Hitchhiker's Guide to Ghosts and Spooks in Particle Physics

On Halloween this year the CDF collaboration at Fermilab's Tevatron announced the presence of ghosts in their detector. And not just one meager Poltergeist rattling his chain, but a whole hundred-thousand army. As for today, the ghosts could not be exorcised by systematical effects. While waiting for theorists to incorporate the ghosts into their favorite models of new physics it is good to know that the CDF anomaly is by no means the only puzzling experimental result in our field. There are other ghosts at large: I guess most of them are due to unknown systematical errors, but some may well be due to new physics. Below I pick up a few anomalous results in subjective order of relevance. The list is not exhaustive - you are welcome to complain about any missing item.

So, off we go. In this post I restrict to collider experiments, leaving astrophysics for the subsequent post.

Muon Anomalous Magnetic Moment

This experimental result is very often presented as a hint to physics beyond the Standard Model. For less oriented: there is nothing anomalous in the anomalous magnetic moment itself - it is a well-understood quantum effect that is attributed to virtual particles. But in the muon case, theoretical predictions slightly disagree with experiment. The E821 experiment in Brookhaven measured $a_\mu = (11 659 208 \pm 6)\cdot 10^{-10}$. The Standard Model accounts for all but $28\cdot 10^{-10}$ of the above, which represents a 3.4 sigma discrepancy.

The discrepancy can be readily explained by new physics, for example by low-energy supersymmetry or by new light gauge bosons mixing with the photon. But there is one tiny little subtlety. The Standard Model prediction depends on low-energy QCD contributions to the photon propagator that cannot be calculated from first principles. Instead, one has to use some experimental input that can be related to the photon propagator using black magic and dispersion relations. Now, the discrepancy between theory and experiment depends on whether one use the low-energy e+e- annihilation or the tau decays as the experimental input. The quoted 3.4 sigma arises when the electron data are used, whereas the discrepancy practically disappears when the tau data are used. It means that some experimental data are wrong, or some theoretical methods employed are wrong, or both.

In near future, a certain measurement may help to resolve the puzzle. The troublesome QCD contribution can be extracted from a process studied in BaBar, in which a photon decays into two pions (+ initial state radiation). There are rumors that the preliminary BaBar results point to a larger QCD contribution (consistent with the tau data). This would eradicate the long-standing discrepancy of the muon anomalous magnetic moment. But, at the same time, it would imply that there is a flaw in the e+e- annihilation data, which would affect other measurements too. Most notably, the electron data are used as an input in determining the hadronic contribution to the electromagnetic coupling, which is one of the key inputs in fitting the Standard Model parameters from electroweak observables. As pointed out in this paper, if the low-energy QCD contribution where larger than implied by the electron data, the central value of the fitted Higgs boson mass would decrease. Currently, the electroweak fit determines the Higgs boson mass as $77^{+28}{}_{-22}$, which is already uncomortable with the 114 GeV direct search limit. Larger QCD contributions consisent with the tau data would increase this tension. Interesting times ahead.

Forward-Backward Asymmetry

CERN's LEP experiment has been desperately successful: it beautifully confirmed all theoretical predictions of the Standard Model. The mote in the eye is called $A_{fb}^b$: the forward-backward asymmetry in decays of the Z-boson into the b-quarks. This observable measures the asymmetry in the Z boson interactions with left-handed b-quarks and right-handed ones. The results from LEP and SLD led to a determination of $A_{FB}^b$ that deviates 3 sigma from the Standard Model prediction. On the other hand, the total decay width of the Z-boson into the b-quarks (summarized in the so-called Rb) seems to be in a good agreement with theoretical predictions.

One possible interpretation of these two facts is that the coupling of the Z-boson to the right-handed b-quarks deviates from the Standard Model, while the left-handed coupling (who dominates the measurement of Rb) agrees with the Standard Model. At first sight this smells like tasty new physics - the Zbb coupling is modified in many extensions of the Standard Model. In practice, it is not straightforward (though not impossible) to find a well-motivated model that fits the data. For example, typical Higgsless or Randall-Sundrum models predict large corrections to the left-handed b-quark couplings, and smaller corrections to the right-handed b-quark couplings, contrary to what is suggested by the electroweak observables.

Maybe this discrepancy is just a fluke, or maybe this particular measurement suffers from some systematic error that was not taken into account by experimentalists. But the funny thing is that this measurement is usually included in the fit of the Standard Model parameters to the electroweak observables because...it saves the Standard Model. If $A_{FB}^b$ was removed from the electroweak fit, the central value of the Higgs boson would go down, leading to a large tension with the 114 GeV direct search limit.

Bs Meson Mixing Phase

The results from BaBar and Belle led to one Nobel prize and zero surprises. This was disappointing, because flavor-changing processes studied in these B-factories are, in principle, very sensitive to new physics. New physics in sd transitions (kaon mixing) and bd transitions is now tightly constrained. On the other hand, bs transitions are less constrained, basically because the B-factories were not producing Bs mesons. This gap is being filled by the Tevatron who has enough energy to produce Bs mesons and study its decays to J/psi. In particular, the mass difference of the two Bs eigenstates was measured and a constraint on the phase of the mixing could be obtained. The latter measurement showed some deviation from the Standard Model prediction, but by itself it was not statistically significant.

Later in the day, the UTfit collaboration combined the Bs meson data with all other flavor data. Their claim is the Bs mixing phase deviates from the Standard Model prediction at the 3 sigma level. This could be a manifestation of new physics, though it is not straightforward to find a well-motivated model where the new physics shows up in bs transitions, but not in bd or sd transitions.

NuTeV Anomaly

Nu-TeV was an experiment at Fermilab whose goal was a precise determination of the ratio of neutral current to charged current reactions in neutrino-nucleon scattering. Within the Standard Model, this ratio depends on the Weinberg angle $\sin \theta$. It turned out that the magnitude of the Weinberg angle extracted from the NuTeV measurement deviates at the 3 sigma level from other measurements.

It is difficult to interpret this anomaly in terms of any new physics scenario. A mundane explanation, e.g. incomplete understanding of the structure of the nucleons, seems much more likely. The dominant approach is to ignore the Nu-TeV measurement.

HyperCP Anomaly

This measurement was sometimes mentioned in the context of the CDF anomaly, because the scales involved are somewhat similar. Fermilab's HyperCP experiment found evidence for decays of the hyperon (a kind of proton with one s quark) into one proton and two muons. This by itself is not inconsistent with the Standard Model. However, the signal was due to three events where the invariant mass of the muon pair was very close to 214 MeV in each case, and this clustering appears very puzzling.

The HyperCP collaboration proposed that this clustering is due the fact that the hyperon first decays into a proton and some new particle with the mass 214 MeV, and the latter particle subsequently decays into a muon pair. It is very hard (though, again, not impossible) to fit this new particle into a bigger picture. Besides, who would ever care for 3 events?

GSI Anomaly

For dessert, something completely crazy. The accelerator GSI Darmstadt can produce beams of highly ionized heavy atoms. These ions can be stored for a long time and decays of individual ions can be observed. A really weird thing was noticed in a study of hydrogen-like ions of praseodymium 140 and promethium 142. The time-dependent decay probability, on top of the usual exponential time-dependence, shows an oscillation with a 7s period.

So far the oscillation remains unexplained. There were attempts to connect it to neutrino oscillations, but this has failed. Another crazy possibility is that the ions in question have internal excitations with a small $10^{-15}$ eV mass splitting.