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Caccia al Fotone November 21, 2008

Posted by dorigo in internet, news, personal, physics, science.
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Radio Città Fujiko will feature an interview with yours truly tomorrow, at 10.30AM italian time. The blog of the scientific program called “Caccia al fotone” announces it in a nice post, which you can visit here.

Here is a quick-and-dirty translation:

A “ghost event” at the Tevatron”

10 years of work, a mysterious result, an italian researcher and a lot of hope are already good ingredients to create a “scientific case”. However… this news is much more well known abroad than in Italy…. In one of the two experiments at the Tevatron, the synchrotron operating at the Fermi National Accelerator Laboratory in Batavia, in the United States, some muons have crept out in a unknown way. Not muons from the standard model, generated by proton and antiproton collisions, but some more, and, in particular, from a direction that appears to be different from the collision point. In technical terms: muons that appear to have a different impact parameter.


About this, and a lot more, we will discuss in real time with Tommaso Dorigo, researcher at CDF, author of the paper, and author of one of the scientific blogs most visited in the blogosphere. Hands to your SMS and the PC for your curiosity!

When and Where

Saturday November 22nd, 10.30 – Caccia al Fotone – Radiocittà Fujiko – 103.1 FM – Bologna.


A couple of media bites for italians and russians November 18, 2008

Posted by dorigo in Blogroll, internet, italian blogs, language, news, personal, physics, science.
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Just for the record, allow me to point out here a couple of media bites on the anomalous muon signal published by CDF. They would be easy to miss otherwise, unless you speak russian or italian; in the latter case, even if you do.

The first is an article just appeared online and in print on the russian edition of Newsweek. It profusely quotes me as well as Peter Woit, and it focusses on the aftermath of the CDF publication rather than on the analysis itself. I obtained a rather fallacious italian translation with google, but you may try your luck with your own mother tongue.

The second is a radio interview I will be giving this Saturday (Nov. 22) on Radio Città Fujiko (at 10.30-11.30AM italian time, on the FM at 103.1MHz), in a science popularization program called “Caccia al Fotone” (photon hunt). I do not know the details of what we will discuss, although I know it will loosely center on the tentative new physics signal unearthed by the CDF collaboration a fortnight ago. If you are interested, you can SMS your questions to the radio at 333-1809494, or via email at cacciafotone@radiocittafujiko.it . The program has its own blog too.

A few remarks on Matthew Strassler’s “Flesh and Blood with Multi-Muons” November 17, 2008

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[I know, I know… I had promised that today I would issue a fourth installment of my multi-threaded post on the multi-muon analysis, and instead this morning (well, that depends where you’re sitting) I am offering you something slightly different: instead than concrete details on the analysis, here is a review of a review of the same. I trust you understand that blogs, like newspapers or magazines, have their own priority lists…]

Last evening I read with a mixture of interest and surprise the paper recently appeared on the Arxiv by Matthew Strassler, a theorist from Rutgers University, and a supporter of so-called “hidden valley” models of physics beyond the Standard Model.

The interest stems from obvious reasons: after CDF published the study on multi-muon events, any discussion of the effect, as much as any tentative explanation -be it a mundane or an exotic one- is worth my undivided attention. And, mind you, let me say from the outset that I salute professor Strassler’s thoughts and considerations as useful and stimulating, and the mechanisms he suggests promising avenues for further research on the subject.

But there’s room for surprise, and not all of it is of pleasant nature.

Some of the surprise comes from a few of the remarks contained in the 20-pages document, and some comes from the way it is written. More on the remarks below, while about the way it is written I can say off-hand that I should probably be grateful to theorists these days, since they have started to make their papers free of complicated formulas, at the expense of a rather large rate of unnecessary adjectives: Strassler’s paper has indeed a remarkable formula count of zero.

In general I feel surprised by reading in an Arxiv paper something one usually finds in a blog: a list of ideas and questions concerning a paper published by a respectable scientific collaboration. It looks like prof. Strassler does not have a blog, and so he uses the Arxiv as a dump of his train of thoughts. Incidentally, this blog is of course open to him for a guest post, if he ever wants to try this kind of arena for his ideas.

I guess my criticism on the style boils down to this: it seems less productive to write an Arxiv paper containing a list of ideas and questions -and quite a bit of criticism-, than just picking up the phone and call the authors of the analysis, as I am told many other theorists are doing these days. No, he apparently has not made the phone call yet. That is quite unfortunate, because if he had he would maybe have learned a thing or two about the CDF analysis beyond what is published, and he would have had a chance to find an answer to some of his questions. Then, his ideas might have gotten some useful input and could have been refined. In his paper, instead, they sometimes read like a laundry list (check for instance pages 18-19, where he has seven bullets of plots he asks CDF to produce).

In his preprint Strassler mentions repeatedly that the multi-muon paper is written by “a subset of the CDF collaboration“. It appears that he stresses this fact on purpose, as if it is a datum of scientific importance. Fortunately he does not go as far as to claim that his observation casts doubt on the results, but his lingering on the issue appears strange, and to me, inappropriate. Calling our publication “a paper by a subset of the CDF collaboration” is plain wrong, because the paper is by the CDF collaboration, regardless of who signs it. The collaboration is one, and it is more than a collection of individuals: it admits no subset. I know theorists are much more promiscuous in the way they associate and disperse in different author lists; but a collaboration is a collaboration, and once a member, you only get to decide whether to sign or not a paper, but the collaboration publishes, not you.

This matter is important, so maybe I need to stress it once more. Let me remind everybody that the multi-muon analysis is a CDF publication, and that the CDF collaboration stands by this paper just as much as it stands by every other one of the half thousand it has published in its long, illustrious life. Signing a CDF paper is a great privilege, and since prof. Strassler does not know personally all of the people in CDF (I, for one, never had the pleasure to meet him), nor does he know about the internal discussions that have taken place concerning the publication, he should be expected to leave this issue aside, lest he gives the impression of discussing matters he is wholly unqualified to discuss. This impression is set from the very beginning in Strassler’s preprint, and remains in the background throughout its 20 pages, resonating in a few specific spots.

Let me now go into the contents of the “flesh and blood” paper very briefly. I cannot discuss all of it here today, but I will make an attempt at showing a couple of further examples of what I do not like in it, thereby creating a biased view of my overall opinion: the parts I liked will be left out of this post. Also, in the process of showing what I object to, I will be quoting out of context: a rather reproachable conduct, I must admit, but I have no real choice if I want to make this post shorter than the paper it deals with.

So here is the very incipit of the Introduction:

“Very recently, an unknown subset of the CDF collaboration has signed its name to one of particle physics’ most extraordinary papers”.

Well, after thanking prof. Strassler for the unnecessary, improbable adjective, one is left wondering whether he can compute the ratio of small integers, like 370/600. But, at least until we get to read about his cross section estimates, we prefer to grant that he can, and so we have to hypothesize that maybe, by “unknown subset” he means to say he does not know the 370 authors who signed the “extraordinary paper”. Paraphrasing Oscar Wilde, “To not know an experimentalist is an accident; to not know 370 is carelessness“. But Strassler does know at least two CDF members: these are two of his Rutgers colleagues, who in fact get thanked in the concluding lines of his paper. Unfortunately, they did not sign the CDF publication. From this one might be tempted to speculate that Strassler only got to hear comments and internal information biased in a particular direction…

Yet prof. Strassler is quite clear to state from the outset he is very interested in the CDF analysis:

“No one would be happier than the author of the present note if this “suggestion of evidence” were to hold up under scrutiny”.

I omit discussing whether I find acceptable or not the way he interprets as a “suggestion of evidence” the conclusions of the CDF study, but I cannot fail to explain that he should rather take a ticket and join the line of happy scientists cheering the discovery of new physics, than single out himself as the one. This is a small bit of immodesty which however, after having noted it, I think we should pardon, given that he has indeed worked on hidden valley models for a long time.

We can also pardon him for saying that the paper is “too short given its potential importance“, right in the next paragraph. On this one count, I think he really manages to stand out of the crowd head and shoulders: of all the comments I have heard about the CDF paper, none went so far as to say that the 70 pages were too few.

Then, a sentence I am still trying to decypher:

No serious attempt is made to interpret the data. This exercise may well be helpful […] even if the specific results of [1] (and a related attempt at an intepretation by the experimentalists involved [11]) are eventually discredited.”

Does Strassler mean to say that the study in [11] (the interpretation of multi-muon events, by the original authors of the study) was unserious ? Or does he rather mean it is useful to put together interpretations of similar effects even if they end up straight in the waste bin ? That would justify the career of a lot of theorists…

After the above sentences, which are contained in the introduction, we find section II, which is called “Preliminary comments“. Here I am puzzled to find Strassler’s paper wrestling with the number of events quoted in the CDF publication, reaching odd conclusions. Strassler incorrectly quotes 75 picobarns as the cross-section for ghost events: a number which comes out of the blue, and for which my explanation is the following: he uses the number of ghost events, “153895” as he quotes (forgetting this number refers to the subset of “ghost events” passing loose SVX criteria, but of that I can pardon him, he has a thing with subsets), and he assumes this corresponds to 2.1 inverse femtobarns of data. Then, \sigma = N/L would do the trick: 150k divided by 2k inverse picobarns is indeed 75 picobarns . Is this what he computed ? Well, it is wrong, since the luminosity corresponding to the 153,895 events is 742 inverse picobarns, and not 2.1/fb. See, this is one of the many instances when one cannot help noticing that a phone call before submitting to the Arxiv would have been a good idea. Cross section estimates are best left with experimentalists, otherwise what will we do for a living ?

Also odd is his following remark:

“if the efficiency estimate were in error for a subclass of events, and the efficiency were only, say, 23.4 percent, then the number of ghost events would drop by 1/5”.

Now, please. CDF publishes a paper, it quotes an efficiency (24.4+-0.2%), and it estimates an excess. What do we get if a theorist, albeit a distinguished one, ventures to say that if the efficiency were wrong (by 5-sigma from the quoted value), the excess would be significantly different ? I miss the scientific value of that sentence. Wait, there is more: only a paragraph below he insists:

“For these two reasons, we must view the number of unexplained ghost events as highly uncertain”.

Excuse me: we own the data, we publish an estimate, we give a uncertainty. You may well question whether it is correct or not, but simply saying an estimate is “highly uncertain” without coming down to explain what mechanisms may have caused an error in the CDF determination of the efficiency, is not constructive criticism, and is rather annoying. Not to mention that the CDF publication where the ingredients for the determination of that efficiency were measured is not quoted in Strassler’s paper!

Ok, I think I have done enough commenting for today. To conclude this post, I will quote without commentary a few sentences which I find peculiar. I have to say it: while the CDF paper is not the clearest I have had the pleasure to sign, I feel the need to stand by it when I see it attacked by non-constructive criticism.

  • “…the paper[…] is far too short given its potential importance, and many critical plots that could support the case are absent”.
  • No serious attempt is made to interpret the data”.
  • “It is not clear why these checks were not performed”.
  • “There are a number of other plots whose presence, or absence, in Appendix B of [1] is very surprising. In particular, though obviously presented so as to support the interpretation of [11], the plots in Appendix B do not actually appear to do so.”
  • “…the challenges that this analysis faces are useful as a springboard for discussion. Clearly, if there were a signal of this type in the data, it would indeed by quite difficult to find it, and the approach used in [1] is far from optimal.”

After this list of less-than-constructive comments, let me quote Freeman Dyson for a change:

“The professional duty of a scientist confronted with a new and exciting theory (or data) is to try to prove it wrong. That is the way science works. This is the way science stay honest. Criticism is absolutely necessary to make room for better understanding.”

Am I the only one to think Dyson meant constructive criticism ?

UPDATE: version 2 of Strassler’s paper came out on November 17th, a week after version 1. This new version makes no mention at all of the “subset” of CDF authors. I thank Matthew Strassler for realizing this correction was useful.

Some notes on the multi-muon analysis – part III November 12, 2008

Posted by dorigo in news, physics, science.
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This is the third part of a multi-part post (see part 1 and part 2) on the recent analysis sent to Phys.Rev.D by the CDF collaboration (including myself -I did sign the paper!) on their multi-muon signal, which might constitute the first evidence for new physics beyond the Standard Model -or the unearthing of a nagging background which has ridden several past CDF analyses, particularly in the B quark sector. I apologize with those of you who feel this post is above your head: the matter discussed is really, really complicated, and it would be almost impossible to make it accessible to everybody. I have made an attempt at simplifying some things, and summarizing each step of the discussion below, but I understand it might remain rather obscure to some of you. Sorry. My only way to repair is to make myself available to explain anything in more detail, at your request…

Today, I wish to discuss one additional source of background to the “ghost” sample, which -I remind you as well as myself- consists of an excess of events where the two triggering muons left no hits in the inner layers of the CDF silicon detector; this excess results from a subtraction of known sources of muon pairs from the original sample. Identified muon tracks in the ghost sample are measured to possess an abnormally large impact parameter (impact parameter is the minimum distance between backward-extrapolated track and collision point, in the plane transverse to the beam direction); the distribution of these impact parameters shows a long tail
suggestive of the decay in flight of a long-lived particle.

As I discussed earlier, there are in principle four different sources of such muons: real or fake muons, with either a well-measured, large impact parameter, or with an impact parameter
which is large because of a wrong reconstruction of the track. In the paper, these combinations are rather divided into the different physical processes that may give rise to such signatures:

  1. punch-through of light hadrons mimicking a muon signal, which are a source of fake muons with large impact parameter;
  2. misreconstructed muon tracks from B decays, which are a source of real muons for which impact parameter may be mismeasured;
  3. in-flight decays of light hadrons (\pi \to \mu \nu, K \to \mu \nu), which are a source of real muons with badly measured impact parameter;
  4. secondary nuclear interactions in the material contained in the tracker, which cause tracks to have a large impact parameter, and may in principle be a source of fake muons.

In this post I would like to discuss the last category among the four listed above: nuclear interactions in the detector material. In a future post of this series we will see why this potential
source of background, together with muonic decays in flight of long-lived hadrons (essentially kaons and pions, \pi^- \to \mu \nu, K^- \to \mu \nu and their charge-conjugate reactions), is particularly important to understand.

Now, the CDF tracker is built with light materials: a thoughtful effort during design and construction was made to insert as little matter as possible, in order to minimize several effects known to worsen the detector performance in terms of momentum resolution, tracking efficiency, occupancy, and other parameters. The most important of these effects are multiple scattering, photon conversions, and indeed, nuclear interactions.

[Incidentally, little material is a good thing, but zero material would be a disaster! In vacuum, charged particles cannot be tracked, because there are no atoms to ionize, and without ionization, the particle path cannot be reconstructed. Gaseous mixtures work well for that purpose, allowing a measurement which does not affect the particle momenta appreciably. But other, more aggressive designs, are possible: silicon wafers throughout the tracker volume, as in the CMS detector, or scintillating fibers, as in the D0 tracker, are two meaningful alternatives.]

So, let me discuss below shortly the three processes mentioned above, for a start.

Multiple scattering affects all electrically charged particles. It is the combined result of all electromagnetic interactions between a charged particle and the atoms of the traversed medium: a cumulative effect that produces a deviation from the original direction of the particle. The deviation increases with the square root of the depth of material traversed, pretty much as random walk, brownian motion, and similar diffusion processes. Multiple scattering is mostly relevant for low-momentum particles, whose trajectory can be affected by relatively small forces.

Photon conversions are instead the result of the process called “pair production”, which is of course only relevant to, well, photons. Since, however, photons are the inevitable result of neutral pion decay (\pi^\circ \to \gamma \gamma), they are actually quite frequent in hadronic collisions, and their phenomenology cannot be ignored. A relativistic photon in vacuum cannot materialize into an electron-positron pair, because it cannot simultaneously conserve energy and momentum in the process; however, the pair creation may occur in the presence of a static source of electromagnetic field, like a heavy nucleus, which absorbs the needed recoil. The thicker with heavy nuclei a particle tracker is, the harder it is for energetic photons to dodge nuclei, wading their way through the tracker and into the surrounding electromagnetic calorimeter, where they are finally encouraged to convert by lead nuclei. In the
calorimeter, pair production and electron bremsstrahlung cause the creation of a cascade, enabling a measurement of the photon’s energy. In principle, the detection of energetic photons, which are quite interesting particles at a collider for a number of reasons, could also happen by the identification of the pair-produced electron and positron in the tracker, but this is less efficient and the produced pairs would increase the detector occupancy, hindering the reconstruction of the events.

[In the figure on the right is shown the distribution of the radius (transverse distance from the beam line) where a photon conversion originated an electron-positron pair inside the CDF tracker. You see spikes at radii where material is concentrated: these are the silicon ladders and support structures, and the inner wall of the COT cylinder (on the right). As you see, photon conversions really provide a radiography of the tracker.]

Finally, nuclear interactions are the means by which the energy of hadrons -both charged and neutral, this time- is measured in hadronic calorimeters. They occur when a hadron hits directly a nucleus of the “absorber” -the passive material used in those devices-, thereby producing a few additional hadrons by strong interaction. These secondary particles may in turn hit other nuclei, with the generation of a hadronic cascade. Like photon conversions, nuclear interactions are to be avoided inside the tracker, because they confuse the event reconstruction. And like conversions, nuclear interactions depend on the amount of nuclear matter. A slight difference exists: conversions, being sensitive to the electrical field of the nucleus, increase with the atomic number Z; nuclear interactions instead depend on the number of nucleons, A. But this is a detail…

Now, if we suppose for a moment that energetic hadrons hitting the detector material contained inside the tracker volume (ladder support structures of the silicon microvertex detector, or the silicon wafers themselves, wires in the tracking chamber, or the inner cylinder of the vessel) are capable of creating showers of secondaries -well, let’s say at least pairs of them-, and if we further imagine that some of those secondaries will produce punch-through (hadrons managing to traverse the calorimeter and leave a signal in the muon chambers), we get a mundane physical process which creates muon candidates with large impact parameter: a large impact parameter is guaranteed by the fact that the secondary interactions occur several centimeters away from the primary interaction point, and any secondary particle emitted at even small angle from the direction of the incoming hadron would not point back to the primary interaction point.

It is to be noted that if hadronic nuclear interactions produced a sizable amount of punch-through in our data we would automatically have an excess of “ghost” muons, because the sample composition, extracted from events where the muons left hits in the inner silicon layers, would not include these “secondary muons”, and an extrapolation towards muons with no inner SVX hits would fail to account for the total, leaving a deficit equal to the size of that background.

It must also be stressed that, in principle, we know that the above hypothesis -nuclear secondaries making it to the muon detector in numbers- is on shaky ground from the outset. That is because nuclear interactions are kept at a minimum by the way the tracker
is built
. We know the amount of material we have used to build the tracker: we have weighted on a scale the darn thing before inserting it inside the solenoid! Moreover, we have conversions, as shown in the plot above, and they cannot lie.

The authors of the multi-muon analysis have studied this background with care anyway. They took all the muons in the sample, and paired each of them up with any track contained in a 40 degree cone around them. Then, the pair was required to have a common origin: with two three-dimensional paths, the best way to check this is to “fit” the two paths together, finding the most likely point in space from where they may have originated. Of course, most pairs of tracks miss each other by kilometers, but a few do fulfil the requirement. This may be due to sheer chance -after all, each muon may be paired with several tracks-, to the two-body decay of a parent particle (we saw two examples in part 2 of this series: K^\circ \to \pi^+ \pi^- and \Lambda \to p \pi^-, where the muon takes the role of one pion), and to nuclear interactions. In the latter case, the muon is a punch-through hadron, by construction: nuclear interactions do not yield real muons!

Once a sample of well-fitting pairs was collected, the authors studied the distance R from the beam line of the point of origin of the pair. While neutral kaons and lambda decays should show an exponential tail in R, nuclear interactions should show spikes in correspondence to the concentrations of nuclear matter, in close similarity to the conversion radius plot shown at the beginning of this post.

The R distributions for muons with hits in the inner silicon layers is shown in the first graph below, while the R distribution for events belonging to the “ghost” sample is shown in the second one.

Let me now try to explain the shape of these distributions.

First of all: what do negative R values mean ??? R is defined as negative when the vertex between the muon and the paired particle occurs on the emisphere opposite to the one containing the muon. The emisphere is centered on the primary interaction vertex: a negative R means that the two tracks have been paired by chance, because there is no known physics that allows a particle to be created in a proton-antiproton collision at the center of the detector, travel one way, decay or interact with a nucleus, and produce two other particles in the opposite direction: momentum must be conserved in the interaction that produced the two vertexed particles!

Second: you observe that R values consistent with zero are the most likely. This is not surprising: most of the tracks in any proton-antiproton collision come from the primary vertex (R=0), so casual combinations of these tracks with muon tracks will favor that radius for the two-track vertex, unless muons are heavily displaced from it. [While the ghost sample does exhibit a very long tail in the impact parameter distribution, there are many of them with a small value of that quantity: the ghost sample is indeed estimated to be contaminated with non “exotic” background sources, and these will have a peak at zero impact parameter regardless of the silicon hits they possess.]

Third: you get a rapidly falling distribution in R, for both positive and negative R. This also is due to the fact observed above, that random tracks primarily come from the primary interaction vertex. Actually, since combinatorics should create two equally populated tails on positive and negative values of R, you get to size up the “excess” of vertices at positive R, which is due
to the combination of nuclear interactions AND V-particle decays (K^\circ \to \pi^+ \pi^- and \Lambda \to p \pi^-), the background we have discussed in part II of this series. For ghost events, V-particle decays contribute about 8%. It is quite unfortunate that a plot of the R distribution for background-subtracted V-particle vertices has not been produced, and overimposed -or subtracted- to the distributions shown above. However, I have to give it to the authors: it is an irrelevant issue. What these plots tell us is that…

Fourth: there are no spikes in these distributions. They are smoothly falling, indicating that there are no concentrations of locations, at fixed R, around the beam pipe from which multiple
hadrons originate. The observation is meaningful, because we know that the material in the tracker is concentrated at very particular values of R -a result of having designed the detector with a roughly cylindrical symmetry around the beam axis. The distributions shown above do not exclude that nuclear interactions may contribute with punch-through muons, because elastic interactions, which are by no means rare, would not appear as two-track vertices; the same can be said of ones producing only one charged hadron plus several neutral ones.

Because of that, nuclear interactions affect the estimate of the ghost component of dimuon data in a way not easy to size up. If the ghost sample was only a numerical excess of muons with very large impact parameter, the case would be closed here: Occam’s razor would force us to stick to known sources to explain our observations, and no new physics could be invoked by a reasonable physicist. However, in the following parts of this multi-thread post we will come to finally discuss the characteristics that make multi-muon events anomalous stuff: the fact that they, indeed, contain multiple muons; and that these additional muons won’t listen to QCD predictions as far as their impact parameter, or the invariant mass they make with the
triggering muon, are concerned.

Some notes on the multi-muon analysis – part II November 8, 2008

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In this post, as I did in the former one, I discuss a self-contained topic relevant for the estimation of mundane sources of “ghost” muons, the anomalous signal recently reported by CDF in data collected in proton-antiproton collisions at 1.96 TeV, generated by the Tevatron collider in Run II. The data have been acquired by a dimuon trigger, a set of hardware modules and software algorithms capable of selecting in real time the collisions yielding two muons of low transverse momentum.

The transverse momentum of a particle is the component of its momentum in the direction orthogonal to the proton-antiproton beams. In hadronic collisions, large transverse momentum is a telling feature: the larger are transverse momenta of particles, the more violent was the interaction that generated them. In contrast, the longitudinal component of momentum is incapable of discriminating energetic collisions from soft ones, because the collisions involve quarks and gluons rather than protons and antiprotons. Quarks and gluons carry a unknown fraction of their parent’s momentum, and they generate collisions whose rest frame has a unknown, and potentially large longitudinal motion. Imagine a 100 mph truck hitting a 10mph bicycle head-on: after the collision the bicycle, and maybe a few glass pieces from a front lamp of the truck, will be found moving in the original direction of the truck, with a speed not too different from that of the truck itself. In contrast, when two 100 mph trucks hit head-on, you will be likely to find debris flying out at high speed in all directions. The transverse speed of the debris is a tale-telling sign that an energetic collision happened, while the longitudinal one is much less informative.

The reason why above I made sure you understood the importance of transverse momentum is that I am going to use that concept below, to explain what may mimic a muon signal in the CDF detector -an issue of crucial relevance to the multi-muon analysis. If you do not know what the multi-muon analysis is about, I suggest you go back to read the former post, and maybe the first one announcing the new CDF preprint. Otherwise, please stay with me.

Now, the dimuon trigger works by selecting events with two charged tracks pointing at hits in the CMU and CMP muon chambers, which are detectors located on the outside of the CDF central calorimeter -a large cylinder surrounding the interaction point, the tracker, and the solenoid which produces the axial magnetic field in which charged particles are made to bend in proportion to their transverse momentum. The dimuon trigger also applies loose requirements on the transverse momentum of the two tracks: 3 GeV or more. By comparison, the single muon trigger used by CDF to collect W and Z boson decays requires transverse momenta in excess of 18 GeV. The loose threshold of the dimuon trigger is possible because of the rarity of two independent, coincident signals in the muon chambers: a single muon trigger with a 3 GeV threshold would instead totally drown the data aquisition system.

Muons are minimum-ionizing particles, and given their momentum we know pretty well how deep they can reach inside the lead and iron which compose the calorimeters: as drivers short of gas, they gradually lose their momentum at a well-defined rate by ionizing the surrounding medium, and they eventually stop. The CMU detectors -wire chambers which indeed detect “hits”, i.e. localized ionization left by muon tracks- are surrounded by 24 inches of steel, and on top of that thick shield lies a second set of muon detectors, the CMP chambers. Muons need at least 2 GeV of transverse momentum to reach the CMU and leave hits there, or at least 3 GeV to make it to the CMP system and leave a signal there as well. When they do, they get to be called “CMUP muon candidates”. A muon candidate which leaves a signal in both the CMU and CMP chambers is a very, very clean one: as good as it gets in CDF.

Why do I insist in calling muons “candidates”, in the face of the cleanness of CMUP muons ? Because a muon signal at a hadron collider will always be plagued with background from hadrons punching through the calorimeter, producing muon chamber hits and thus faking real muons. Hadrons, unlike muons, are made of quarks, and so they cannot traverse large amounts of dense matter unscathed. As they leave the interaction point and enter the calorimeters, most of the times hadrons hit a heavy nucleus, producing some downstream debris which in turn gets absorbed by other nuclei. Thus, because hadrons are not minimum-ionizing particles, they have a much harder time than muons to reach the CMU detector, and a harder time still to make it to the CMP. Despite that, hadrons are so copiously produced in proton-antiproton collisions that one of them occasionally punches through the calorimeter system and reaches the CMU or the CMP detectors: the rarity of the punching through the calorimeter is compensated by the enormous rate with which hadrons enter it.

Now, if muons may be faked by hadrons, one has to reckon with the possibility that the “ghost” sample evidenced by CDF -muon candidates with abnormally large impact parameters, I venture to remind- may be composed, or at least contaminated, by hadrons with very large impact parameter. Hadrons with very large impact parameter ? This immediately brings a particle physicist to think of short K-zeroes and Lambdas!

Short K-zeroes, labelled K_S^\circ, have a lifetime of about a tenth of a nanosecond. They may thus travel several centimeters in the CDF tracker before disintegrating into a pair of charged pions, K \to \pi^+ \pi^- (a relativistic particle makes a bit less than 30 centimeters in a nanosecond). These pions will have definitely a large impact parameter. Now, imagine it is a lucky day for one of these pions: it gets shot through the calorimeter by the kaon decay, and it sees heavy nuclei whizzing around as it plunges deep in the dense matter. After dodging billions of nuclei, and losing energy at a rate not too different from that of a muon through ionization of the medium, it makes it to the CMU chamber, leaves a hit there, enters the 24 inches of iron shield, dodges a few billion more nuclei, and makes it through the CMP too, creating further hits! A CMUP muon candidate!

The same mechanism discussed above can in principle provide a large impact parameter muon candidate through the decay to a proton-pion pair, \Lambda \to p \pi^-: here the negative pion may be the hero of the day. Lambdas have a lifetime of 0.26 nanoseconds: together with short K-zeroes, these particles were called “V-particles” in the fifties, because they appeared as V’s in the bubble chamber pictures, such as the one below.

[In this picture we see the process called “associated production of strangeness”. The strong interaction of a negative pion (the track entering from the left which disappears) with a proton at rest produces two strange particles -a anti-kaon and a Lambda, which produce the two “V’s”. The reaction is \pi^- p \to \Lambda \bar K \to p \pi^- \pi^+ \pi^-. I remind you that the anti-kaon has the quark content d \bar s, while the Lambda is a uds triplet. Strong interactions conserve additively the strangeness quantum number, and since S=0 in the initial state, S must be zero after the strong collision, so the S=+1 of the Lambda must be balanced by the S=-1 of the anti-kaon. Also, note that the weak decay of the two strange particles violates strangeness conservation: at the end of the chain, we are left with no strange particles!]

How to estimate the background due to V particles to the ghost muon signal ? Again, we use the very same dimuon data containing ghost events. We take a muon candidate and pair it up with any oppositely-charged track detected in the CDF tracker. We only care to select pairs which may have a common point of origin, and this fortunately reduces quite a bit the combinatorics. What do we make of these odd pairs ? We assume that the muon is in truth a charged pion, and that the other particle too is a pion, and we proceed to verify whether they are the product of the decay of a K^\circ. Lo and behold, we do see a peak in the pair’s invariant mass distribution, as shown in the plot on the right! The peak sits at the 495 MeV mass of the neutral kaon, as it should, and has the expected resolution.

“Now wait a minute,” I can hear the courageous reader who reached this deep into this post say, “you said you took a muon and a pion and made a mass with them, and you find a K-zero ? But K-zeroes do not make muons!”. Sure, of course. That is the whole point: the muon candidates which belong to the nice gaussian bump shown in the plot are not real muons, but heroic pions that made it through the calorimeter: fake muons!

A similar procedure produces the plot shown on the left, where this time we tentatively assigned the proton mass to the other track. A sizable \Lambda^\circ signal appears on top of a largish combinatorial background!

We are basically done: we count how many V particles we found in the data, we divide this number by the efficiency with which we find the V’s once we have one leg in the muon system (a number which the Monte Carlo simulation cannot get wrong too much, and which is roughly equal to 50%), and we get an estimate of the number of ghost muons due to hadron punch-through with lifetime. Since there are about 5300 kaons and 700 lambdas, this makes an estimate of about 6000/0.5 = 12,000 fake muons in the ghost sample: about 8% of the original signal.

Actually, we can be even tidier than just counting fake muons. We can play a nice trick that experimental particle physicists find elegant and simple. You see the mass distribution for the kaon signal above ? Imagine you make three vertical slices around the kaon: a central one including the gaussian bump, and two lateral ones half as wide. To be precise, let us say we select events with 445<M<470 MeV as the left sideband; events with 470 < M < 520 MeV as the signal band, and <520 < M < 545 MeV as the right sideband. To first approximation, the number of non-kaon track pairs making the two “sidebands” is equal to the number of non-kaon track pairs in the central band, because they approximately contain the same number of events, once you neglect the gaussian signal -which is due to kaons. The approximation amounts to assuming that the background has a constant slope: certainly not far from the truth.

Now, you can take the events in the central band, and create a distribution of the impact parameter of the muon candidate track they contain (a sure fake muon, for the K signal; and a regular muon for the rest of the events). Then, you can take the sidebands and make a similar distribution with the muon candidates those sideband events contain. Finally, you can subtract this second impact parameter distribution (non-classified muons) from the first one (certified fake muons). Mind you, it will not happen frequently to you to subtract signal from a background to study the background -it usually happens the other way around! In any case, what you are left with is an histogram of the impact parameter distribution expected from fake muons from hadronic punch-through with large impact parameter. Neat, ain’t it ?

The impact parameter distribution is shown in the plot on the right above. Observe that these V-particle decays (hyperons have been also added to the distribution shown) do produce muon candidates with quite large impact parameters: I remind you that B-hadrons have died out when the impact parameter is larger than about five millimeters. Is this the source of ghost events ? Well, yes, 8% of it. In the CDF article, the authors are careful to explain from the outset that they treat ghost muons as a unidentified background, and they proceed to try and explain it away -eventually failing. Well: the simple punch-through mechanism discussed here accounts for 8% of it, but not much more.

The plot of the impact parameter of fake muons from hadron punch-through seen above can be directly compared with the plot of impact parameters of ghost muons, since both the x-axis and the y-axis have the same boundaries. I attach the original ghost-muon IP plot on the left, so that one can compare the two effortlessly. You can see that while the distribution of impact parameter is not too different in the two plots, the ghost muons (black points here) are more than one order of magnitude more numerous, especially at large impact parameters.

Some notes on the multi-muon analysis – part I November 8, 2008

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Of all the critics to my stand in the recent online discussion about the connection between Giromini’s and Arkani-Hamed’s papers, the only one who managed get me upset was Andrea, who argued that I was wasting my time on the issue, answering vacuous comments in the thread with vacuous objections, while it would have been much better if I spent it to discuss the CDF paper, about which I could maybe produce some useful details and insight for my readers.

The comment got me upset because Andrea was right, damnit. The problem is that the CDF paper discusses such a complicated analysis, and my time the last few days has been so limited, that I just was unable to do it; while answering comments is a duty which I cannot bring myself to neglect, and which after all can be handled with less concentration, bit-by-bit when I have small chunks of spare time.

Today, I want to start commenting on some aspects of the multi-muon analysis produced by CDF. I have little time to invest, so I will do a poor job. But maybe concentrating on a detail at a time may allow me to shed some light without saying just obvious things.

Now, we have learned that CDF is seeing an excess of muon candidates with abnormally large values of impact parameter.

What is a particle’s impact parameter ? Imagine you are shooting an arrow at a target, and imagine you miss the bull’s eye by a foot. That one foot is the impact parameter of the arrow’s path: the minimum distance between the arrow’s trajectory and the bull’s eye. Of course particles fly away from the point where protons and antiprotons collide, and not toward it: so the example is rather deceiving, but its ease of visualization makes it worth using it.

There are many other features of these weird events that require an explanation, but let us focus today on the very existence of these muon candidate tracks, in “ghost events”: ones that, by definition, have the muon apparently produced outside of the beam pipe, a 1.5-cm radius cylinder surrounding the beam axis inside the CDF detector. There are several possible sources of muon candidates with large impact parameter. These sources can belong to four distinct categories:

(1) ones that produce real muons with real large impact parameter;

(2) ones that produce real muons with badly measured impact parameter;

(3) ones that yield fake muons with real large impact parameter;

(4) ones that yield fake muons with badly measured impact parameter.

I will discuss class (2) in this post, but let me take (1) for a start, to make a few points. Real muons are a rare thing at a hadron collider, because they are the result of weak interactions, and weak interactions are rare in comparison to the strong interaction processes characteristic of hadron collisions. If we exclude a process called Drell-Yan (which is an electromagnetic process, but still relatively rare, and responsible only for an instantaneous creation of muon pairs, which thus have impact parameters compatible with zero) and the very distinguishable decay of W and Z bosons, all muons at a hadron collider are the result of the weak decay of hadrons: B hadrons (ones containing a long-lived b-quark), D hadrons (ones containing a c-quark), and lighter ones – especially kaons and pions, which are extremely frequent (tens per event, typically).

B hadrons are the most notable source of muons with large impact parameter: they disintegrate on average in 1.5 picoseconds, and by the time they do, they have traveled a few millimeters from the point where they are created -the primary interaction point. About 10% of the times, B hadrons produce a muon in the decay; and even when they do not, they produce particles which in turn may disintegrate producing a muon: all in all, about 23% of the times you should expect a B hadron to yield one muon track. So, B hadrons are indeed a source of real muons with large impact parameter: the B-hadron-originated muon does not, in general, point back to the proton-antiproton interaction point, any more than a bit of an exploding grenade is emitted in the same direction of  motion of the grenade before the explosion.

The authors of the multi-muon analysis took great care to determine the fraction of the analyzed data (which is made by events which contain at least two muons) due to the production of B hadrons. There are several ways to do this, and I do not wish to discuss that issue here; indeed, the same CDF paper does not discuss the estimation of B hadrons in the data carefully, because this has been done in a previous publication by the same authors. In any case, the result is that B hadrons have no chance of explaining the presence of muons with impact parameters in excess of a few millimeters in CDF data. The B hadrons simply do not live long enough to travel that far.

Despite the lapidary sentence above, B hadrons do not just contribute to class (1) above, but also, in principle, to classes (2) and (3). This should not surprise you too much: real muons from B hadron decays might be subjected to reconstruction errors by the tracking algorithms, creating a badly measured impact parameter, resulting in a signature of class (2); and on the other hand, B hadrons do create many tracks with large impact parameter -not just muons- by means of their long lifetime, and if the tracks have even a slight chance of mimicking a muon, you get just that: fake muons with large impact parameter, class (3).

A problem with the tracking algorithm is not something easy to study with Monte Carlo simulations -these are to some extent idealizations which picture a rosier world than the intricate one we live in-, so the best way to check for the possibility of class (2) contributing to the signal of muons with abnormally large impact parameter is to use experimental data. A nice feature of B hadron decays is that when these particles contain a b-quark, their semi-leptonic decay may produce a negative muon and a charm quark; while when they contain a anti-b-quark, the decay yields a positive muon and a anti-charm quark. Oftentimes, the (anti)charm will bind into a neutral (anti)D meson, which soon in turn decays to a pion-kaon pair. We thus get the following decay chains:

B^- \to \mu^- D^\circ \to \mu^- K^- \pi^+;

B^+ \to \mu^+ \bar D^\circ \to \mu^+ K^+ \pi^-.

By examining the two decay chains above, you immediately observe that the muon has the sign of the kaon. This makes a very good way to find out whether the “ghost” events behave like B decays or not: whether, that is, one can identify the muons in ghost events to B-decay muons which have badly measured impact parameters.

The authors have searched the detector close to their muon tracks for pair of oppositely-charged tracks which made a common vertex, thus reconstructing D^\circ \to K \pi decay candidates. In events where the muon originates within the beampipe (the subset of the data which should contain most of the B quark decays), one observes that when the muon and the track assigned to the kaon have the same charge, a prominent D signal appears in the invariant mass distribution of the pion-kaon pairs; while, when muon and kaon have opposite charge, no D signal is present: this is well-known and it in fact is a sanity check that allows to spot and size-up the B hadron content of the data. However,  when “ghost” events are selected (ones where muons are produced outside of the beam pipe, i.e. farther than 1.5 centimeters from the beam line), no D signal is evident either in right or wrong sign combinations. What this tells us is that the muon in ghost events is not produced by B hadron decays.

On the right are shown four K-\pi invariant mass distributions in two panels. On the first one (above) you can see the D° signal appear as a gaussian bump on top of a large background in right-sign combinations (black histogram) in the track-track mass distribution, which contains “beam pipe muons”; wrong-sign combinations (red, hatched) do not have the D° signal, as expected. On the bottom panel, no difference is evident between right-sign (in black) and wrong-sign (in red, hatched) combinations: no D° signal is associated with “ghost” muons, underlining the fact that these events are not due to B decays.

One comment is in order. This bit of the multi-muon analysis is maybe the least controversial among the complex chain of logical inferences which constitute it. There can be really no doubt that, among all the plausible sources of “ghost” events unearthed by CDF, B hadron decays cannot play a significant role. As I have had the occasion to mention in this blog elsewhere, particle physicists usually drop all objections when presented with clear, significant resonance peaks such as the one contained in the top graph above: those are the real “smoking guns” of the reality of elementary particles, and no argument holds against them!

In the next post of this series I will discuss another source of background to the tentative new-physics signal evidenced by the CDF multi-muon analysis: punch-through muons from kaon and pion decays.

Nima Arkani-Hamed’s letter on multi-muons – and my reply November 3, 2008

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I had the pleasure of seeing Nima Arkani-Hamed -an IAS/Harvard University theoretician- visit this blog this morning. Nima, together with some colleagues, published three weeks ago a couple of papers where they discussed the possibility that hadron colliders put in evidence a signature of new physics in the form of lepton jets, produced by particles with long lifetime – a signature strikingly similar to the one CDF published a few days ago.

In the thread developed at Peter Woit’s site Neal Weiner, a colleague of Nima and a co-author of his papers, claimed:

“I can tell you officially we had no word on this. This blog is, in fact, the first I’d heard of it.”

and I replied, in my usual talk-first-think-later style:

“that is pretty hard to digest. Lepton jets with lifetimes. Come on. I think you owe it to the physics community to let us know where the leak came from.”

I later regretted, as I often do, to have been so explicit in saying what I think. But the fact remains that many among my colleagues think the same thing, so the physics community does need some sort of explanation. Nima’s comment, which I paste below, somehow fills that gap, although he also complains with me for what I wrote, implying I said Neal is a liar. I did not call Neal a liar: their paper has many authors, and even just one of them might have heard news about a multi-lepton signal in CDF to come out soon, and this might have been the source of the coincidence. Anyway, here is what Arkani-Hamed wrote:


Interpretation of multi-muons! November 3, 2008

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The CDF authors of the study which is causing ripples in the blogosphere have published tonight a second paper, where they try to interpret the excess of events with large impact-parameter muon tracks within a phenomenological model of new physics. You can find their paper here.

In short, they try to fit the observed muon multiplicity within narrow cones, as well as their quite peculiar kinematic characteristics, with the decay of a heavy object which produces a cascade of long-lived particles, ending with a multi-muon signature.

The paper was born as part of the other document (see the story in the post below), but was extracted from it and published separately since this was the best way to proceed promptly to a publication of both. As you see by checking the arxiv entry, this second preprint has only the names of the very authors of the study on the multi-muon anomaly.

I will have more detail on the physics later…

CDF publishes multi-muons!!!! October 31, 2008

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NB: This post is aimed at physicists.. However if you are not one, but you are really curious, you might find out that for once the annoying feeling of reading cryptic jargon is paid back by some real news!

I guess the most important message of the post you are about to read is: Do not check the arxiv today if you really cannot spend a couple of hours reading. Make it three. The  paper just released by CDF, titled “Study of multi-muon events produced in ppbar collisions at sqrt(s)=1.96 TeV” is guaranteed to have you fastened to the chair until you are done with its 70 pages.

The article reports on a very careful investigation produced by CDF, using Run II data collected by a trigger selecting events with two (or more) muons of low transverse energy. The study addresses two or three long-standing inconsistencies in measurements of bottom quark production and phenomenology at the Tevatron:

  • the cross section for b \bar b production appears in good agreement with next-to-leading order QCD predictions when b-quarks are tagged by a reconstruction of their decay vertex, while it is found to be significantly larger when the cross section is measured by identifying b-quarks through their semileptonic decay;
  • the invariant mass spectrum of pairs of leptons produced in sequential semileptonic decays (b \to l X \to l l' Y) is not well modeled by the simulation of b-flavored hadrons in CDF;
  • the value of the time-integrated mixing probability of b flavoured hadrons is measured at the Tevatron to be significantly larger than that measured by LEP experiments.

The source of these apparently unrelated inconsistencies is traced back by the study to a sample of events where muons are originated several centimeters away from the primary interaction point (the proton-antiproton collision vertex), which makes b-quark decay as implausible a source as any other Standard Model process, no better than the other backgrounds which the study shows to be insufficient explanation for the observed events: punch-through from pions and kaons, or secondary hadronic interactions in the detector material.

Once a large sample of such weird events are statistically isolated -better say evidenced- in the sample, a further anomaly is found in the number of additional muons contained in narrow cones around the original ones, something which cannot be easily explained with conventional physics. The paper discusses the characteristics of these events, without falling in the trap of putting together an exotic explanation. Instead, what is made clear in the paper is that those measurements quoted above -lepton-based cross sections and phenomenology of b-quarks studied in high-energy hadron collisions- are affected by the findings described in this paper.

Below I offer two plots extracted from the preprint. The first one shows the impact parameter distribution of muons in the events constituting the anomalous signal (black points), compared to the impact parameter of muons attributable to QCD sources (in red). The impact parameter resolution for these tracks is 2.5 times smaller than the bin size. One observes a abnormal tail of muons with very large impact parameter. I recall that the impact parameter, which is measured in the plane transverse to the beam direction, is the distance of closest approach of the backward extrapolation of the track to the primary interaction vertex. A impact parameter of one centimeter is huge, given that the typical decay length of a B meson is of the order of a pair of millimeters.

On the right you see an exponential fit to the impact parameter distribution of the trigger muons for the anomalous events, for events with just two (top) or more than two (bottom) muons inside two narrow cones around the trigger muons. The distribution agrees with the decay of a particle with a lifetime in the 20 picosecond range.

To quote the paper, the first lines of the Introduction offer a quite clear picture of the situation:

“This article presents the study of events, acquired with a dedicated dimuon trigger, that we are currently unable to fully explain with our understanding of the CDF II detector, trigger, and event reconstruction. We are continuing detailed studies with a longer timescale for completion, but we present here our current findings.

The conclusions are also clear, but I will leave them to those of you who want to read a paper which might, just might, constitute the first evidence of physics beyond the Standard Model, ever.

That said, if you have read this blog long enough, you know me for a tough sceptic. I of course would be simply delighted if the CDF signal of multi-muons really were a first evidence for new physics; but I have to play the devil’s advocate, and so one word of caution, make it five paragraphs, is mandatory. Of course, despite the evidence is pretty solid from a statistical standpoint, one must lean back and take a breath. We are discussing the possibility that something really spectacular has just lurked out of CDF data. Extraordinary claims require extraordinary evidence, and once statistical evidence is plain, one must delve with systematics. CDF did, and they have not found any significant source which might account for the effect. But investigations should and will continue.

Is CDF sure about the impossibility of explaining this effect away ? No, CDF does not exclude that possibility, although it is my opinion that the collaboration has reviewed the paper with more care and detail than most of the other papers it has published in its illustrious, 25-year-long life. That means nothing in terms of the likelihood that this result is indeed new physics. It just says we are as sure as we can be that we cannot presently explain it with known sources. Also worth mentioning is that CDF is a really disciplined collaboration, which has really been careful with their claims so far. And the present paper is no exception.

Is there a simple New Physics explanation of the observed effect ? No, as far as I understand no existing model of new physics predicted such a signature in advance, although one must acknowledge that a few ideas exist in the literature which might have a connection with the effect, if proven real. However, there is a paper discussing a similar signature, which probably benefitted from knowing the CDF result in advance from an internal source. I will leave this issue to another time and another place.

Can CDF find more evidence in the near future ? Yes, the analysis of electron events may shed more light on the matter, and although electrons are harder to isolate than muons when they have a low energy, the analysis will be carried out.

Can D0 find a similar signal ? Surely. D0 is a similar detector to CDF, and although their charged particle tracking is slightly inferior to CDF’s, their muon system is more extended, and their silicon detector is also at least as good as that of CDF (ok, even slightly better). The problem with D0, I think, is the time it will take to perform such a complicated analysis. One must not forget that before focusing on these anomalous events, CDF produced a lengthy investigation of the correlated b \bar b cross section, which is the back-bone of the multi-muon analysis, since it demonstrates the understanding of heavy flavors in low-transverse-momentum lepton samples in CDF when particles with large impact parameter are excluded. So, it may take a while to D0 to confirm or disprove the effect CDF is now publishing.

Does the signal hint at other anomalies in different analyses ? That, I am sorry to say, is anybody’s guess. If the multi-muon events are a signal of new physics, then I am sure there is something else to be found, somewhere. The problem is: what is that ? One might be tempted to speculate that data samples collected in past experiments could in principle contain a similar signature: charged tracks with very large impact parameter have been seldom studied at colliders, and tracking algorithms might have purposely discarded those tracks, or could be proven inefficient in their collection. For instance, CDF does collect, with its fantastic SVT trigger, events containing tracks showing a significant impact parameter. However, the efficiency with which the SVT collects those events, if studied as a function of impact parameter, dies out much too soon. Hell, nobody designs a detector aimed at collecting a new physics signature no theorists have thought about!

I imagine hordes of theoretical physicists canceling flights, conferences, and courses today, making room for some serious thinking in their agendas. Good luck!

UPDATE: see the interesting discussion developing at Peter Woit’s site, where he points out a paper by Arkani-Hamed and collaborators which appears quite extraordinarily to have foreseen the above signature of new physics, in a very timely fashion!

UPDATE: there are other bloggers who’ve discussed this. Lubos, Carl, Matti (happy birthday Matti). Others to be added soon…

UPDATE: other excellent, entertaining bloggers have added their own comments to the story: Jester, Chad, theorema egregium. In italian: Marco. In dutch: astroblogs.

UPDATE: John, a fellow collaborator in CDF and one very skilled physicist, explains the result at cosmic variance.