On CDF Anomaly

Mhm, it seems that I chose the wrong side of the Atlantic. First, the LHC produces a big firework display instead of small black holes, and then the CDF collaboration at the Tevatron discovers new physics. About the CDF anomaly in multi-muon events, see Tommaso's post or the original paper. Together with a few CERN fellows we had an impromptu journal club today, and we have reached the conclusion that, well, we don't know :-). The anomaly occurs in a theoretically difficult region, the B-baryon spectrum is poorly known, the local Monte Carlo magicians are very sceptical about modeling the b-quarks, etc, etc. It does not mean, of course, that one should shrug it off. Whether we want it or not, the CDF anomaly will dominate particle model-building for the next few months.

Meanwhile, there is already one model on the market that, incidentally:-), looks relevant for the anomaly: SuperUnified Theory of Dark Matter. One can immediately cook up $e^N$ variations of that model, but there seem to be 3 basic building blocks:
1) The "visible" sector that consists of the usual MSSM with the supersymmetry breaking scale $M_{MSSM} \sim$ few hundred GeV.
2) The dark sector with a smaller supersymmetry breaking scale $M_{dark} \sim $ GeV. It includes a dark gauge group with dark gauge bosons and dark gauginos, a dark Higgs that breaks the dark gauge group and gives the dark mass to the dark gauge bosons of order 1 dark GeV. In fact it's all dark.
3) The dark matter particle that is charged under the dark group and has a large mass, $M_{DM} \sim $ TeV. Unlike in a typical MSSM-like scenario, dark matter is not the lightest supersymmetric particle, but rather some new vector-like fermion whose mass is generated in the similar fashion as the MSSM mu-term.

The dark group talks to the MSSM thanks to a kinetic mixing of the dark gauge bosons with the Standard Model photon, that is via lagrangian terms of the type $f_{\mu\nu} F_{\mu \nu}$. Such mixing terms are easily written down when the dark group is U(1), although for non-abelian gauge groups there is a way to achieve that too (via higher-dimensional operators). Once the dark gauge boson mixes with the photon, it effectively couples to the electromagnetic current in the visible sector. Thanks to this mixing, the dark gauge boson can decay into the Standard Model particles.

The SuperUnified model is tailored to fit the cosmic-ray positron excess PÀMELA and ATIC/PPB-BETS. The dark matter particle with a TeV scale mass is needed to explain the positron signal above 10 GeV (as seen by PAMELA) all the way up to 800 GeV (as suggested by ATIC/PPB-BETS), see here. The dark gauge bosons with a GeV mass scale play a two-fold role. Firstly, they provide for a long range force that leads to the Sommerfeld enhancement of the dark matter annihilation rate today. Secondly, the 1 GeV mass scale ensures that the dark matter particle does not annihilate into protons/antiprotons or heavy flavors, but dominantly into electrons, muons, pions and kaons. The second point is crucial to explain why PAMELA does not see any excess in the cosmic-ray antiprotons. Supersymmetry does not play an important role in the dynamics of dark matter, but it ensures "naturalness" of the 1 GeV scale in the dark sector, as well as of the electroweak scale in the visible sector. I guess that analogous non-supersymmetric constructions based, for example, on global symmetries and axions will soon appear on ArXiv.

What connects of this model to the CDF anomaly is the prediction of "lepton jets". In the first step, much as in the MSSM, the hadron collider produces squarks and gluinos that cascade down to the lightest MSSM neutralino. The latter mixes into the dark gauginos, by the same token as the dark gauge boson mixes with the visible photon. The dark gaugino decays to the dark LSP and a dark gauge boson. Finally, the dark gauge boson mixes back into the visible sector and decays into two leptons. At the end of this chain we obtain two leptons with the invariant mass of order 1 GeV and a small angular separation, the latter being due the Lorentz boost factor $\gamma \sim M_{MSSM}/M_{dark} \sim 100$.

The perfect timing of the "lepton jets" prediction is unlikely to be accidental. A new spying affair is most welcome, now that the paparazzi affair seems to by dying out. While waiting for CDF to find the traitor and hang him on the top pole, I keep wondering if the SuperUnified model does indeed explain the CDF excess. If you take a look at the invariant mass distribution of the anomalous muon-pair events (right panel) it does not resemble a 2-body decay of a narrow-width particle (for comparison, admire the J/Psi peak in the left panel), which it should if the muons come from a decay of the dark gauge boson. Or am I missing something? Furthermore, it has been experimentally proved that bosons are discovered in Europe, while only fermions can be discovered in the US. This is obviously inconsistent with the Tevatron finding the dark gauge boson ;-)

Thanks to Bob, Jure and Tomas for the input.
See also Lubos' post on the SuperUnified model.
For more details and explanations on the CDF anomaly, see the posts of Peter and Tommaso and John.