an electron-positron pair in this sector.

There is a whole set of decays that gives lots of leptons, all soft in their sector. They are coming from the decay of a 100 GeV particle. The signature could be jets of leptons. Every SUSY event will contain two. Two jets of leptons, with at least two, if not many more, leptons with high-Pt, but featuring small opening angles and invariant masses. That is the smoking gun. As for lifetime, these leptons are typically prompt, but they might also have a lifetime. However the preferred situation is that they would not be displaced, they would be typically prompt.