As for today, the CDF anomaly has no convincing explanation. Strangely enough, HEP-ph is not flooded by new physics models (yet?), maybe because a down-to-earth explanation appears far more likely to most of us. The situation will clarify when D0 presents their own analysis of the analogous multi-muon events. I'm confident that D0 is working hard now, since the prospect of kicking the CDF butt (if the anomaly is a detector effect) must be tempting for them. While waiting for D0, one may wonder if there is a new physics scenario that could address the signatures reported by CDF. The so-called hidden valley scenario was pointed here and there, so I thought it would useful to explain the idea behind that romantic name.

Hidden valley refers to a large class of theories which, apart from the Standard Model, contain a hidden sector with a low mass scale. Here, low means no more than 100 GeV; could be 10 GeV, could be 1 GeV... In order to explain why the new particles were not copiously produced at LEP,

the hidden sector must be very weakly coupled to the SM. For example, the interactions between the Standard Model and the hidden valley might be mediated via a new U(1) gauge symmetry under which both sectors are charged. The Higgs boson could also be a mediator between the two sectors. If the mass of the mediator is large (more than, say, 100 GeV), then the interactions between the two sectors is very weak at low energies. This is illustrated in the picture on the right. While LEP has not enough energy to climb over the potential barrier produced by the large mass of the mediator, the LHC is powerful enough to overcome the barrier and explore the new sector. The Tevatron is not in this picture because everybody thought it was already passè.

What makes the hidden sector? Basically, the sky and your imagination is the limit. Below, I will talk about one particular scenario that is especially interesting from the point of view of collider studies. It might be that the hidden sector is described by a strongly interacting theory somewhat resembling our QCD. That is to say, there are hidden quarks confined by hidden strong forces that binds them into hidden mesons, hidden pions and similar stuff. A particle collision in our collider, after crossing the potential barrier, would produce a pair of hidden quarks who subsequently hadronize and cascade-decay to lighter hidden hadrons. But one crucial difference between our QCD and the hidden QCD is that the latter does not have a stable particle at the end of the decay chain (or at least, not all the decay chains end in a stable hidden particle) so that the hidden stuff eventually decays back into the Standard Model particles. Because of the small interaction strength between the two sectors, some hidden hadrons may have a relatively long life-time, which leads to highly displaced vertices in our detector. Often, with large multiplicities of soft particles in jets. Sounds familiar?

The hidden-valley scenario was proposed more than 2 years ago by Matt Strassler and Kathryn Zurek. They didn't have a particular motivation in mind other than exploring exotic collider signatures (although strongly interacting hidden sectors are common in supersymmetric model-building, and no commandment forbids the mass scale in those sectors be GeV-ish, they could also host the dark matter particle). This approach represents the recent change of season in particle theory. In the old days, the particle folk touched only to those models that were "strongly motivated" or "leading candidates". The outcome may prove valuable to posterity, especially to anthropologists. With the LHC approaching, the emphasis has shifted to interesting collider signatures, and fundamental motivations are no longer mandatory. It may well be that shooting at random will prove more successful than following our theoretical prejudices. In this respect hidden valleys have much in common with unparticles, who are similarly unmotivated. The reason why unparticles received much more attention is that they are quite sharply defined, and for this reason they are more comfortable as a bandwagon. On the other hand, hidden valley is a very wide concept, and by the time the model B-71 variant 69 is discussed, the audience is switching to online newspapers. But things may change soon, if the CDF anomaly won't go way...

It should be clear, however, that for the moment there is no hidden-valley model that would explain the CDF anomaly. The biggest problem is the large number of anomalous events reported by CDF. Given that CDF sees some $10^5$ anomalous events, the cross section for the production of the hidden valley particles should be larger than 100 pb. That's already a lot - much more than the standard Higgs production cross section at the Tevatron, and of the similar of magnitude as the production b-quark pairs. Moreover, the required cross section may be even more ridiculous if not all decays of the unknown particles go into muons. For example, in this attempt to fit the signal with 8-tau decays the estimate for the cross-section is 100nb. This seems to be at odds with the assumption that the hidden sector is very weakly coupled to the Standard Model. Furthermore, CDF sees no sign of resonant production, which would be expected if the mediator between the two sectors is not too heavy. Clearly, there's some work to do, for experimenters and theorists alike.

Update: As if a blog post were not enough ;-), here is Matt's brand new paper discussing possible connections of the hidden-valley scenario to the CDF anomaly.

## 6 comments:

Hi Jester

>It may well be that shooting at >random will prove more successful >than following our theoretical >prejudices.

Let x measure the amount of progress in science, by definition.

Probably, random shooting only leads to diffusive development of progress with x \sim \sqrt{t} behavior, while following theoretical prejudices will produce ballistic behavior x \sim t if prejudices are correct :-)

Cheers

Dear Dmitry,

there's a semicanonical compromise of these two approaches to look for the "best".

One tries to go linearly in the direction of the gradient, towards the local optimum, but adds a noise that allows one to jump from a local minimum and find a better valley elsewhere, in the case that the local minimum is not global.

The ratio of these two strategies is dictated by the temperature: the hotter the system is, the higher proportion of the Brownian motion you use. Of course, the more you're certain that you're in the ballpark of the global optimum, the cooler system you should use.

Best

Lubos

Sorry, by x I meant of course x**2 :-)

Lubos, exactly, diffusive behavior of x comes from the Langevin eq., and the white noise strength in the latter is temperature. I think if you cool down too much, then quantum effects may become important - and allow something like tunneling. The tunneling time is exponentially long however, so it's probably always good to get some heat.

Cheers

Arrh,

x**2 \sim t, expectation value of x is proportional to t.

Random walk unfortunately does not reach all locations in dimension >2...

Of course there are much more efficient ways to scan over parameter space of any given model, but if model-building is a random walk in an infinite space of new concepts or local minima, we are unlikely to predict the correct result - even if LHC is infinitely delayed.

Thomas, true. And taking into account the fact that each new step in this walk is exponentially more expensive makes one feel rather depressive.

Cheers

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