It rarely happens that four days pass without a new post on this site, but it is never because of the lack of things to report on: the world of experimental particle physics is wonderfully active and always entertaining. Usually hiatuses are due to a bout of laziness on my part. In this case, I can blame Vodafone, the provider of the wireless internet service I use when I am on vacation. From Padola (the place in the eastern italian Alps where I spent the last few days) the service is horrible, and I sometimes lack the patience to find the moment of outburst when bytes flow freely.

Things I would have wanted to blog on during these days include:

• The document describing the DZERO search of a CDF-like anomalous muon signal is finally public, about two weeks after the talk which announced the results at Moriond. Having had in my hands a unauthorized draft, I have a chance of comparing the polished with the unpolished version… Should be fun, but unfortunately unbloggable, since I owe some respect to my colleagues in DZERO. Still, the many issues I raised after the Moriond seminar should be discussed in light of an official document.
• DZERO also produced a very interesting search for production. This is the associated production of a Higgs boson and a pair of top quarks, a process whose rate is made significant by the large coupling of top quarks and Higgs bosons, by virtue of the large top quark mass. By searching for a top-antitop signature and the associated Higgs boson decay to a pair of b-quark jets, one can investigate the existence of Higgs bosons in the mass range where the decay is most frequent -i.e., the region where all indirect evidence puts it. However, tth production is invisible at the Tevatron, and very hard at the LHC, so the DZERO search is really just a check that there is nothing sticking out which we have missed by just forgetting to look there. In any case, the signature is extremely rich and interesting to study (I had a PhD doing this for CMS a couple of years ago), thus my interest.
• I am still sitting on my notes for Day 4 of the NEUTEL2009 conference in Venice, which included a few interesting talks on gravitational waves, CMB anisotropies, the PAMELA results, and a talk by Marco Cirelli on dark matter searches. With some effort, I should be able to organize these notes in a post in a few days.
• And new beautiful physics results are coming out of CDF. I cannot anticipate much, but I assure you there will be much to read about in the forthcoming weeks!

Hot off the press: Mark Williams, a DZERO member speaking at Moriond QCD 2009 -a yearly international conference in particle physics, where HEP experimentalists regularly present their hottest results- has shown today the preliminary results of their analysis of dimuon events, based on 900 inverse picobarns of proton-antiproton collision data. And the conclusion is…

DZERO searched for an excess of muons with large impact parameter by applying a data selection very similar, and when possible totally equivalent, to the one used by CDF in its recent study. Of course, the two detectors have entirely different hardware, software algorithms, and triggers, so there are certain limits to how closely one analysis can be replicated by the other experiment. However, the main machinery is quite similar: they count how many events have two muons produced within the first layer of silicon detector, and extrapolate to determine how many they expect to see which fail to yield a hit in that first layer, comparing to the actual number. They find no excess of large impact parameter muons.

Impact parameter, for those of you who have not followed this closely in the last few months, is the smallest distance between a track and the proton-antiproton collision vertex, in the plane transverse to the beam direction. A large impact parameter indicates that a particle has been produced in the decay of a parent body which was able to travel away from the interaction point before disintegrating. More information about the whole issue can be found in this series of posts, or by just clicking the “anomalous muons” tab in the column on the right of this text.

There are many things to say, but I will not say them all here now, because I am still digesting the presentation, the accompanying document produced by DZERO (not ready for public consumption yet), and the implications and subtleties involved. However, let me flash a few of the questions I am going to try and give an answer to with my readings:

• The paper does not address the most important question – what is DZERO’s track reconstruction efficiency as a function of track impact parameter ? They do discuss with some detail the complicated mixture of their data, which results from triggers which enforce that tracks have very small impact parameter -effectively cutting away all tracks with an impact parameter larger than 0.5cm- and a dedicated trigger which does not enforce an IP requirement; they also discuss their offline track reconstruction algorithms. But at a first sight it did not seem clear to me that they can actually reconstruct effectively tracks with impact parameters up to 2.5 cm as they claim. I would have inserted in the documents an efficiency graph for the reconstruction efficiency as a function of impact parameter, had I authored it.
• The paper shows a distribution of the decay radius of neutral K mesons, reconstructed from their decay into pair of charged pions. From the plot, the efficiency of reconstructing those pions is excessively small -some three times smaller than what it is in CMS, for instance. I need to read another paper by DZERO to figure out what drives their K-zero reconstruction efficiency to be so small, and whether this is in fact due to the decrease of effectiveness with track displacement.
• What really puzzles me, however, is the fact that they do not see *any* excess, while we know there must be in any case a significant one: decays in flight of charged kaons and pions. Why is it that CDF is riddled with those, while DZERO appears free of them ? To explain this point: charged kaons and pions yield muons, which get reconstructed as real muons with large impact parameter. If the decay occurs within the tracking volume, the track is partly reconstructed with the muon hits and partly with the kaon or pion hits. Now, while pions have a mass similar to that of muons, and thus the muon practically follows the pion trajectory faithfully, for kaons there must be a significant kink in the track trajectory. One expects that the track reconstruction algorithm will fail to associate inner hits to a good fraction of those tracks, and the resulting muons will belong to the “loose” category, without a correspondence in the “tight” muon category which has muons containing a silicon hit in the innermost layer of the silicon detector. This creates an excess of muons with large impact parameter. CDF does estimate that contribution, and it is quite large, of the order of tens of thousands of events in 743 inverse picobarns of data! Now where are those events in the DZERO dataset, then ?

Of course, you should not expect that my limited intellectual capabilities and my slow reading of a paper I have had in my hands for no longer than two hours can produce foulproof arguments. So the above is just a first pass, sort of a quick and dirty evaluation. I imagine I will be able to give an answer to those puzzles myself, at least in part, with a deeper look at the documentation. But, for the time being, this is what I have to say about the DZERO analysis.

Or rather, I should add something. By reading the above, you might get the impression that I am only criticizing DZERO out of bitterness for the failed discovery of the century by CDF… No, it is not the case: I have always thought, and I continue to think, that the multi-muon signal by CDF is some unaccounted-for background. And I do salute with relief and interest the new effort by DZERO on this issue. I actually thank them for providing their input on this mystery. However, I still retain some scepticism with respect to the findings of their study. I hope that scepticism can be wiped off by some input – maybe some reader belonging to DZERO wants to shed some light on the issues I mentioned above ? You are most welcome to do so!

UPDATE: Lubos pitches in, and guess what, he blames CDF… But Lubos the experimentalist is not better than Lubos the diplomat, if you know what I mean…

Other reactions will be collected below – if you have any to point to, please do so.

• Matti Pitkanen
• Marco Dal Mastro”

The paper by Thomas Gehrmann and collaborators I cited a few days ago has inspired me to have a closer look at the problem of understanding the features of extensive air showers – the phenomenon of a localized stream of high-energy cosmic rays originated by the incidence on the upper atmosphere of a very energetic proton or light nucleus.

Layman facts about cosmic rays

While the topic of cosmic rays, their sources, and their study is largely terra incognita to me -I only know the very basic facts, having learned them like most of you from popularization magazines-, I do know that a few of their features are not too well understood as of yet. Let me mention only a few issues below, with no fear of being shown how ignorant on the topic I am:

• The highest-energy cosmic rays have no clear explanation in terms of their origin. A few events with energy exceeding $10^{20} eV$ have been recorded by at least a couple of experiments, and they are the subject of an extensive investigation by the Pierre Auger observatory.
• There are a number of anomalies on their composition, their energy spectrum, the composition of the showers they develop. The data from PAMELA and ATIC are just two recent examples of things we do not understand well, and which might have an exotic explanation.
• While models of their formation suppose that only light nuclei -iron at most- are composing the flux of primary hadrons, some data (for instance this study by the Delphi collaboration) seems to imply otherwise.

The paper by Gehrmann addresses in particular the latter point. There appears to be a failure in our ability to describe the development of air showers producing very large number of muons, and this failure might be due to modeling uncertainties, heavy nuclei as primaries, or the creation of exotic particles with muonic decay, in decreasing order of likelihood. For sure, if an exotic particle like the 300 GeV one hypothesized in the interpretation paper produced by the authors of the CDF study of multi-muon events (see the tag cloud on the right column for an extensive review of that result) existed, the Tevatron would not be the only place to find it: high-energy cosmic rays would produce it in sizable amounts, and the observed multi-muon signature from its decay in the atmosphere might end up showing in those air showers as well!

Mind you, large numbers of muons are by no means a surprising phenomenon in high-energy cosmic ray showers. What happens is that a hadronic collision between the primary hadron and a nucleus of nitrogen or oxygen in the upper atmosphere creates dozens of secondary light hadrons. These in turn hit other nuclei, and the developing hadronic shower progresses until the hadrons fall below the energy required to create more secondaries. The created hadrons then decay, and in particular , decays will create a lot of muons.

Muons have a lifetime of two microseconds, and if they are energetic enough, they can travel many kilometers, reaching the ground and whatever detector we set there. In addition, muons are very penetrating: a muon needs just 52 GeV of energy to make it 100 meters underground, through the rock lying on top of the CERN detectors. Of course, air  showers include not just muons, but electrons, neutrinos, and photons, plus protons and other hadronic particles. But none of these particles, except neutrinos, can make it deep underground. And neutrinos pass through unseen…

Now, if one reads the Delphi publication, as well as information from other experiments which have studied high-multiplicity cosmic-ray showers, one learns a few interesting facts. Delphi found a large number of events with so many muon tracks that they could not even count them! In a few cases, they could just quote a lower limit on the number of muons crossing the detector volume. One such event is shown on the picture on the right: they infer that an air shower passed through the detector by observing voids in the distribution of hits!

The number of muons seen underground is an excellent estimator of the energy of the primary cosmic ray, as the Kascade collaboration result shown on the left shows (on the abscissa is the logarithm of the energy of the primary cosmic ray, and on the y axis the number of muons per square meter measured by the detector). But to compute energy and composition of cosmic rays from the characteristics we observe on the ground, we need detailed simulations of the mechanisms creating the shower -and these simulations require an understanding of the physical processes at the basis of the productions of secondaries, which are known only to a certain degree. I will get back to this point, but here I just mean to point out that a detector measuring the number of muons gets an estimate of the energy of the primary nucleus. The energy, but not the species!

As I was mentioning, the Delphi data (and that of other experiments, too) showed that there are too many high-muon-multiplicity showers. The graph on the right shows the observed excess at very high muon multiplicities (the points on the very right of the graph). This is a 3-sigma effect, and it might be caused by modeling uncertainties, but it might also mean that we do not understand the composition of the primary cosmic rays: yes, because if a heavier nucleus has a given energy, it usually produces more muons than a lighter one.

The modeling uncertainties are due to the fact that the very forward production of hadrons in a nucleus-nucleus collision is governed by QCD at very small energy scales, where we cannot calculate the theory to a good approximation. So, we cannot really compute with the precision we would like how likely it is that a 1,000,000-TeV proton, say, produces a forward-going 1-TeV proton in the collision with a nucleus of the atmosphere. The energy distribution of secondaries produced forwards is not so well-known, that is. And this reflects in the uncertainty on the shower composition.

Enter CMS

Now, what does CMS have to do with all the above ? Well. For one thing, last summer the detector was turned on in the underground cavern at Point 5 of LHC, and it collected 300 million cosmic-ray events. This is a huge data sample, warranted by the large extension of the detector, and the beautiful working of its muon chambers (which, by the way, have been designed by physicists of Padova University!).  Such a large dataset already includes very high-multiplicity muon showers, and some of my collaborators are busy analyzing that gold mine. Measurements of the cosmic ray properties are ongoing.

One might hope that the collection of cosmic rays will continue even after the LHC  is turned on. I believe it will, but only during the short periods when there is no beam circulating in the machine. The cosmic-ray data thus collected is typically used to keep the system “warm” while waiting for more proton-proton collisions, but it will not be a orders-of-magnitude increase in statistics with respect to what has been already collected last summer.

The CMS cosmic-ray data can indeed provide an estimate of several characteristics of the air showers, but it will not be capable of providing results qualitatively different from the findings of Delphi -although, of course, it might provide a confirmation of simulations, disproving the excess observed by that experiment. The problem is that very energetic events are rare -so one must actively pursue them, rather than turning on the cosmic ray data collection when not in collider mode. But there is one further important point: since only muons are detected, one cannot really understand whether the simulation is tuned correctly, and one cannot achieve a critical additional information: the amount of energy that the shower produced in the form of electrons and photons.

The electron- and photon-component of the air shower is a good discriminant of the nucleus which produced the primary interaction, as the plot on the right shows. It in fact is a crucial information to rule out the presence of nuclei heavier than iron, or the composition of primaries in terms of light nuclei. Since the number of muons in high-multiplicity showers is connected to the nuclear species as well, by determining both quantities one would really be able to understand what is going on. [In the plot, the quantity Y is plotted as a function of the primary cosmic ray energy. Y is the ratio between the logarithm of the number of detected muons and electrons. You can observe that Y is higher for iron-induced showers (the full black squares)].

Idea for a new experiment

The idea is thus already there, if you can add one plus one. CMS is underground. We need a detector at ground level to be sensitive to the “soft” component of the air shower- the one due to electrons and photons, which cannot punch through more than a meter of rock. So we may take a certain number of scintillation counters, layered alternated with lead sheets, all sitting on top of a thicker set of lead bricks, underneath which we may set some drift tubes or, even better, resistive plate chambers.

We can build a 20- to 50-square meter detector this way with a relatively small amount of money, since the technology is really simple and we can even scavenge material here and there (for instance, we can use spare chambers for the CMS experiment!). Then, we just build a simple logic of coincidences between the resistive plate chambers, imposing that several parts of our array fires together at the passage of many muons, and send the triggering signal 100 meters down, where CMS may be receiving a “auto-accept” to read out the event regardless of the presence of a collision in the detector.

The latter is the most complicated thing to do of the whole idea: to modify existing things is always harder than to create new ones. But it should not be too hard to read out CMS parasitically, and collect at very low frequency those high-multiplicity showers. Then, the readout of the ground-based electromagnetic calorimeter should provide us with an estimate of the (local) electron-to-muon ratio, which is what we know to determine the weight of the primary nucleus.

If the above sounds confusing, it is entirely my fault: I have dumped here some loose ideas, with the aim of coming back here when I need them. After all, this is a log. a Web log, but always a log of my ideas… But I wish to investigate more on the feasibility of this project. Indeed, CMS will for sure pursue cosmic-ray measurements with the 300M events it has already collected. And CMS does have spare muon chambers. And CMS does have plans of storing them at Point 5… Why not just power them up and build a poor man’s trigger ? A calorimeter might come later…

In this post -the fourth of a series (previous parts: part I, part II, and part III)- I wish to discuss a couple of attributes possessed by the “ghost” events unearthed by the CDF multi-muon analysis. A few months have passed since the publication of the CDF preprint describing that result, so I think it is useful for me to make a short summary below, repeating in a nutshell what is the signal we are discussing and how it came about.

Let me first of all remind you that “ghost events” are a unknown background component of the sample dimuon events collected by CDF. This background can be defined as an excess of events where one or both muons fail a standard selection criterion based on the pattern of hits left by the muons in the innermost layers of the silicon tracker, SVX. I feel I need to open a parenthesis here, in order to allow those of you who are unfamiliar with the detection of charged tracks to follow the discussion.

Two words on tracks and their quality

The silicon tracker of CDF, SVX, is made up by seven concentrical cylinders of solid-state sensors (see figure on the right: SVX in Run II is made by the innermost L00 layer in red, plus four blue SVX II layers, plus two ISL layers; also shown are the two innermost Run I SVX’ layers, in hatched green), surrounding the beam line. When electrically charged particles created in a proton-antiproton collision travel out of the interaction region lying at the center, they cross those sensors in succession, leaving in each a localized ionization signal -a “hit”.

CDF does not strictly need silicon hits to track charged particles, since outside of the silicon detector lies a gas tracker called COT (for Central Outer Tracker), capable of acquiring up to 96 additional independent position measurements of the ionization trail; however, silicon hits are a hundred times more precise than COT ones, so that one can define two different categories of tracks: COT-only, and SVX tracks. Only the latter are used for lifetime measurements of long-lived particles such as B hadrons, since those particles travel at most a few millimeters away from the primary interaction point before disintegrating: their decay products, if tracked with the silicon, allow the decay point to be determined.

Typically, CDF loosely requires an SVX track to have three or more hits; however, a tighter selection can be made which requires four or more hits, additionally enforcing that two of those belong to the two innermost silicon layers. These tight SVX tracks have considerably better spatial resolution on the point of origin of the track, since the two innermost hits “zoom in” on it very effectively.

Back to ghosts: a reminder of their definition

Getting back to ghost events, the whole evidence of their presence is that one finds considerably more muon pairs failing the tight-SVX tracking selection than geometry and kinematics would normally imply in a homogeneous sample of data. Muons in ghost events systematically fail hitting the innermost silicon layers, just as if they were produced outside of it by the decay of a long-lived, neutral particle.

Because of its very nature -an excess of muon pairs failing the tight-SVX criteria- the “ghost sample” is obtained by a subtraction procedure: one takes the number of events with a pair of tight-SVX muons, divides their number by the geometrical and kinematical efficiency that muons from the various known sources pass tight-SVX cuts, and obtains a number , which subtracted from the number of observed dimuon pairs allows to spot the excess G, as follows: .

Mind you, we are not talking of a small excess here: if you have been around this blog for long enough, you are probably accustomed to the frequent phenomenon of particle physicists getting hyped up for 10-event excesses. Not this time: the number of ghost muon events exceeds 70,000, and the nature of this contribution is clearly of systematic origin. It may be a background unaccounted by the subtraction procedure, or a signal involving muons that are created outside of the innermost silicon layers.

In the former three installments of this multi-threaded post I have discussed with some detail the significant sources of reconstructed muons which may contribute to the ghost sample, and be unaccounted by the subtraction procedure: muons from decays in flight of kaons and pions, fake muon tracks due to hadrons punching through the calorimeter, and secondary nuclear interactions. Today, I will rather assume that the excess of dimuon events constitutes a class of its own, different from those mundane sources, and proceed to discuss a couple of additional characteristics that make these events really peculiar.

The number of muons

In the first part of this series I have discussed in detail how the excess of ghost events contains muons which have abnormally large impact parameters. Impact parameter -the distance of the track from the proton-antiproton collision point, as shown by the graph on the right- is a measure of the lifetime of the body which decays into the muons, and the observation of large impact parameters in ghost events is the real alarm bell, demanding that one needs to really try and figure out what is going on in the data. However, once that anomaly is acknowledged, surprises are not over.

The second observation that makes one jump on the chair occurs when one simply counts the number of additional muon candidates found accompanying the duo which triggered the event collection in the first place. In the sample of 743,000 events with no SVX hit requirements on the two triggering muons, 72,000 events are found to contain at least a third muon track. 10% is a large number! By comparison, only 0.9% of the well-identified decays contained in the sample is found to contain additional muons besides the decay pair. However, since the production of particles is a quite peculiar process, this observation need not worry us yet: those events are typically very clean, with the meson accompanied by a relatively small energy release. In particle physics jargon, we say that mesons have a soft spectrum: they are produced almost at rest in most cases. There are thus few particles recoiling against it -and so, few muons too.

Now, the 10% number quoted above is not an accurate estimate of the fraction of ghost events containing additional muons, since it is extracted from the total sample -the 743,000 events. The subtraction procedure described above allows to estimate the fraction in the ghost sample alone: this is actually larger, 15.8%, because all other sources contribute fewer multi-muon events: only 8.3%. These fractions include of course both real and fake muons: in the following I try to describe how one can size up better those contributions.

Fake muons

A detailed account of the number of additional muons in the data and the relative sources that may be originating them can be tried by using a complete Monte Carlo simulation of all processes contributing to the sample, applying some corrections where needed. As a matter of fact, a detailed accounting of all the physical processes produced in proton-antiproton collisions is rather an overkill, because events with three or more muon candidates are a rare merchandise, and they can be produced by few processes: basically the only sizable contributions come from sequential heavy flavor decays and fake muon sources. Let us discuss these two possibilities in turn.

Real muon pairs of small invariant mass, recoiling against a third muon, are usually the result of sequential decays of B-hadrons, like in the process (see picture on the left, where the line of the decaying quark is shown emitting sequentially two lepton pairs in the weak decays). The two muons from such a chain decay cannot have a combined mass larger than 5 GeV, which is (roughly speaking) the mass of the originating B hadron. In fact, by enforcing that very requirement () on the two muons at trigger level, CDF enriches the collected dataset of events where two independent heavy-flavor hadrons (B or D mesons, for instance) are produced at a sizable angle from each other. A sample event picture is shown below in a transverse section of the CDF detector. Muon detection systems are shown in green, and in red are shown the track segments of two muons firing the high-mass dimuon trigger.

(You might well ask: Why does CDF requires a high mass for muon pairs ? Because the measurements that can be extracted from such a “high-mass” sample are more interesting than those granted by events with two muons produced close in angle, events which are in any case likely to be collected into different datasets, such as the one triggered by a single muon with a larger transverse momentum threshold. But that is a detail, so let’s go back to ghost muons now.)

When there are three real muons, one thus has most likely a $b \bar b$ pair, with one of the quarks producing a double semileptonic decay (two muons of small mass and angle), and the other producing a single semileptonic decay (with this third muon making a large mass with one of the other two): for instance, , in the case of two B mesons; in the decay chain above, X and Y denote a generic hadronic state, while D is a hadron containing a anti-charm quark. B hadron decays can produce three muons also when one of them decays to a meson, which in turn decays to a muon pair. Other heavy flavor decays, like those involving a pair, can at most produce a pair of muons, and the third one must then be a fake one.

The HERWIG Monte Carlo program, which simulates all QCD processes, does make a good guess of the production cross-section of b-quark pairs and c-quark pairs produced in proton-antiproton collisions, in order to simulate all processes with equanimity; but those numbers are not accurate. One improves things by taking simulated events that contain those production processes such that they match the and cross-sections which are measured with the tight-SVX sample, the subset devoid of the ghost contribution.

The CDF analysis then proceeds by estimating the number of events where at least one muon track is in reality a hadron which punched through the detector. The simulation can be trusted to reproduce the number of hadrons and their momentum spectrum, but the phenomenon of punch-through is unknown to it! To include it, a parametrization of the punch-through probability is obtained from a large sample of decays, collected by the Silicon Vertex Tracker, a wonderful device capable of triggering on the impact parameter of tracks. The meson lives long enough that the kaon and pion tracks it produces have sizable impact parameter, and millions of such events have been collected by CDF in Run II.

The extraction of the probability is quite simple: take the kaon tracks from D decays, and find the fraction of these tracks that are considered muon candidates, thanks to muon chamber hits consistent with their trajectory. Then, repeat the same with the pion candidates. The result is shown in the graphs below separately for kaon and pion tracks. In them, the probability has been computed as a function of the track transverse momentum.

Besides the above probabilities and the tuning of the cross section, a number of other details are needed to produce a best-guess prediction of the number of multi-mion events with the HERWIG Monte Carlo simulation. However, once all is said and done, one can verify that there indeed is an excess in the data. This excess appears entirely in the ghost muon sample, while the tight-SVX sample is completely free from it. Its size is again very large, and its source is thus systematical -no fluctuation can be hypothesized to have originated it.

The mass of muon pairs in multi-muon events

To summarize, what happens with ghost events is that if one searches for additional muon tracks around each of the triggering muons, one finds them with a rate much higher than what one observes in the tight-SVX dimuon sample. It is as if a congregation of muons is occurring! The standard model is unable to even getting close to explain how events with so many muons can be produced. The source of ghost events is thus really mysterious.

Now, if you give to a particle physicist the momenta and energies of two particles produced together in a mysterious process, there is no question on what is going to happen: next thing you know, he will produce a number, . is the invariant mass of the two-particle system: if they are the sole products of a decay process, m is a unbiased measurement of the mass of the parent body. If, instead, the two particles are only part of the final state, m will be smaller than ; still, a distribution of the quantity m for several decays will say a lot about the parent particle X.

Given the above, it is not a surprise that the next step in the analysis, once triggering muons in ghost events are found to be accompanied by additional muons at an abnormal rate, is to plot the invariant mass of those two-muon combinations.

There is, however, an even stronger motivation from doing that: an anomalous mass distribution of lepton pairs (then electron-muon pairs, not dimuons -I will come back to this detail later) had been observed by the same authors in Run I. That excess of dilepton pairs was smaller numerically -the dataset from which it had been extracted corresponded to an integrated luminosity 20 times smaller- but had been extracted with quite different means, from a different trigger, and with a considerably different detector (the tracking of CDF has been entirely changed in Run II). The low-mass excess of dilepton pairs remained a unexplained feature, calling for more investigation which had to wait a few years to be performed. The mass distribution of electron-muon combinations found by CDF in Run I is shown in the graph on the right: the excess of data (the blue points) over known background sources (the yellow histogram) appears at very low mass.

In Run II, not only does CDF have 20 times more data (well, sixty times so by now, but the dataset on which this analysis was performed was frozen one and a half years ago, thus missing the data collected and processed after that date): we also have more tools at our disposal. The mass distribution of muon pairs close in angle, belonging to ghost events with three or more muon candidates, can be compared with the tuned HERWIG simulation both for ghost event sample and for the tight SVX sample: this makes for a wonderful cross-check that the simulation can be trusted on producing a sound estimate of that distribution!

The invariant mass distribution of muon pairs close in angle in tight-SVX events with three or more muon tracks is shown on the left. The experimental data is shown with full black dots, while the Monte Carlo simulation prediction is shown with empty ones. The shape and size of the two distributions match well, implying that the Monte Carlo is properly normalized. Indeed, the tight-SVX sample is the one used for the measurements of and cross sections: once the Monte Carlo is tuned to the values extracted from the data, its overall normalization could mismatch the data only if fake-muon sources were grossly mistaken. That is not the case, and further, one observes that the number of decays -which end up all in one bin in the histogram, at 3.1 GeV of mass- are perfectly well predicted by the simulation: again, not a surprise, since those mesons can make it to a three-muon dataset virtually only if they are originated from B hadron decays. So, the check in tight-SVX events fortifies our trust on our tuned Monte Carlo tool.

Now, let us look at how things are going in the ghost muon sample (see graph on the right). Here, we observe more data at low invariant mass than what the Monte Carlo predicts: there is a clear excess for masses below 2.5 GeV. This excess has the same shape as the one observed in Run I in electron-muon combinations!

Please take a moment to record this: in CDF, some of the collaborators who objected to the publication of the multi-muon analysis did so because they insisted that more studies should be made to confirm or disprove the effect. One of the objections was that the electron-muon sample had not been studied yet. The rationale is that if the ghost events are due to a real physical process, then the same process should show up in electron-muon combinations; otherwise, one is hard-pressed to avoid having to put into question a thing called lepton universality, which -at least for Standard Model processes- is a really hard thing to do. However, the electron signature in CDF is very difficult to handle, particularly at low energy: backgrounds are much harder to pinpoint than for muons. Such a study is ongoing, but it might take a long time to complete. Run I, instead, is there for us: and there, the same excess was indeed present in electron events too!

Finally, there is one additional point to mention: a small, but crucial one. The signal is in perfect match with the simulation prediction! This observation confirms that the tuned cross section of production is right dead-on. Whatever these ghost events are, they sure cannot be coming from B production. Also, note that the agreement of the signal with Monte Carlo expectations constitutes proof that the efficiency of the tight-SVX requirements -the 24% number which is used to extract the numerical excess of ghost events- is correct. Everything points to a mysterious contribution which is absent in the Monte Carlo.

The above observations conclude this part of the discussion. In the next installment, I will try to discuss the additional oddities of ghost events -in particular, the rate of muons exceeding the triggering pair is actually four times higher than in QCD events. I will then examine some tentative interpretations that have been put forth in the course of the three months that have passed since the publication.

Blogging is one of the activities that will get slightly reduced this week, along with others that are not strictly necessary for my survival. Mariarosa has left for Athens this morning with three high-school classes of her school, Liceo Foscarini. They will visit Greece for a whole week, and be back to Venice on Saturday.

I am not scared by the obligation of having to care for my two kids, and I do like such challenges -I maintain that my wife should not complain too much when it is me who leaves for a week, much more frequently- but of course the management of our family life will take all of my spare time, plus some.

Blogging material, in the meantime, is piling up. There are beautiful results coming out of CDF these days (isn’t that becoming a rule?). Furthermore, recently the Tevatron has been running excellently, and the LHC seems in the middle of a crisis over whether to risk a second, colossal failure by pushing the energy up to 10 TeV to put the Tevatron off the table in the shortest time possible, or to play it safe and keep the collision energy at 6 TeV, accepting the risk of being scooped of the most juicy bits of physics left over to party with.

And multi-muons keep me busy these days. Besides the starting analysis in the CMS-Padova group, there are papers worth discussing in the arxiv. This one was published a few days ago, and we had in Padova last Thursday one of the authors, Thomas Gehrmann, discussing QCD calculations of event shapes observables in a seminar- which of course allowed me to chat with him about his hunch on the hidden valley scenarios he discusses in his paper. More on these things next week, after I set my kids to sleep!

This post is not it but no, I have not given up on my promise to complete my series on the anomalous multi-muon signal found by CDF in its Run II data. In fact, I expect to be able to post once more on the topic this week. There, I hope I will be able to discuss the kinematic characteristics of multi-lepton jets. [I am lazy today, so I will refrain from adding links to past discussions of the topic here: if you need references on the topic, just click on the tag cloud on the right column, where it says "anomalous muons"!]

In the meantime, I am happy to report that I have just started working at the same analysis for the CMS experiment! In Padova we have recently put together a group of six -one professor, three researchers, a PhD student, and a undergrad- and we will pursue the investigation of the same signature seen by CDF.  And today, together with Luca, our new brilliant PhD student, I started looking at the reconstruction of neutral kaon decays , a clean source of well-identified pion tracks with which we hope to be able to study muon mis-identification in CMS.

Meanwhile, the six-strong group in Padova is already expanding. Last Wednesday professor Fotios Ptochos, a longtime colleague in CDF, a good friend, and crucially one of the authors of the multi-muon analysis, came to Padova and presented a two-hour-long seminar on the CDF signal in front of a very interested group of forty physicists spanning four generations -from Milla Baldo Ceolin to our youngest undergraduates. The seminar was enlightening and I was very happy with the result of a week spent organizing the whole thing! (I will have to ask Fotios if I can make the slides of his talk available here….)

Fotios, a professor at the University of Cyprus, is a member of CMS, and a true expert of measurements in the B-physics sector at hadron machines. We plan to work together to repeat the controversial CDF analysis with the first data that CMS will collect -hopefully later this year.

The idea of repeating the CDF analysis in CMS is obvious. Both CDF and D0 can say something on the signal in a reasonable time scale, but whatever the outcome, the matter will only be settled by the LHC experiments. Imagine, for instance, that in a few months D0 publishes an analysis which disproves the CDF signal. Will we then conclude that CDF has completely screwed up its measurement ? We will probably have quite a clue in that case, but we will need to remain possibilistic until at least a third, possibly more precise, measurement is performed by an independent experiment.That measurement is surely going to be worth a useful publication.

And now imagine, on the contrary, that the CDF signal is real…

Here is the second part of the list of useful physics posts I published on this site in 2008. As noted yesterday when I published the list for the first six months of 2008, this list does not include guest posts nor conference reports, which may be valuable but belong to a different place (and are linked from permanent pages above). In reverse chronological order:

December 29: a report on the first measurement of exclusive production of charmonium states in hadron-hadron collisions, by CDF.

December 19: a detailed description of the effects of parton distribution functions on the production of Z bosons at the LHC, and how these effects determine the observed mass of the produced Z bosons. On the same topic, there is a maybe simpler post from November 25th.

December 8: description of a new technique to measure the top quark mass in dileptonic decays by CDF.

November 28: a report on the measurement of extremely rare decays of B hadrons, and their implications.

November 19, November 20, November 20 again , November 21, and November 21 again: a five-post saga on the disagreement between Lubos Motl and yours truly on a detail on the multi-muon analysis by CDF, which becomes a endless diatriba since Lubos won’t listen to my attempts at making his brain work, and insists on his mistake. This leads to a back-and-forth between our blogs and a surprising happy ending when Motl finally apologizes for his mistake. Stuff for expert lubologists, but I could not help adding the above links to this summary. Beware, most of the fun is in the comments threads!

November 8, November 8 again, and November 12: a three-part discussion of the details in the surprising new measurement of anomalous multi-muon production published by CDF (whose summary is here). Warning: I intend to continue this series as I find the time, to complete the detailed description of this potentially groundbreaking study.

October 24: the analysis by which D0 extracts evidence for diboson production using the dilepton plus dijet final state, a difficult, background-ridden signature. The same search, performed by CDF, is reported in detail in a post published on October 13.

September 23: a description of an automated global search for new physics in CDF data, and its intriguing results.

September 19: the discovery of the baryon, an important find by the D0 experiment.

August 27: a report on the D0 measurement of the polarization of Upsilon mesons -states made up by a pair- and its relevance for our understanding of QCD.

August 21: a detailed discussion of the ingredients necessary to measure with the utmost precision the mass of the W boson at the Tevatron.

August 8: the new CDF measurement of the lifetime of the baryon, which had previously been in disagreement with theory.

August 7: a discussion of the new cross-section limits on Higgs boson production, and the first exclusion of the 170 GeV mass, by the two Tevatron experiments.

July 18: a search for narrow resonances decaying to muon pairs in CDF data excludes the tentative signal seen by CDF in Run I.

July 10: An important measurement by CDF on the correlated production of pairs of b-quark jets. This measurement is a cornerstone of the observation of anomalous multi-muon events that CDF published at the end of October 2008 (see above).

July 8: a report of a new technique to measure the top quark mass which is very important for the LHC, and the results obtained on CDF data. For a similar technique of relevance to LHC, also check this other CDF measurement.

I wish 2009 will bring an answer to a few important questions:

• Can LHC run ?
• Can LHC run at 14 TeV ?
• Will I get tenure ?
• Are multi-muons a background ?
• Are the Pamela/ATIC signals a prologue of a new scientific revolution ?
• Will England allow a NZ scientist to work on Category Theory on its soil ?
• Is the Standard Model still alive and kicking in the face of several recent attempts at its demise ?

I believe the answer to all the above questions is yes. However, I am by no means sure all of them will be answered next year.

The regulars here will have already noticed by now that my posting rate has fallen this week. I have been busy with three different physics analyses, trying to make some progress in each.

The first project is the calibration of the momentum scale in CMS. I have discussed the issue elsewhere a couple of times; I am slowly converging to an understanding of how to treat the Z boson lineshape -which receives contributions from a number of different sources and effects: parton distribution functions in the projectiles, electromagnetic and weak radiation effects, interaction of the final state products of Z decay with the material of the tracker. All this must be dealt with in a coherent fashion to extract the most information possible from the Z decays we will reconstruct in CMS. We have a small but focused group working at the momentum scale calibration, including worthy physicists from Torino University, plus Marco and me. This week, I have tried to determine the effect of parton distribution functions alone, to insert it in our algorithm, but something still escapes me, and I want to do things as well as I can -which sometimes take little extra effort from a mediocre result, but in this case seems to be requiring a lot more care.

The second is the search for Higgs boson decays in the final state arising when H decays to two Z bosons, and one of the Z decays to a lepton pair, while the other decays to a pair of jets. Usually this final state, which is very hard to exploit at low Higgs masses due to the large backgrounds, is used for high-mass searches only (above 200 GeV). We want to extend it to lower masses, where the Higgs is more likely to be, using the decay, which Mia and I have a lot of experience in detecting in hadronic environments. Mia will present some results of this study tomorrow at CERN, so we have been working at this heavily this week.

The third topic is the evaluation of the chances of CMS to detect a similar signature of multi-muon events that CDF has seen in its data. The CDF signal is probably just a not well understood background, but it makes sense to size up the capability of CMS to detect a similar signature with early data. This requires understanding muon sources without using real data, and it is a bit far-fetched, but it is perfectly sound as a masters’ thesis topic, one on which Franco and I in fact have a student working. I have not worked much on this topic this week, but it still has absorbed a little of CPU.

I have a thick agenda of pending things to do, which has grown longer in the last few days. One thing is to post more commentaries on the multi-muon analysis by CDF here. Another is to progress with a document I am writing. A third is to review a 40-pages long CDF paper draft for the Spokespersons Reading Group, to which I proudly belong. A fourth is to organize the upcoming meeting of the CMS-Padova software-analysis group, which will convene in ten days. A fifth is to prepare my next trip to CERN, which will be from next Monday to next Friday. I do hope that I will be able to post more in the next few days… if I survive.

In less than an hour I will participate in the program “Caccia al Fotone”, aired by Radio Città Fujiko, on 103.1FM (if you are in Italy). If you want to follow it on the internet, there is a streaming available:

• OGG

• MP3

You can send an SMS or an email to ask questions. See the site of the program for directions.

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.

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.

[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, 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.

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 (, ), 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, , 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 (), 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: and , 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 ( and ), 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.

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 , 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, (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, : 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 . I remind you that the anti-kaon has the quark content , while the Lambda is a 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 . 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 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 as the left sideband; events with as the signal band, and < 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.

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:

;

.

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 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 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.

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:

Hi,

As most of my friends and colleagues know, I have a very dim view of
the physics blogosphere, and avoid interacting with it. However, your
statements about me and my collaborators in connection with the recent CDF anomaly quite clearly crossed a line, and I feel compelled to respond. In doing so I am adopting an attitude Howard Georgi once described when dealing with non-perturbative QCD effects in heavy quark effective theory: once I am finished dealing with the brown muck, I will wash my hands.

It was stimulating to see the CDF paper. However, this is an extremely challenging analysis, and many further cross-checks will have to be done to take it as a serious indication for physics beyond the standard model. We are all well aware that particle physics anomalies have come and gone in the past two decades, in analyses that are less complicated than this one; of course the collaboration made no claim to have discovered new physics. Keeping this in mind, let me first make comments on some physics I have been involved with, and end with some comments on sociology.

I have been working recently with Doug Finkbeiner,Tracy Slatyer and Neal Weiner on a theory for dark matter motivated by a growing number of anomalies in astrophysics, most recently PAMELA/ATIC.
This work is a direct continuation of (in my view) beautiful earlier work pioneered by Neal, Doug and Dave Tucker-Smith, who have collectively pushed it for many years. In fact, Neal, Doug and others previously talked about GeV scalars decaying to leptons in the context of “exciting” dark matter, to explain the INTEGRAL signal, as well as the HEAT excess predecessor to PAMELA. So the idea of GeVish mass particles decaying to leptons, motivated by Dark Matter anomalies, goes back to Feb 2007–Feb 2008. See e.g. astro-ph/0702587 and especially arXiv:0802.2922.

What we did in our four author paper was to show that all these strands fit together into a simple unified picture that also makes very good particle physics sense. The idea can be summarized in one sentence: Dark Matter is charged under a non-Abelian gauge symmetry broken at the GeV scale. We pointed out two additional major motivations for the GeV scale–first, the new vectors with this mass naturally “Sommerfeld enhance” the annihilation cross section as appears necessary to explain the PAMELA/ATIC signals from DM
annihilation; second, the broken gauge symmetry at the GeV scale radiatively induces splittings between the different states in the DM multiplet at the \sim MeV scale, which is precisely what is needed in “exciting” and “inelastic” DM explanations of the INTEGRAL and DAMA signals. All of these phenomena, scattered over energy scales ranging from a TeV to an MeV, are essentially a consequence of the single sentence I used to describe our picture above. We find this compelling.

Since the GeV gauge sector is non-Abelian, there are a number of
states, minimally including vectors and higgses, all GeVish in mass.
One thing that happens when at least some of these GeV particles are vectors is that they can easily talk to the Standard Model, via kinetic mixing with the photon. The mixing is naturally small, so directly producing this particle is challenging–though people have
talked about doing it at low-energy e+ e- machines (B-factories,
DAPHNE, BESS). Neal and I considered the simplest marriage of our DM picture with low-energy SUSY, which further naturally generates the GeV dark gauge symmetry breaking scale. We also
pointed out that in this set-up, one could produce particles in this new GeV sector much more copiously, not directly, but indirectly through SUSY production: every SUSY event will end with MSSM LSP’s which then decay into the true LSP in the dark sector; essentially all of these will also be accompanied by some of the GeVish particles that re-decay back into SM leptons. One would expect a cascade of decays in the GeV sector given the multiplicity of states, and thus the aptly named “lepton jets”. We discussed displaced vertices as a possibility, though they are not guaranteed. So, seeing “lepton jets” as an O(1) fraction of SUSY signals is what we talked about as the smoking gun of our model at the LHC. It would indeed be an amazing signal, which is why we were and continue to be very excited about it!

Now, even if the CDF anomalies are an indication of new physics–which I think in all of our views is _very_ far from obvious– it can not be due to the signal Neal and I talked about, arising from SUSY cascade decays. The rate of the CDF anomaly is absolutely
enormous–you are talking about 70,000 “ghost” events! If there is a connection to our model at all, it would likely have to be through direct production of the GeV sector particles, that still cascade decay in the dark sector and produce the lepton jets. As I mentioned there are limits one can put on this from e+ e- data, and a number of us had been wondering what could be done at hadron colliders, but at least my instinct was that the rates wouldn’t be high enough and it would be far too messy and difficult to extract a signal. We were planning on thinking about this in more detail soon, but the exploration of the consequences of our model is very new, and for now most of us have been focusing on getting out the important predictions on the DM side for GLAST/Fermi, as well as fleshing out the big O(1) LHC predictions. Obviously, stimulated by the CDF result, studying the question of direct production at the Tevatron is much higher on our list of priorities, and we are looking at it now to see if it can even be in the right ballpark. But to re-iterate: even if the CDF anomaly is new physics, and even if it is connected to our model, (and needless to say these are two very big “ifs”), it would be a wonderful surprise to me since I had expected probing direct production of the GeV sector to be incredibly difficult at a hadron collider.

So much for the physics. Turning to the sociology: you publicly suggested that we had gotten wind of the CDF experimental result ahead of time, and casually wrote this paper pointing out the signal before the experimental result was published. Your only evidence is that we made a surprising prediction of a signal experimentalists hadn’t thought of before and put it out before the experimental
results were made public–Gasp! Shocking! Scandalous! Never happened in the history of physics! Not contained in the definition of the word “pre”diction! This was a hilariously preposterous accusation;
however it stopped being funny when you went further and all but
called Neal a liar when he stated unequivocally that we had no advance knowledge of the CDF result–this is outrageous. As Neal said, we had no knowledge about the experimental result ahead of time _at all_. We didn’t even talk about the Tevatron in our paper! And as I said above, even if this anomaly is real and even if it is related to our model, it can not be literally the signal we talked about. Also, the thought that we could somehow cook up a model motivated by explaining dark matter anomalies as a cover to explain rumored events at CDF is absurd–ask any theorist friends you may have whether this is feasible and you will get a good chuckle out of them. You think this signal “came out of the blue”, but if you have been following any of the developments in BSM collider physics in the past couple of years you will realize that signals involving high particle multiplicities with displaced vertices have been discussed for quite a while–check out the repeated use of the phrase “hidden valley” in my paper with Neal for references to work by Strassler, Zurek et. al. Our contribution is that a rather specific version of such a picture–with the GeV mass scale and coupling to the SM through kinetic mixing with the photon–is naturally singled out by the new picture of dark matter we put forward with Doug and Tracy, giving a potentially exciting connection between what we are now seeing in the sky and what we might see at colliders. As it happens this type of hidden valley model had not been discussed in the literature, so we happily pointed out some of their possibly dramatic LHC consequences. Perhaps if you had bothered to even superficially read our papers and think about the physics, it wouldn’t seem so “out of the blue” to you, and you would understand that these light GeV particles decaying to leptons are a necessary feature of our model of Dark Matter, whether CDF saw any hints for them or not.

I find your cynicism remarkable. We are entering what promises to be a golden era of amazing experiments in high-energy physics, astrophysics and cosmology, which may very well lead to profound advances in our understanding of Nature at a fundamental level. All of us–experimentalists and theorists alike–are fantastically excited about this and are doing everything we can to give it the best chance of happening. And at least most of us don’t think of physics as a soap opera rife with rumor and innuendo, or spend the precious time we have cynically tossing around completely baseless and deeply offensive accusations.

Speaking of precious time, I’m sure you’ll agree that there is more critical physics to do than there are hours in the day to do it,
and I for one would like to get back to work.

Nima Arkani-Hamed

And here is my reply:

Dear Nima,

thank you for taking the time to explain more in detail what was the creative process behind the two papers you recently published. If you read my comment on Peter’s blog, you know I did ask for something like what you wrote above: an explanation of how you came to consider the striking signature we are discussing about.

If I insulted you or your colleagues with my remark, then please accept my apology, and forward these to them. I am a sceptic not only with respect to SUSY (which may be excused, since I am in good company), but also with respect of the CDF result itself. And I found it really a remarkable coincidence, to avoid putting new words out which may be found aggressive, that no more than three weeks before the CDF result is aired, you come up with lepton jets, with long lifetime, and with small invariant mass. Of course, that is not a copyrighted signature, so I am the one at fault – I am speculating. But indeed, I was not the only one who found this coincidence fishy. Many of my colleagues in CDF did, and so did others outside.

So, to summarize: I am pleased that you chose to come down to this blog to explain what caused you to discuss that signature. I will need time to digest what you wrote, because I am basically an ignorant. In earnest, I have to say I am still sceptical that there were no influences in your creative process. But I guess that is ok. The material is there for anybody to read and make their own opinion, and your text above will help creating those opinions.

Keep up with the good work,
T.

So, I should like to open a poll for those heroic readers who came to the bottom of this post: did you read Nima’s papers ? Do you think there was a leak or do you rather think it was their own cooking ? I would be happy to hear I am the only one who still believes there was some internal information which was passed to the group who wrote those papers…

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…

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 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 () 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 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.