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.

PAMELA's coming-out

Yesterday, PAMELA finally posted on ArXiv her results on the cosmic-ray positron fraction. In the last months there was a lot of discussion whether it is right or wrong to take photographs of PAMELA while she was posing. Here at CERN, people were focused on less philosophical aspects: a few weeks ago Marco Cirelli talked about the implications for dark matter searches, and Richard Taillet talked about estimating the positron background from astrophysical processes in our galaxy. Finally, PAMELA had her coming-out seminar two days ago. PAMELA is a satellite experiment that studies cosmic-ray positrons and anti-protons. She has a better energy reach (by design up to 300GeV, although the results presented so far extend only up to 100 GeV) and much better accuracy than the previous experiments hunting for cosmic anti-matter. Thanks to that, she was able to firmly establish that there is an anomaly in the positron flux above 10 GeV, confirming the previous hints from HEAT and AMS.

Here are the PAMELA positron data compared with the theoretical predictions. The latter assume that the flux is dominated by the secondary production of positrons due to collisions of high-energy cosmic rays with the interstellar medium. The two lines are almost perpendicular to each other :-). In fact, the discrepancy below 10 GeV is not surprising, and is interpreted as being due to solar modulation. It turns out that the solar wind modifies the spectrum of low-energy cosmic rays, and in consequence the flux depends on solar activity which changes in the course of the 22-years solar cycle. Above 10 GeV the situation is different, as solar modulation is believed to produce negligible effects. Even though the secondary production of positrons has large theoretical uncertainties, one expects that it decreases with energy. Such a power-law decrease has been observed in the flux of anti-protons who also may originate from secondary production. The positron fraction, instead, significantly increases above 10 GeV.

Thus, PAMELA shows that the secondary production is not the dominant source of high-energy positrons. The excess can be due to astrophysical sources, for example young near-by pulsars have been proposed as an explanation. But what makes particle physicists so aroused is that dark matter annihilation is a plausible explanation too. It might be that PAMELA is a breakthrough in indirect dark matter searches. It is less known that there are other experiments that see some excess in the cosmic ray flux. Most interestingly, two balloon-borne experiments called ATIC and PPB-BETS see an excess in the total electron+positron flux (they cannot distinguish the two) with a peak around 700 GeV. This adds to the EGRET gamma-ray excess at a few GeV, and to the WMAP haze - an excess of diffuse microwave background from the core of our galaxy.

A dark matter candidate that fits the PAMELA excess, must have rather unexpected properties. If the observed dark matter abundance has a thermal origin, the dark matter annihilation cross section naively seems too small to explain the observed signal. As usual, theorists have magic tricks to boost the annihilation rate today. One is using the so-called boost factor: if dark matter clumps, its density is locally higher than average, and then the average annihilation rate also increases with respect to the case of a uniform distribution. However, this does not save the day for the most popular dark matter candidates. For example, the MSSM neutralino typically requires a boost factor of order a few hundred, which is probably stretching the point. The latest trick is called the Sommerfeld enhancement: if the dark matter particle feels some attractive long range forces (other than electromagnetism, of course), a pair of particles may form a bound state, which enhances the annihilation rate.

Another challenge for particle models is the fact that PAMELA sees no excess in the antiproton flux. This means that the dark matter particle must be hadrophobic, that is to say, it should decay preferentially into leptons. Again, the most popular dark matter candidates, like the MSSM neutralino, do not satisfy this criterion. However, particle models compatible with the PAMELA data do exist, for example Minimal Dark Matter (though this one is not compatible with the ATIC/PPB-BETS peak), or recent Exciting Dark Matter.

So, it seems, we have to wait and see till the smoke clears up. Certainly, a single indirect detection signal has to be taken with all due scepticism (so many have died before). Only combined efforts of several experiments can lead to a convincing conclusion. As for the moment, if somebody pointed a gun to my face and made me choose one answer, I would probably go for an astrophysical explanation. On the other hand, if the PAMELA excess is really a manifestation of dark matter, the LHC could concentrate on more interesting issues than discovering and undiscovering the MSSM. It seems that astrophysicists have at least one more year to sort this thing out by themselves.

A Long-Expected Party

Today, soon after publishing the damage report, CERN is organizing the LHC Inauguration Ceremony. Given that the restart date is unclear (in private conversations, the estimate September 2009 appears most often), some lesser souls may feel dissonance. However, CERN is here to push the frontiers of science, and organizing an opening of a damaged accelerator is truly innovatory. The current DG himself must have had some doubts, as he cautiously writes "Dear Council Delegates, I would like to thank you for your reactions to my suggestion to maintain the LHC Inauguration Ceremony on October 21 2008, as initially foreseen...". Fortunately, the diplomats vehemently supported the idea, since they were already promised molecular cuisine.

Thus, CERN is overrun today by men in suits normally unseen at this latitude. This must be the first time foreign diplomats ever visit Geneva, so that unprecedented security measures were taken. All CERN parkings had to be emptied from cars, and those that remained are likely to be exploded. The roads connecting CERN to Geneva and France are now closed. The public buses that normally take this route run with a police escort, and they are not allowed to stop near CERN. It is not clear if the trespassers will be shot, or only impaled.

If you're curious what's on the menu, there will be a webcast here. This time there will be no live commentary, unless something funny happens. There is a rumor that during the ceremony the current DG will give a speech and vanish.

Gia's Hairy Black Holes

Now that the hope for a quick LHC start-up has literally vaporized, I have six more months to play with particle theory without worrying about experimental constraints. This is a good moment to return to the workshop on black holes that is still trickling here at CERN. Last Friday, Gia Dvali was presenting his ideas concerning gravity theories with a large number of particle species. The subject is more than one year old and I already wrote about it in this blog. Gia is trying to derive general features of field theory coupled to gravity, without making specific assumptions about the underlying quantum gravity theory. To this end he produces gedanken black holes (at the LHC, or anywhere in the Universe) and employs unitarity plus general properties of semi-classical black holes to obtain some interesting conclusions.

In particular, Gia argued one year ago that in a theory with N species of particles there is a bound on the fundamental scale $M_*$ where the gravitational interactions become strong. Namely, the bound reads $M_* \leq M_P/\sqrt{N}$ where $M_P \sim 10^{19}$ GeV is the Planck scale as we know. This opens a possibility to solve the hierarchy problem by postulating $N = 10^{32}$ new particle species at TeV. One can immediately see the analogy to the ADD (as in Arkani-Hamed, Dimopoulos, Dvali) large extra dimensions. In ADD, the relation between the fundamental scale and the Planck scale is $M_P^2 = M_*^2 (M_* R)^n$, where n and R are the number and the radius of the extra dimensions. This relation is in fact equivalent to $M_* = M_P/\sqrt{N}$ because in ADD $(M_* R)^n$ is just the number of graviton KK modes below the cutoff of the theory. Gia argues that the ADD solution to the hierarchy problem is just one example in a larger class: gravity must become strong well below the Planck scale whenever there is a large number of particles species, regardless whether extra dimensions exist or not. The fact that in ADD the multitude of particles species are Kaluza-Klein modes of a higher dimensional graviton is just a red herring.

After the initial proposal Gia has posted several papers further developing this idea. On Friday Gia talked mostly about the consequences for black hole physics summarized in this paper. It turns out that micro black holes in theories with a large number of species have peculiar properties that make them quite distinct from ordinary black holes in Einsteinian gravity. First of all, small black holes with sizes of the order of $M_*^{-1}$ are hairy. This Freudian feature can be argued as follows. Consider a collision of a particle and an anti-particle of one species at center-of mass energies of order $M_*$. The production rate of micro black holes in that collision must also be of order $M_*$ because it is the only scale available. By unitarity, the decay into the same species must also proceed at the rate $M_*$. However, this cannot be true for the decay in the remaining N-1 species: the decay rate can be at most $\sim M_*/N$, while assuming a faster decay rate leads to a contradiction. For example, black hole exchange would lead to a too fast growth of scattering amplitudes that would be at odds with the assumption that the cut-off of the theory is at $M_*$. Thus, the micro black holes in a theory with N species are highly non-democratic, and they need to carry a memory of the process in which they were produced.

As black holes grow heavier and older they should start losing their hair. The scale where the Einsteinian behavior is recovered cannot however be smaller than $M_* N$. Thus, black holes in the mass range $M_P/\sqrt{N} < M_{BH} < M_P \sqrt{N}$ must be non-standard, hairy and undemocratic. The proper black hole behavior, which entails democratic decay to all available species via Hawking radiation, can be expected only for heavier black holes. Again, these properties can be readily understood in the specific example of ADD large extra dimensions as a consequence of the geometric structure of the extra dimensions (for example, the crossover scale to the Einsteinian behavior is related to the radius of the extra dimension). Gia's arguments just generalize it to any theory with a large number of particle species. It seems that some kind of "emergent geometry" and "localization" must be a feature of any consistent low scale quantum gravity theory.

Of course there is a lot of assumptions that enter in that game (no black hole remnants, for example), and it is not unthinkable that the true quantum gravity theory may violate some of these assumptions. Nevertheless, I find amusing that such simple hand-and-all-body-waving arguments lead to quite profound consequences.

More details in the paper.

AdS/CFT goes cold

Last week Dam Son gave two nice talks about phenomenological applications of AdS/CFT:
one about heavy ions, and the other about non-relativistic conformal field theories (CFTs). While the former application is widely discussed in pubs and blogs, the latter is a relatively new development. It seems that, after having entrenched in the heavy ion territory, particle theory has launched another offensive on the unsuspecting condensed matter folk. Not later than yesterday I saw two new papers on the subject posted on ArXiv.

AdS/CFT as we know it relates strongly coupled gauge theories to gravity theories in one more dimension. In the original tables received at Mount Sinai by Maldacena it speaks about highly symmetric and all-but-realistic theories: N = 4 super Yang-Mills on the gauge theory side and 10D type IIB supergravity in $AdS_5\times S_5$ background on the gravity side. Later, the correspondence was vulgarized to allow for phenomenological applications. In particular, some success was reported in postdicting meson spectra of low-energy QCD and explaining large viscosity of the quark-gluon plasma. Heavy ion collisions are total mess, however, and one would welcome an application in the field where the experimental conditions can be carefully tuned. Condensed matter physics enjoys that privilege and, moreover, laboratory systems near a critical point are often described by CFT. The point is that in most of the cases these are non-relativistic CFTs.

A commonly discussed example of a condensed matter system is the so-called fermions at unitarity (what's in the name?). This system can be experimentally realized as trapped cold atoms at the Feshbach resonance. Theoretically, it is described using a fermion field with the non-relativistic free lagrangian $\psi^\dagger \pa_t \psi - |\pa_x\psi|^2/2m$ and short range interactions provided by the four-fermion term $c_0 (\psi^\dagger \psi)^2$. The experimental conditions can be tuned such that $c_0$ is effectively infinite. In this limit the system has the same symmetry as the free theory and, in particular, it has scale invariance acting as $x \to \lambda x$, $t \to \lambda^2 x$. The full symmetry group includes also the non-relativistic Galilean transformations and special conformal transformations, and it is called the Schrodinger group (because it is the symmetry group of the Schrodinger equation). Most of the intuition from relativistic CFT (scaling dimensions, primary operators) carries over to the non-relativistic case.

The most important piece of evidence for the AdS/CFT correspondence is matching of the symmetries on both sides of the duality. For example, the relativistic conformal symmetry SO(2,4) of the SYM gauge theory in 4D is the same as the symmetry group of the AdS spacetime. In the case at hand we have a different symmetry group so we need a different geometric background on the gravity side. The Schrodinger group Sch(d) in d spatial dimensions can be embedded in the conformal group SO(d+2,2). For the interesting case d = 3 this shows that one should look for a deformation of the AdS background in six space-time dimensions, one more than in the relativistic case. In the paper from April this year, Dam Son identified the background with the desired symmetry properties. It goes like this
$ds^2 = \frac{-2 dx^+ dx^- + dx^i dx^i + dz^2}{z^2} - \frac{(dx^+)^2}{z^4}$.
The first term is the usual AdS metric, the last term is a deformation that reduces the symmetry down to the Schrodinger group Sch(d). The light-cone coordinate $x^-$ is compactified, and the quantized momentum along that coordinate is identified with the mass operator in the Schrodinger algebra.

So, the hypothesis is that fermions at unitarity have a dual description in terms of a gravity theory on that funny background. Many details of the correspondence are still unclear. One obstacle seems to be that fermions at unitarity do not have an expansion parameter analogous to the number of colors of relativistic gauge theories. A more precise formulation of the duality is clearly needed.

Quench

Yesterday, CERN was buzzing with rumours that the first LHC collisions should take place during the week-end. This morning, however, there was a major quench in Sector 3-4. As you can see here, some magnets in the affected sector are now at almost 100K. LHC-progress addicts report that pretty scaring entries were appearing in the LHC logbook this morning (fire alarm, power failure, helium leaking into the tunnel), though all the record seems to be deleted now. Although there has been no official news so far, this problem appears to be serious (unlike all the problems reported by the media earlier this week) and may cause a lot of delay. It is not certain if operation will be resumed before the winter shutdown. So you can relax for the moment.

Update: there is a press release explaining what happened:

During commissioning (without beam) of the final LHC sector (sector 34) at high current for operation at 5 TeV, an incident occurred at mid-day on Friday 19 September resulting in a large helium leak into the tunnel. Preliminary investigations indicate that the most likely cause of the problem was a faulty electrical connection between two magnets which probably melted at high current leading to mechanical failure(...)

The crucial information is

(...)it is already clear that the sector will have to be warmed up for repairs to take place. This implies a minimum of two months down time for the LHC operation...

In fact, warming up and cooling of one sector usually takes 3 months, so there is little hope for a beam before the winter shutdown (end of November).

Update 2: :-(

What will the LHC discover

The excitement generated by the LHC kick-off last week is still in the air. I'm beginning to realize that soon we will k.n.o.w. Which means that it's the last moment for gambling and wild guessing. Here are my expectations. The probabilities were computed using all currently available data and elaborated Bayesian statistics.

Higgs boson. Probability 80%
Peter Higgs' kid is ugly and problematic, however his big advantage is that he does his job right. Firstly, he knows how to break electroweak symmetry in such a way that the scattering amplitudes of W and Z bosons remain unitary at high energies. Secondly, if he is not much heavier than 100 GeV, he is consistent with stringent precision tests performed by LEP and Tevatron. No one else can achieve both without complicated gymnastics. That's why Higgs is the safest bet.

Non-SM Higgs boson. Probability 50%
The Standard Model uniquely predicts the couplings of the Higgs to all fermions and gauge bosons. From experience, these couplings are very sensitive to new physics in any form.That's why a precise measurement of the Higgs production cross section and all possible decay rates may be far more exciting than the discovery itself.

New Beyond SM Particles. Probability 50%
That's what particle physics is about, isn't it ;-) Almost any extension of the Standard Model that explains electroweak symmetry breaking predicts some particles in the TeV range. So it seems a good bet that we will see some of the junk. The question is if we will be able to make sense of the pattern that will reveal...

Strong Interactions. Probability 20%
Nature has repeated this scenario all over again: interactions between fundamental constituents become strong and new collective degrees of freedom emerge. Condensed matter physicists see it everyday in their laboratories. In particle physics, the theory of quarks and gluons knowns as QCD at low energies undergoes a transition to a confining phase where it is more adequately described by mesons and baryons. It is conceivable that some of the Standard Model particles also emerge in this manner from a TeV scale strongly interacting dynamics. The problem is that we should have already seen the hints of the composite structure in low-energy precision tests, flavor physics and so on, but we see none of that. The reason why the probability for this scenario remains relatively high is our shameful ignorance of strongly interacting dynamics -- we might have easily missed something.

Dark matter. Probability 5%
All hopes lie in numerology: a stable particle with a weak-scale mass and a typical weak annihilation cross-section of order 1 picobarn would have roughly the right thermal abundance to explain the observed dark matter abundance. If this is the right track, the LHC would grab the most important discovery in the history of collider physics. But we know dozens of other plausible scenarios where the dark matter particle is either too heavy or too weakly interacting to be discovered at the LHC.

Little Higgs and friends. Probability 1%
It is a plausible possibility that the Higgs boson is a pseudo-Goldstone boson whose mass is protected from radiative corrections by approximate global symmetries, a sort of mechanism we see at work in the pion sector of QCD. Proof-of-principle models have been constructed: Little Higgs and Gauge-Higgs unification scenarios. But they are all kind of elephants on elephants...

Supersymmetry. Probability 0.1%
Supersymmetry is just behind the corner. After the LHC she will just pick another corner to hide behind. Supersymmetry will of course be seen at the LHC, just like she was seen in all previous hadron colliders. But, once the data are well understood, she will take a leave and come back into hiding where she clearly feels more comfortable. Susy aficionados should not however be worried. The field will flourish as a new, vast and exciting parameter space above 3 TeV will open for exploration. The wealth of new experimental constraints from the LHC, satellite missions, and dark matter detection experiments will make the-allowed-parameter-space plots colorful and sexy.

Dragons. Probability $e^{-S_{dragon}}$
This possibility was recently pointed out by Nima Arkani-Hamed. The laws of quantum mechanics allow anything to happen, albeit the probability may be exponentially suppressed for complicated (large entropy) objects. CERN officials maintain there is no imminent danger since the putative LHC dragons will be microscopic (small dragons have the smallest entropy, hence the largest probability to appear in particle collisions) and anyway they will quickly suffocate in the vacuum of the beam pipe. Some researchers, however, have expressed concerns that the dragons might survive, grow, burn ATLAS, kidnap ALICE and lock her in a tower. A more comprehensive study of the potential risks is underway.

Black Holes. Probability $0.1*e^{-S_{dragon}}$
Although microscopic black holes have smaller entropy than typical dragons, the advantage of the latter is that they are consistent with the established laws of physics, whereas TeV-scale black holes are not. There are many indirect arguments against TeV scale gravity, from precision tests, through flavor physics, to cosmology. Certainly, dragons are a bit safer bet.