ATLAS has better fluctuations…

and CMS has the better analysis.

Fabiola Gianotti made a masterful presentation of the ATLAS Higgs search, and Guido Tonelli made a highly insightful and detailed one for CMS. The presentations were both excellent with a wealth of information that will take time to digest. The bottom line, though, is that both collaborations observe a modest excess around 125 GeV which may – or may not – be the first signs of a standard mode-like Higgs boson.

This is an extremely exciting time, despite all the sober and cautious statements by the speakers, DG, audience and by nearly all colleagues – people are excited by these results. Few people would claim that the Higgs has been found, but its definitely not not there, if you know what I mean.

I will share some personal first impressions here – but I should state clearly that I am a member of the CMS Collaboration, not involved in any of the Higgs searches but heavily involved in electroweak topics, some of which have a direct bearing on the Higgs results. Anyway…

It is plain that the statistical significance of the Higgs results from ATLAS is higher, if interpreted as evidence (not really the right word…) for a signal. They report a combined significance of 3.6σ compared to the CMS combined significance of 2.4σ. To be clear – this does not mean that ATLAS has done a better job or that their analyses are more sensitive. Indeed, they used less integrated luminosity, employed fewer channels and did not utilize any multi-variate techniques. Monte Carlo studies indicate that the CMS search is more sensitive, a priori, but the ATLAS Collaboration was luckier with the roll of the dice – they were dealt a luckier set of cards.

Both Fabiola and Guido made interesting comments within the context of their talks.

Fabiola pointed out that 120 – 130 GeV is a very nice region for the Higgs boson. At first this may seem peculiar, because it is a most challenging one at the LHC. But her point is a very good one: only in this low-mass region can the LHC collaborations expect to see a signal in several different final states (WW, ZZ, 2-photon, ττ, bb, etc.) which would, eventually, allow us to learn a lot about relative branching ratios, mass, spin and couplings. This would not be the case if a Higgs boson showed up at 250 GeV, in which case only WW and ZZ channels would be fruitful. So if the present hint is confirmed, LHC physicists can enjoy years of data analysis and slowly reveal the properties of the Higgs boson signal (if, indeed, that is what they would be observing).

Guido made the clear point that the CMS constraints on the Higgs boson are distinctly weaker than they should be due to the excess in the data – that there is essentially no difference in the mass limit at 95% Cl and 99% CL. This “difficulty” is precisely what one would expect if a new signal indeed is present. In his words, “the excess in the CMS data prevent to go below 127 GeV.” The same is true, of course, for the ATLAS data. He also showed how there is a broad excess in the WW + ττ + bb channels “modulated” by the γγ + ZZ channels. This is a pithy way of describing the current preliminary result.

Anyway, to return to my opening statement (which is tongue-in-cheek of course). I can phrase my impression another way:

1. CMS did more with less, (the apparatus is much smaller than ATLAS) while
2. ATLAS got more for less (the results are “luckier”).

Now let’s see what next year brings!

Update: A very complete set of documents, plots, videos, etc. from CMS is available here: http://cms.web.cern.ch/news/cms-search-standard-model-higgs-boson-lhc-data-2010-and-2011.

ICFA report and Beacons of Discovery

The latest report from ICFA (International Committee for Future Accelerators) was released yesterday, and you can obtain it from http://www.interactions.org/beacons/. The title is Beacons of Discovery – The Worldwide Science of Particle Physics.

The report seems to be aimed at the general public and perhaps politicians who are responsible for science funding – you will not find any critical evaluation of different avenues of future research in this report. For that, you might prefer to view the HEPAP Report from the U.S. Department of Energy, or something like that.

It is interesting that the main emphasis is on the global nature of particle physics research, for example: “Reaching a grand synthesis [of ideas] or discovering the next set of mysteries will require a spectrum of research approaches in nations around the world.” This is a far cry from the competitive approach of “U.S. vs. Europe vs. Japan” that characterized science thirty years ago.

The science questions posed are suitably grand:

1. What message do neutrinos bring from the beginning of time?
2. What’s the matter with antimatter?
3. How can we solve the mystery of dark energy?
4. Are we on the threshold of a whole new understanding of nature’s particle and forces?
5. What is the trajectory of our universe? How did it evolve?
6. Do invisible processes leave their imprint on the world we can observe?
7. What is dark matter?
8. Are there extra dimensions of space?
9. Is there a simple explanation for it all?

There are appropriate pictures of T2K, ATLAS, superconducting RF, various DM experiments and Pierre Auger and Noνa. The importance of particle physics to, e.g., medical techniques and research, and to training and inspiring young minds, is presented.

It is a nice report, very well executed. What grabbed me the most, however, is this (page 22 of the full report):

Members of the CMS group at Northwestern, in front of the CMS detector

I nearly jumped out of my chair when I came to this page, since it shows my group in front of the CMS detector. From the left, the people are Prof. Mayda Velasco, me, Dr. Radek Ofierzynski (postdoc), Steve Won (graduate student) and Andy Kubik (also a graduate student). This picture was taken, among dozens of others, by a professional photographer around 2009, when I was at CERN on sabbatical. None of us knew that our images would be used in a public document like this – not that we are displeased.

It certainly made my day to see our group depicted as a Beacon of International Collaboration!

Theories about Superluminal Neutrinos

Predictably, and happily, several theorists have posted calculations and speculations to the archives, spurred by the observation by the OPERA Collaboration that neutrinos appear to travel faster than the speed of light.

I say “happily” because a result like this one provokes new ideas in the heads of theorists and we all learn something in the process. Of course, experimenters have ideas, too, and I’ll bet that people in MINOS and T2K are hard at work, hoping to confirm or refute the OPERA result.

The theoretical ideas are wildly diverse and most of them are tentative. Although I am not a theorist and I am not capable of judging any of these ideas, I’ll try to convey the essence of the papers I liked the best. No offense to papers that I don’t cite here.

The first paper by Giacomo Cacciapaglia, Aldo Deandrea, Luca Panizzi (arXiv:1109.4980 23-Sep) describes a rather careful quantitative analysis of the available neutrino data – mainly SN1987a, MINOS and OPERA. As I explained
earlier this week, the authors find it difficult to reconcile the lack-of-spread of the MINOS data with a quadratic energy dependence and indicate that some kind of step function at E_ν around 1 GeV is required.

The second paper by Jean Alexandre, John Ellis and Nick E. Mavromatos (arXiv:1109.6296 28-Sep) also look at the question of how strong the E_ν dependence has to be in order to satisfy SN1987a and OPERA. They point out that conventional tachyons don’t fit because the effect should decrease with energy – i.e., the effect for SN1987a would be huge. Despite the difficulties with the data, the authors forge ahead to construct two example theories that allow for superluminal neutrinos. Their first speculation involves a Lifshitz-type Field Theory of gravity, leading to an interesting dispersion relation ω² = m⁶ + M⁴p² + 2M²p⁴ + p⁶, where m is a dynamical mass, M is a mass parameter characterizing Lorentz Violation and p is the momentum. Clearly this rises faster than p², but it still does not fit the data all that well. Their second speculation is more interesting and is based on a Lorentz-violating gauge theory, involving a fermion coupling to a new U(1) gauge field. In this scenario, the light cone seen by fermions differs from the one seen by photons. An interesting point is that this theory generates fermion masses dynamically, and a Higgs mechanism is not needed. A Lorentz-violating term is included in the Lagrangian which alters the fermion propagator. In general, subluminal velocities result from this term, unless one adds a constant background gauge field B_μ. If the couplings are weak but the field is strong, superluminal velocities can occur. An important point is that neutrinos and anti-neutrinos would have different velocities. Also, the velocity would depend on the angle with respect to the background field, B_μ – so some experiments would see a positive TOF with respect to light, others a negative, and some no effect at all. This field B_μ could vary in strength on galactic distance scales, and have little effect on SN1987a while a major effect on earth-based neutrino sources. In any case, a like one of the closing statements by the authors: Superluminal neutrinos should not be discarded as a phenomenological impossibility, but rather be regarded as a scenario to be probed and constrained by experiment. Right on.

The third paper could not be farther in spirit form the second. Written by Andrew G. Cohen, Sheldon L. Glashow (arXiv:1109.6562 29-Sep), the abstract contains the sentence Thus we refute the superluminal interpretation of the OPERA results! The authors have noticed that superluminal particles can slow down by emitting radiation including pairs of fermions, and they completed the lowest-order calculation for neutrinos. The dominant mechanism is ν→ν+e⁺e^-. Although the prefactor is roughtly 10^-6G_F², the rate of emission of the e⁺e^- pairs by the neutrino is proportional to E⁶ and the energy loss is proportional to E⁵. For the 730 km baseline of the OPERA experiment, the terminal energy is 12.5 GeV which is much lower than observed by OPERA – the neutrinos have radiated away the rest. According to Cohen and Glashow, the OPERA energy distribution directly contradicts the notion that the neutrinos are traveling faster than the speed of light. They go on to say that observations by the IceCube Collaboration of multi-TeV neutrinos passing through the earth is an extremely strong constraint on the order of δv/c < 1.7×10^-11. This is a formidable result and its hard to think that the calculation is wrong.

Nonetheless, let me put aside the objection from Cohen and Glashow to point to two interesting papers.

The fourth paper is by A. Nicolaidis (arXiv:1109.6354 28-Sep) who sketches how [sterile] neutrinos could take a “short-cut” through the bulk in an extra-dimensional scenario. You’ll recall that these theories attempt to solve the hierarchy problem by extending Gauss’s Law to extra dimensions in which gravity can propagate but the gauge interactions of the standard model cannot. In essence, the neutrino can follow a geodesic in a many-dimensional space while light and other standard model particles are constrained to move along a curved surface. He writes down a toy model and concludes that one can match the OPERA result with the size of one extra dimension of about 2.7μm and a curvature parameter Ak on the order of 10^-2. He does not discuss the facts from SN1987a or MINOS, however, and hopes that an experiment can be done with NESTOR which is 1676 km away from CERN.

The last paper I’ll mention today (-again- sorry that I do not try to discuss all of the papers that have appeared) was written by Marco Matone (arXiv:1109.6631 29-Sep). This curious paper begins with Hamilton-Jacobi theory in quantum mechanics. I don’t understand the calculations at all but the upshot seems to be that some extra constants of integration appear when one addresses the time evolution of the particle. In a particular rather generic case, the usual result for the velocity of a quantum particle is modified by a function of these extra constants, and this function can have a value greater than one, thereby leading to superluminal solutions. While Matone’s calculation is relativistic, it ignores field theory so it probably cannot be taken at face value. That said, I think it is great that the OPERA result can spur thoughts about fundamental quantum mechanics!

So here’s what we have – ad hoc parametrization of the dispersion relation, two or more parametrizations pulled out of Lorentz-violating field theory, extra dimensions and unconventional quantum mechanics – plus an observation based on “simple” physics that the OPERA results are simply impossible. You might look upon this as theoretical bedlam, but I am happy to see so many creative ideas emerging, which can help shape the experiments we need to do in order to verify or refute the OPERA results.

 

 

SCIENCE hosts a live chat about superluminal neutrinos

If you are reading this blog, then you know I care about the latest results from OPERA. No one knows whether they are right or wrong (most people are highly skeptical, perhaps too much so…) but there is no doubt that this issue has attracted a lot of attention.

SCIENCE magazine does some of the best reporting on science, thanks to the excellent science reporters employed there. So I am happy that SCIENCE will host a live chat about neutrinos traveling above the speed of light. In order to participate, click here:

http://news.sciencemag.org/sciencenow/2011/09/live-chat-have-neutrinos-broken.html

I hope we all can enjoy it!

Trying to Reconcile OPERA, MINOS and SN1987a

I’ve written twice about the contradiction of the OPERA results on high-energy neutrino velocities by the low-energy SN1987a results. I tried to show that this contradiction should not be taken for granted and certainly should not be used to dismiss the OPERA results.

A much better analysis was put forth by Giacomo Cacciapaglia, Aldo Deandrea and Luca Panizzi (arXiv:1109.4980, 23-Sep-2011). The authors made some interesting theoretical remarks regarding possible dispersion relations. I had considered only a quadratic relation (δv/c) = (E_ν/M)² but there are good arguments for other relations, and the authors allowed the exponent to vary (in other words, to be non-integer).

When considering the SN1987a and MINOS data, there are two things to keep in mind:

• the arrival times (or times of flight) of the neutrinos
• the spread of arrival times, or the lack thereof

The authors emphasized the importance of the latter.

For SN1987a, there are a couple dozen events recorded with energies in the 5 – 40 MeV range, and times spreading across 10 or 12 seconds. The range in energies is quite large and should result in a much larger spread of recorded times, if the dispersion relation depends quadratically on the energy. This fact holds quite independently of the near-coincidence of the neutrino signals with the photons coming from SN1987a.

For MINOS, the story is similar. The neutrino energy spectrum peaks around 3 GeV but there is a long tail up to 120 GeV. So if the dispersion is a strong function of the energy, the time structure will be broader than the length of the spill, but this is not observed. If we write δv/c = (1/2)(E_ν/M)^α, then α should not be large. A fit to the MINOS data favors α < 0.5 which means that the actual observed δv/c from MINOS is in tension with SN1987a. The OPERA results make this tension only worse, even without an analysis of the time structure of the OPERA data. (The authors intend to do such an analysis in the near future.)

So the OPERA, MINOS and SN1987a data don’t really allow an interpretation along the lines of δv/c = (1/2)(E_ν/M)^α. (My own analysis did not incorporate the constraints from the lack of spread in time of the SN1987a and MINOS data, and hence was much weaker than this analysis.)

This means that the data require a stronger – perhaps bizarre – dispersion relation. An exponential curve does not work, as it turns out, but a smooth step curve, parametrized by a hyperbolic tangent, can be made to work. The position of the threshold would have to be around 1 GeV, and the rise would have to be quite fast, occurring within 0.1 GeV or so. Here is an example of the allowed parameter space, where δ is δv/c, μ controls the rise at the step, which is given by m.

Cacciapaglia Fig 6c. Solid blue line is the bound from the lack of spread in the SN1987a data, while the dotted line is the arrival time. The green region is preferred by MINOS, and the red, by OPERA.

No one claims that a step function parametrized by a hyperbolic tangent is well-motivated or pleasing. The point is that simpler functions don’t work so well. A second point is that the data are still sparse and poorly understood, so ad hoc treatments meant to give relatively soft answers to the question “Does this all make sense?” are justified.

Certainly an actual quantitative analysis like the one by Cacciapaglia, Deandrea and Panizzi is much better than simple dismissive statements one sees in the blogosphere…

Fitting OPERA’s Result

Yesterday I tried to point out that the results from OPERA are not necessarily contradicted by the SN1987a results.

Today I have tried to take this simple analysis one step further, by fitting a simple quadratic ansatz for the OPERA results and comparing to the SN1987a and also the MINOS measurement (Phys. Rev. D76 072005 2007).

I assumed that

δv/c = (E/M)²

where E is the energy of the neutrino and M is a phenomenological mass parameter to be determined by measurements. A simple χ² linear regression analysis indicates that

M = 7.9 ± 1.4 TeV.

I ignored the systematic uncertainties which are fully correlated between the two OPERA measurements. Continuing to take only the statistical uncertainties into account, I find χ² = 5.9 for one degree of freedom, which is rather poor, but including the systematic uncertainty would improve this value somewhat.

Here is a plot showing the fit:

fit to two OPERA measurements, linear scales

The fit looks incorrect (it passes close to the second point but is far from the first point) because it is constrained to come from the origin (ie, zero neutrino energy means zero deviation). This is not a parabolic fit — it is a linear fit to 1/M². The MINOS data were not included in the fit.

Taking the fit as it is, we can compare to SN1987a again:

fit to OPERA data, compared to SN1987a

The SN1987a constraint is indicated by the dashed line – the region above the line is disallowed. Clearly the red line is not excluded by the SN1987a data.

The MINOS data point appears to be inconsistent with the red line, but one has to be quite careful with a double-log plot like this one. The solid error bars are one-sigma limits as reported by MINOS. The lower two-sigma limit, however, encompasses zero and is indicated by the dotted line. As you can see in the linear plot above, the MINOS data is consistent with the red curve at better than the two-sigma level.

This little analysis does not indicate that the OPERA results are correct, of course. The experimental work done is very impressive and I admire the Lyon group for their achievement. But I agree with everyone else, including the OPERA Collaboration, that confirmation by another experiment is needed before the result can be taken to be true. Meanwhile, common statements that SN1987a rules out the OPERA result should be couched in more tentative language, in my opinion.

OPERA not contradicted by SN1987a

Everyone is talking about the exciting results from OPERA on the superluminal velocities of neutrinos (arXiv:1109.4897, 23-Sep-2011), which were explained in an excellent CERN EP Seminar given this afternoon. The speaker was Dario Autiero (Institut de Physique Nucleaire de Lyon):

Dario Autiero (Institut de Physique Nucleaire de Lyon)

(For excellent accounts of the measurement and implications, see, for example, viXra log and Matt Strassler, among others.)

Many people point out that the OPERA result:

δv/c = (2.48 ± 0.28(stat) ± 0.30(syst)) × 10^-5,

would seem to be contradicted by constraints coming from Supernove 1987a. viXra quotes this constraint as δv/c < 2 × 10^-9 for typical neutrino energies of 10 MeV.

The OPERA analysis was essentially described in a paper by John Ellis, Nicholas Harries, Anselmo Meregaglia, Andre Rubbia, Alexander Sakharov
(arXiv:0805.0253, May 2008) who are motivated by considerations of Quantum Gravity. They consider two scenarios, in which the deviations from c depend linearly or quadratically on the neutrino energy.

Motivated by this idea, and the number quoted on viXra log, I made the following plot. It shows the upper limit on δv/c as a function of the neutrino energy, for the quadratic and the linear assumptions. These limits are drawn as continuous curves (straight lines on a double-log plot). The region above the curve is excluded.

SN1987a limits on δv/c and the OPERA measurements

As you can see, the OPERA points are not exluded by the SN1987a limit as cited by viXra log, in the quadratic case. In the linear case, there is apparently a contradiction.

Of course, this does not mean that the OPERA results are right. Only confirmation by an independent experiment, preferably with different metrology techniques, will convince me and everyone else that this astounding result is correct.

Top background shapes and the CDF MJJ Anomaly

The CDF di-jet anomaly has justly received a lot of attention both in the blogosphere and in the professional scientific press. If real, it would be the biggest discovery in particle physics in several decades.

As discussed on many blogs, from Peter Woit and Adam Falkowski through Sean Carroll and Tommaso Dorigo, the D0 Collaboration released results which appear to refute any claims of new physics in the CDF data. So the question is: how do we explain the CDF bump?

Within the LHC community, a lot of discussion centered on the jet energy scale. If one rescales the energies of the jets, the bump can be accommodated and the description of the W peak improved, but the size of the rescale factor is a bit too large given the knowledge of the calorimetry and the physics of jets. Tommaso has written clearly about this, early on. So I don’t expect this to be the main explanation.

A better possibility, in my opinion, is that the background shapes are not accurate enough. Of course the CDF and D0 collaborations use the best tools available to them, but that does not mean that those tools cannot lead to bad background estimates.

An interesting study was recently posted by Campbell, Martin and Williams from the Fermilab theory group (arXiv:1105.4594, 23-May-2011). I think this paper has not received enough attention. The authors checked the difference between leading-order (LO) parton-shower predictions for the sizes and shapes of the backgrounds to next-to-leading order (NLO) prediction.

They confirmed that the requirement of exactly two jets in the event does reduce the top background significantly, and in that basic sense is a useful cut. Unfortunately, it also increases the systematic uncertainties on the background predictions.

The authors changed the requirement of exactly two jets to at least two jets, as part of their study. The top background is larger by a factor of seven, and has a peaking structure around 150 GeV. Here is the plot from their simulation:

Simulated M_JJ spectra.

Note the broad peak in the top background (blue histogram). This peak coincides with the mass of the CDF anomalous peak. Keep in mind, however that these cuts are not the same as the CDF cuts – the requirement on the number of jets is looser, allowing a lot more top background.

The authors make an additional comparison of the shape of the top background, still with the looser jet requirement. They find that the MCFM Monte Carlo program gives rise to a more peaked version of the top background than the ALPGEN + PS Monte Carlo program used by CDF:

Comparison of top background shapes

The distinction is less impressive, however, for the tighter jet cuts (red histograms). The predictions for the normalization of the backgrounds are very similar for the two Monte Carlo programs.

They also checked the main background, W+jets, and found no important shape differences.

Finally they conclude that large enhancements due to missing higher orders cannot explain the CDF anomaly, and that the background shape should be smooth in the M_JJ region around 150 GeV. So they do not claim to explain the CDF results on the basis of standard model processes, but for me, they do point out that the shape of the top background is somewhat uncertain and happens to peak in the 150 GeV region.

One of the earliest suggestions that top backgrounds may be to blame for the CDF anomaly was made by Plehn and Takeuchi (arXiv:1104.4087, 20-April-2011). Below is a plot showing one of their results. ΔN is an estimate of the change in the background if the WV and top backgrounds are rescaled in mimicry of a systematic error.

WV and top shapes and a mock systematic error

The shifts in background normalization are not small, however, but the authors believe they can be accommodated especially through single-top production. They also point to a lack of theoretical understanding of the jet survival probabilities – important for estimating the amount of top background which survives the N_jet=2 requirement.

A paper by Sullivan and Menon (arXiv:1104.3790, 19-April-2011) comes to very similar conclusions.

It is not obvious that problems with the top backgrounds explain the CDF anomaly, but the issues raised – especially as regards jet vetos – are serious, and instructive for searches at the LHC.

A Discovery At the Tevatron! – Maybe

The CDF Collaboration released this plot today (arXiv:1104.0699, 6-April-2011):

M_JJ distribution, after background subtraction, from CDF

The blue peak at M_JJ = 145 GeV is not predicted by the standard model, of course.

The CDF paper is very clear and sober, and it is good that the collaboration reported these results. Let me outline the analysis in a few paragraphs.

The result does not come from a search for new physics (take note of this please) but rather from an attempt to measure the cross section for di-boson production in which one W decays leptonically (e or μ) and the other boson decays to a pair of jets. The invariant mass distribution includes a peak near the W and Z masses – the red peak in the plot above – as it should. The mass resolution is about 12 GeV and hence not good enough to resolve individual W and Z peaks; the W peak dominates anyway.

There is a huge continuum background from W bosons produced with two jets. At the Tevatron, these jets typically come from radiation off the incoming quarks. Here is the distribution before background subtraction:

M_JJ observed, and compared to SM expectations

As you can see, most events are pedestrian W+2 jets, and the excess clearly shown in the first plot above appears on a rapidly falling spectrum.

CDF have studied V + jets for many years, and have written several important papers on the jet E_T and M_JJ spectra. They also have a long distinguished record in QCD jet studies, so I would not suggest that they simply don’t know how to model the W+jets background. But one can see, looking at the second plot, how challenging this analysis is.

The elements of the analysis are simple: select a good quality, central, isolated electron or muon, and veto an event if there is a second lepton. Ask for a missing transverse energy MET > 25 GeV, to account for the neutrino from the W decay. Reconstruct jets with the CDF standard methods (cone algorithm with ΔR = 0.4) and require E_T > 30 GeV and |η| < 2.4. Furthermore, the di-jet system must have p_T 30 GeV and |Δη| < 2.5. These cuts are dictated by the properties of WV production (i.e., the original aim of the analysis), and do not sculpt the M_JJ spectrum above 100 GeV, according to the article. Nothing weird, tricky or obscure, here.

As already stated, the main background is W+jets, which CDF simulates using ALPGEN+PYTHIA. The normalization of this component comes from fitting the MET distribution. The minor backgrounds are harmless and are normalized by theoretical and measured cross sections.

The initial fit, with no extra peak (red curve in the first plot above), does not describe the data in the 120-160 GeV mass range. For that regions, a Kolomogorov-Smirnov test gives 6×10^-5, which is a very small number (roughly speaking, a p-value). So speculation as such is motivated.

The CDF physicists did the obvious and reasonable thing – they included an extra Gaussian in the fit to the M_JJ spectrum, fixing its width according to the known di-jet mass resolution (13.5 GeV) and allowing the peak position and the height to float. Not surprisingly, they get a good fit, as you can see in the first plot.

They did a careful job evaluating the statistical significance of the peak. No smoke and mirrors here, happily. They took Δχ² as their statistic and used a toy MC technique to evaluate the significance of the peak, including the look-elsewhere effect. They included systematic uncertainties and found that the probability to observe an excess larger than what they see in the data is 7.6×10^-4, corresponding to 3.2σ. If they leave out the systematics (the most important ones are the W+jets renormalization scale, the jet energy scale and the shape of the QCD multijet background), they obtain a probability that is more than seven times lower.

Of course a number of cross checks were done. The excesses in the e and μ channels are compatible. Together they amount to about half of the WV signal, which itself validates the analysis. The physicists tried altering the background shapes by changing the theoretical parameters in their simulations. They varied kinematic thresholds. They tried reweighting the simulation according to the observed R_JJ distribution. This quantity is a measure of the angular separation between the jets, and hence is highly correlated with M_JJ. This test is a bit ambiguous so the question of a mis-modeling of the di-jet angular correlations might not be completely closed. But in any case the excess does not disappear.

Other obvious things to look at: There is no excess in Z+jets. And the jets here in the W+jets sample don’t appear to be b-jets. They simulated a generic di-jet resonance with a cross section of 4 pb, and found that changes in the spectrum as jet thresholds were varied are consistent with the data. There is no structure in M_lν.

So we have a nice, statistically-significant bump in this mass spectrum. Some theorists already posted their hypothesis (Buckley, Hooper, Kopp and Niel, arXiv:1103.6035, 31-Mar-2011) — even before the CDF Collaboration released their results! (I agree completely with Gordon Watts’ comments about this.) You can also read a report in the New York Times. I’ll not comment on that.

Of course, the observation requires confirmation. I am very sure that physicists at both ATLAS and CMS are studying their data carefully. Most probably, the D0 Collaboration will try to say something soon about it, too. So let’s pay attention and keep an open mind. Speculation is fun, but fluctuations do come and go….

(Disclosure: I am in inactive member of the CDF Collaboration but played no part in this analysis. I devote all of my research time to CMS.)

Other bloggers have already commented, ahead of me: See Physics and Physicists, Not Even Wrong, The Reference Frame, A Quantum Diaries Survivor and Cosmic Variance. I’m sure there will be lots of discussions on these blogs – and if I am lucky, a little bit here, too.

Impressive New Results from LHCb

The LHCb Collaboration has accomplished with 37 pb^-1 what the Tevatron experiments required several fb^-1 to do. They put the limit (arXiv:1103.2465, 12-Mar-2011):

Br(B_s→μ⁺μ^-) < 5.6 × 10^-8 at 85% C.L.

Impressive!

What is this about? The B_s meson is neutral and contains a b-quark and an s-quark. In the standard model, the complete annihilation of these two quarks to produce a rather neutral but very distinctive μ⁺μ^- pair is exceedingly rare – the predicted branching ratio is about 0.3×10^-8. Since it is so very small, one can hope that new physics would lead to a large enhancement. Indeed, factors of 10 or a 100 are possible in SUSY if tanβ is large. Observation of this extremely rare decay would constitute an unequivocal discovery of physics beyond the standard model, albeit through a loop effect.

How did the LHCb Collaboration achieve such an impressive result? The main answer is: they have a wonderful detector and they made an intelligent analysis. Here are some of the salient points:

They are looking for a narrow peak on an almost-flat background, so the resolution on the μ⁺μ^- mass is crucial. They truly have a wonderful spectrometer – the momentum resolution is 0.5% at 100 GeV, which is two or three times better than CMS, which is better that ATLAS. This means they can make a narrow window in which to look for B_s decays: they choose ±60 MeV to be compared to the ±120 MeV window from CDF. This already means less background.

Another important fact about their muon sample is its purity. Only 10% of the muons selected for this analysis are really hadrons decaying in flight. So their combinatorial and physics backgrounds can be studied and understood through simulations. In fact, though, their analysis makes minimal use of simulations and follows the kind of self-calibrating methods used in the CDF analysis (arXiv:0712.1708).

Aside from the mass, LHCb uses a so-called geometrical likelihood (GL) which incorporates topological and kinematic information independent from the mass: the decay time, the muon impact parameter, the B impact parameter, the distance of closest approach of the muons, a kind of isolation variable, and the p_T of the B. This GL gives a huge boost to background suppression.

LHCb use an interesting strategy based on bins in mass and the GL. They fit the background and signal in each bin, knowing that some will have background only even if a B_s→μ⁺μ^- signal is present. This allows a nice control of the data – it builds in the concept of control regions in an organic way. Here are the plots of the four bins in GL:

LHCb mass distributions in four GL bins

As you can see, there is plenty of background at low GL, which diminishes quickly for higher GL values. There are, alas, no peaks.

There are many other technical details that I won’t describe here. They concern the careful control of uncertainties on the efficiencies, the handling of the normalization modes and the trigger which is rather amazing in and of itself. Please read through the paper if this analysis interests you.

In the absence of signal, LHCb sets limits on the branching ratio using the standard CLs method:

LHCb limit on B_s

Their limit is completely consistent with expectation, and compares well to the best limit from the Tevatron: 4.3×10^-8, a preliminary CDF result based on 3.7 fb^-1 — i.e., based on one hundred times more luminosity.

(Note: they also set a limit on B_d→μ⁺μ^- but the interest from the SUSY point of view is with the B_s limit.)

This result will not extend exclusion regions in MSSM parameter space because it is not better than existing Tevatron bounds. But one expects some tens or hundreds of pb^-1 by the summer, and at that point, LHCb might actually see a signal (even if only from the standard model). That would be very interesting indeed!