- CoGeNT, for making us drunk with light dark matter.

This experiment created the largest stir in theory this year. CoGeNT, a dark matter detection experiment, announced that it could be seeing dark matter with a relatively light mass, around 10 GeV. The dominating paradigm is dark matter at the weak scale, 100 GeV to 1 TeV, but the CoGeNT result made us stop and think about a wider range theoretical possibilities. Unfortunately, recent exclusion limits results from Xenon10, Xenon100 and CDMS make it highly unlikely that CoGeNT is really observing dark matter. Nevertheless, the lesson we have learned is that dark matter does not have to be where everyone is looking. - D0, for keeping the hopes for new physics alive.

Good old Tevatron gave us one very intriguing result this year. The D0 collaboration looked into same-sign di-muon events, and found that events with two negative muons occur 1 percent more often that those with two positive muons. This result can be interpreted as CP violation in the B-meson system: the Bbar-mesons oscillate into B-mesons a bit more often than the other way around. The Standard Model predicts such an effect, but the asymmetry should be 100 times smaller that what is observed. Is this new particles contributing to the B-meson mixing? Or did D0 screw up? The jury is still out. - PSI, for extending the new physics battlefield into atom spectroscopy.

The surprise of the year, no doubt about it. A laser spectroscopy experiment at PSI measured the Lamb shift in muonic hydrogen, and found it to be 5 sigma away from the prediction based on theory and earlier experiments with ordinary hydrogen. Given that simple new physics models cannot provide a consistent explanation, and that QED is doing shamelessly well everywhere else, we all expect that some theoretical or experimental error is at the root of this anomaly. But the possibility that some quirky new physics manifests itself here is still hanging in the air. - Tevatron, for its tireless Higgs chase.

Tevatron gave us also a completely expected yet very cute result. 10 years ago LEP excluded the Higgs masses below 115 GeV, now Tevatron tells us that Higgs between 156-175 GeV is not the right answer either. Combining that with precision electroweak tests, we deduce that Higgs is cowardly hiding somewhere between 115 and 155 GeV. Poor bastard is thus cornered, and with the LHC joining in the chase he should surrender in no time. Unless he is not there after all... - LHC, for the overall impression.

After a series of setbacks and delays this year LHC surprised us, for a change, with a stream of good news. We had been told that the first year would be a total mess, as it should take a long time to understand the detectors enough to produce meaningful results. Instead, physics results have been delivered basically from day 1, even in difficult channels like jets + missing energy. LHC already published several important limits, e.g. on 4-quark operators (gracefully called "bounds on compositeness"), or on high-energy high-multiplicity events (under the sexy name of "limits on black hole production"). And much more is due to arrive for the winter conferences. It's easy to predict that the LHC will make it to the 2011 highlights on Resonaances; the only question is whether I will remember it for "important limits" again, or for crazy new discoveries...

## Friday, 31 December 2010

### 2010 Highlights

It's the end of the year when blogosphere and old-fashioned press alike indulge in a nostalgic mood. Here is my list of the most exciting events of the passing year in the field of particle physics. From the year 2010 I remember (in chronological order):

## Thursday, 23 December 2010

### Is the CKM matrix going to crack?

During the last decade the Standard Model description of flavor transitions has been put to multiple tests, especially in the B-meson sector. The overall agreement between theory and experiment is excellent, much better than what we should expect assuming exotic particles lurking just behind the corner. Here and there, however, one finds a few glitches - most likely experimental flukes or underestimated theory errors but intriguing enough to keep a flicker of hope alive. This year there has been a lot of commotion about the D0 observation of the same sign di-muon asymmetry, since the Standard Model predicts this effect should be well below the current experimental precision. If the D0 result is confirmed, it would be a clear indication of new physics contribution to CP violation in the mixing of neutral B-mesons. Another, less publicized 3-sigma blip is the tension between:

All this fuzz is about measuring the entries of the CKM matrix - a 3x3 unitary matrix that is the source of all flavor violation in the Standard Model. See the usual parametrization pasted on the right. The parameters λ and A are well measured in several different ways that yield consistent results. Therefore one is more interested in constraints on the remaining two parameters called ρ and η. The 2 processes mentioned in the previous paragraph are sensitive to slightly different combinations of these parameters. The B → τν decay proceeds at tree-level via an off-shell W-boson, so the branching fraction is proportional to the Vub, that is the (13) element. Thus, the measurement of this branching fraction carves out a circle in the ρ,η plane. On the other hand, the CP asymmetry Bd → J/ψ K is due to an interference of tree-level decays and one-loop B-meson mixing, and the final result depends on Sin(2β) where β ∼ Arg[Vtb Vtd/Vcs Vcb ] is one of the angles in the unitarity triangle. This measurement appears as a diagonal line in the ρ,η plane. Now let us see how these two processes combine with several other measurements of ρ and η:

The point is that one can reconcile either of the two measurements with the other constraints on ρ,η but accommodating both is difficult. For example, in the upper plot B → τν is included in the fit to ρ and η. That best fit value uniquely predicts Sin(2β), but the result is off from the experimental value by more than 3 sigma. Conversely, if one uses Bd → J/ψ K in the fit, then B → τν is off by almost 3 sigma. The authors prefer the former interpretation because it provides a better overall consistency of the fit. This interpretation is also more plausible from the new physics point of view, since in general it is easier for new physics to compete with Standard Model loop processes than with tree-level processes. Moreover, this way it may go along better with the D0 di-muon anomaly as the latter is also related to B-meson mixing...

Now, how large is the tension clearly depends on the choice of observables going into the fit,

as well as on your personal beliefs in the errors quoted by various theoretical, experimental and lattice groups whose results enter the fit. For example, in the similar plots presented by the CKMfitter collaboration the errors are more conservative and the tension is not apparent. Clearly, on tabloid blogs such as Resonaances the aggressive approach is promoted, but one should remember that the cautious approach to flavor anomalies is usually right, at least historically. Asymptotically in the future, the new generation of B-factories (who should go online in late two-thousand-teens) will shrink the errors and swipe the floor. In a shorter time perspective, updates from Tevatron may clarify or further blur the situation. And then we're dying to see LHCb joining in the game, some time next year. But the last one is a perfect subject for a separate post...

- the CP asymmetry in the Bd meson decay into J/ψ + kaon,
- the branching fraction of the decay of a charged B meson into a tau lepton and a tau neutrino.

All this fuzz is about measuring the entries of the CKM matrix - a 3x3 unitary matrix that is the source of all flavor violation in the Standard Model. See the usual parametrization pasted on the right. The parameters λ and A are well measured in several different ways that yield consistent results. Therefore one is more interested in constraints on the remaining two parameters called ρ and η. The 2 processes mentioned in the previous paragraph are sensitive to slightly different combinations of these parameters. The B → τν decay proceeds at tree-level via an off-shell W-boson, so the branching fraction is proportional to the Vub, that is the (13) element. Thus, the measurement of this branching fraction carves out a circle in the ρ,η plane. On the other hand, the CP asymmetry Bd → J/ψ K is due to an interference of tree-level decays and one-loop B-meson mixing, and the final result depends on Sin(2β) where β ∼ Arg[Vtb Vtd/Vcs Vcb ] is one of the angles in the unitarity triangle. This measurement appears as a diagonal line in the ρ,η plane. Now let us see how these two processes combine with several other measurements of ρ and η:

The point is that one can reconcile either of the two measurements with the other constraints on ρ,η but accommodating both is difficult. For example, in the upper plot B → τν is included in the fit to ρ and η. That best fit value uniquely predicts Sin(2β), but the result is off from the experimental value by more than 3 sigma. Conversely, if one uses Bd → J/ψ K in the fit, then B → τν is off by almost 3 sigma. The authors prefer the former interpretation because it provides a better overall consistency of the fit. This interpretation is also more plausible from the new physics point of view, since in general it is easier for new physics to compete with Standard Model loop processes than with tree-level processes. Moreover, this way it may go along better with the D0 di-muon anomaly as the latter is also related to B-meson mixing...

Now, how large is the tension clearly depends on the choice of observables going into the fit,

as well as on your personal beliefs in the errors quoted by various theoretical, experimental and lattice groups whose results enter the fit. For example, in the similar plots presented by the CKMfitter collaboration the errors are more conservative and the tension is not apparent. Clearly, on tabloid blogs such as Resonaances the aggressive approach is promoted, but one should remember that the cautious approach to flavor anomalies is usually right, at least historically. Asymptotically in the future, the new generation of B-factories (who should go online in late two-thousand-teens) will shrink the errors and swipe the floor. In a shorter time perspective, updates from Tevatron may clarify or further blur the situation. And then we're dying to see LHCb joining in the game, some time next year. But the last one is a perfect subject for a separate post...

## Friday, 3 December 2010

### Update on Muonic Hydrogen

5 months ago an experimental group at PSI announced the measurement of the Lamb shift in muonic hydrogen. Since muon is 200 times heavier than electron, the muonic hydrogen atom is 200 times smaller than the ordinary hydrogen. Therefore, finite proton size effects are far more pronounced in the former, and end up contributing as much as 2 percent to the Lamb shift. Assuming that the system is adequately described by QED, the PSI result can be interpreted as a new measurement of the size (charge radius) of the proton. The surprise was the deduced value of the charged radius turned out to be inconsistent at the 5 sigma level with the previous determinations based on the spectroscopy of hydrogen and electron-proton scattering data. Something is wrong. Either there is an experimental error, or there is an error in the theoretical computations of the Lamb shift, or maybe some new forces are in the game.

Of course, it is the last of the above possibilities that makes the anomaly attractive to hoards of hungry-eyed particle theorists. In fact, it's not the first mysterious result related to the muon: a 3-point-something-sigma anomaly in the muon anomalous magnetic moment has been nudging us for years. It is tempting to speculate that both these muon anomalies have a common explanation in terms of yet unknown fundamental forces. Furthermore, as I explained here, new hidden forces have recently become very popular in the particle circles for other, completely unrelated reasons. Yet ArXiv has not been flooded with theory papers on muonic hydrogen, so far. The reason is that it's difficult to write down a new physics model that explains the measured Lamb shift without violating constraints from atomic precision physics. The most painful constraints come from

The paper proposes how to shift the energy levels of muonic hydrogen without violating other experimental constraints. The first part is easy: a scalar or vector particle could provide for the new attractive force that does the job. One possibility is to take the mass of the new particle to be of order MeV, and the coupling to muons and protons of order $10^{-4}$ (the contribution to the Lamb shift scales as $g_\mu g_p/m^2$ for m above 1 MeV and $g_\mu g_p m^2/m_\mu^4$ for m less than 1 MeV; thus other choices of the parameters are possible, for example, for a larger mass one would need correspondingly larger couplings). With the couplings and the mass in the same ballpark one could also obtain a new contribution to the muon anomalous magnetic moment that resolves the tension with experiment, see the blue band in the plot.

Now comes the tricky part, that is addressing other experimental constraints. There are some older muonic-atom experiments, for example the one with Mg and Si, who constrain the couplings of new force carriers to muons and protons. However, they are not inconsistent with the coupling strength needed to explain the muonic hydrogen anomaly. But it seems the new force carrier has to couple only to muons and protons and virtually nothing else. For example, the coupling to electrons has to be at least an order of magnitude smaller than that to muons in order to avoid excessive contributions to the anomalous magnetic moment of the electron. The coupling to neutrons is even more strongly constrained by some prehistoric experiments (from 1966!!! back when England last won the world cup!!! ;-) involving low energy neutrons scattering on lead atoms. Furthermore, B-factories strongly constrain the couplings to b-quarks, neutrino experiments strongly constrain the couplings to neutrinos, and so on.

It is simple to cook up a model where the coupling of the new force carrier to electrons is suppressed (a particle coupled to mass), or when the coupling to neutrons is suppressed (a particle coupled to charge), but to achieve both at the same time is a model-building challenge. However this possibility cannot be excluded in a model independent manner, so it open to experimental verification. If a new force carrier is the reason for the muonic anomalies, there should be shifts in the spectrum of other muon systems, such as muonic helium or the true muonium (a bound state of muon and antimuon). Those systems have not been investigated yet, but with the present technology they seem to be within reach. So, if you have some free time this weekend you could try to make the true muonium and measure its energy levels. Depending on the result, life could get very interesting, or it could get as usual...

See also here and here to better appreciate the problems with model building. For a fresh review and reevaluation of the standard QED contributions to the muonic hydrogen energy levels, see here.

Of course, it is the last of the above possibilities that makes the anomaly attractive to hoards of hungry-eyed particle theorists. In fact, it's not the first mysterious result related to the muon: a 3-point-something-sigma anomaly in the muon anomalous magnetic moment has been nudging us for years. It is tempting to speculate that both these muon anomalies have a common explanation in terms of yet unknown fundamental forces. Furthermore, as I explained here, new hidden forces have recently become very popular in the particle circles for other, completely unrelated reasons. Yet ArXiv has not been flooded with theory papers on muonic hydrogen, so far. The reason is that it's difficult to write down a new physics model that explains the measured Lamb shift without violating constraints from atomic precision physics. The most painful constraints come from

- Ordinary hydrogen spectroscopy,
- Anomalous magnetic moment of the electron,
- Low energy neutron scattering experiments,
- Interactions of neutrinos with matter.

The paper proposes how to shift the energy levels of muonic hydrogen without violating other experimental constraints. The first part is easy: a scalar or vector particle could provide for the new attractive force that does the job. One possibility is to take the mass of the new particle to be of order MeV, and the coupling to muons and protons of order $10^{-4}$ (the contribution to the Lamb shift scales as $g_\mu g_p/m^2$ for m above 1 MeV and $g_\mu g_p m^2/m_\mu^4$ for m less than 1 MeV; thus other choices of the parameters are possible, for example, for a larger mass one would need correspondingly larger couplings). With the couplings and the mass in the same ballpark one could also obtain a new contribution to the muon anomalous magnetic moment that resolves the tension with experiment, see the blue band in the plot.

Now comes the tricky part, that is addressing other experimental constraints. There are some older muonic-atom experiments, for example the one with Mg and Si, who constrain the couplings of new force carriers to muons and protons. However, they are not inconsistent with the coupling strength needed to explain the muonic hydrogen anomaly. But it seems the new force carrier has to couple only to muons and protons and virtually nothing else. For example, the coupling to electrons has to be at least an order of magnitude smaller than that to muons in order to avoid excessive contributions to the anomalous magnetic moment of the electron. The coupling to neutrons is even more strongly constrained by some prehistoric experiments (from 1966!!! back when England last won the world cup!!! ;-) involving low energy neutrons scattering on lead atoms. Furthermore, B-factories strongly constrain the couplings to b-quarks, neutrino experiments strongly constrain the couplings to neutrinos, and so on.

It is simple to cook up a model where the coupling of the new force carrier to electrons is suppressed (a particle coupled to mass), or when the coupling to neutrons is suppressed (a particle coupled to charge), but to achieve both at the same time is a model-building challenge. However this possibility cannot be excluded in a model independent manner, so it open to experimental verification. If a new force carrier is the reason for the muonic anomalies, there should be shifts in the spectrum of other muon systems, such as muonic helium or the true muonium (a bound state of muon and antimuon). Those systems have not been investigated yet, but with the present technology they seem to be within reach. So, if you have some free time this weekend you could try to make the true muonium and measure its energy levels. Depending on the result, life could get very interesting, or it could get as usual...

See also here and here to better appreciate the problems with model building. For a fresh review and reevaluation of the standard QED contributions to the muonic hydrogen energy levels, see here.

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