A Quantum Diaries Survivor

Some notes on the multi-muon analysis – part IV February 2, 2009

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.

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

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.

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

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.