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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


1. tripitaka - November 13, 2008

Just curious T, are you still at the 1% level for betting on new physics?

2. Ralf Hofmann - November 13, 2008

Very nice job! I am eagerly waiting for the next post.

3. Thomas D - November 13, 2008

Perhaps I missed this part of a previous post, but — if there is new physics with a large cross-section producing particles that are rather easy to detect, why had no previous experiment given any hint of it?

Possible answers I can think of are
1) new physics operates at high energy so requires TeVatron to get ‘over the hill’
2) no previous experiment had the required detection/triggering
3) no previous experiment worked hard enough to analyze relevant events…

4. dorigo - November 13, 2008

Yes Tripitaka, 1% is huge as a possibility to see something beyond the SM; but it is still what it is, a small chance.

Thanks Ralf, I expect at least three more posts on this issue.

Thomas, you answered it yourself. We do not know, and all the three reasons you listed stand. Of course there is a fourth: it is a CDF detector effect.


5. Thomas D - November 13, 2008

By the way, there is definitely an experimenter effect: it is called misanthropic conformal transformation of graphs.

This means that, for some as-yet-unknown reason, any graph of data in an experimentalist’s review paper or talk shrinks until it is indecipherable to the naked eye. Generally the axis labels also obey the same laws. Therefore no-one who doesn’t already know what the graph represents can extract any information from it.
See for example 0810.5730. Can you get anything out of Fig 3,4,6 without using at least 150% magnification? I can scarcely tell which curve or set of points is meant to be which. Each of the points is less than a millimetre in size and yet we are supposed to distinguish between an open circle, a filled circle, an open diamond and a filled square.

(I wonder how people would react if theorists did the same to their equations – shrink them until the symbols become unreadable…) It’s not that they save electrons by making the figures smaller, is it?

6. Amos - November 13, 2008

So how long should we expect D0 to take to issue their confirmation or disagreement?

7. dorigo - November 14, 2008

I believe it will take D0 at least four to six months to produce an answer of any kind. If they do things seriously, as I have every reason to believe will be the case, they need to determine the sample composition of dimuon data with muons possessing hits in the inner silicon layers, and extrapolate this properly to muons selected with looser cuts. Then, backgrounds have to be properly evaluated.

I would be happy to have to acknowledge that D0 can do things much more quickly than this… What I am confident is that an analysis of this kind has already started, despite the shortness of manpower: the opportunity of prove its older brother wrong is too juicy!


8. Amos - November 14, 2008

Thanks. One more question: did CDF detect any non-conservation or assymetries in the events, or is this analysis not yet complete? I’m curious about why I haven’t read anything about that in any of the reports I’ve seen (maybe it was in the parts of the paper that were too dense for me).

The whole thing is just so tremendously exciting, however it turns out.

9. carlbrannen - November 14, 2008

Tommaso, I don’t have anything useful to say except that this series is wonderful and we are all waiting, with abated breath, for installment number IV.

The small number of comments is due to the thoroughness and clarity of the writing, not because of any lack of interest.

10. dorigo - November 14, 2008

Hi Amos,
no, there is no asymmetry that I can recall in the observed features of the events. Of course, the analysis is incomplete. It is written in clear words in the abstract and summary, that although CDF is presently unable to explain the anomalous excess, it is pursuing more studies on the matter.

Hello Carl,
thank you for your continued support, I do appreciate your interest in the matter and it is a motivation for continuing this series. I will probably have another part out on Sunday.


11. Guess Who - November 15, 2008

Re #9, #10: I too am not saying anything about this because I have nothing intelligent to say about it, but I am looking forward to the rest of the series.

12. trying to recall - November 15, 2008

I believe DELPHI had similar signal, but they lacked of stat. And also in CDF, vista or sleuth analysis had some excess in muon channel….

13. Andrea Giammanco - November 15, 2008

I agree with #9 and #11.
I’ve been silently reading all the series so far…

14. dorigo - November 16, 2008

And thank you all for your interest in this story.

TTR, I do not know about delphi, but the vista excess is, indeed, interesting and relevant to the present analysis. Here is what I had to say about it in the post where I discussed it:

“I have the feeling that the muons in those distributions contain a sizable fraction of fakes, which the simulation does not account properly. Fake muons may be caused by hadrons, which manage to traverse the detector and get detected in the muon chambers. In case that happens, there is no real reason for the muon and the electron to be of opposite sign, since their production is uncorrelated. Beware, this implies that also opposite-sign electron-muon pairs should contain a similar excess: well noted, but in that case, such an excess would have to fight much larger backgrounds from correlated electron-muon production by physical processes such as top-antitop production, WW production, etcetera. If that is what really happened, poor Sleuth was stuck with finding the same-sign excess, since opposite-sign data had too large statistics to make a few odd events stick out.”

Food for thought, ain’t it ?


15. A few remarks on Matthew Strassler’s “Flesh and Blood with Multi-Muons” « A Quantum Diaries Survivor - November 17, 2008

[…] trackback [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 […]

16. Matti Pitkänen - November 18, 2008

Dear Tommaso,

as I told ealier, the leptonic color predicted by TGD promises a solution to large number of anomalies, also CDF anomaly. The predicted lifetime for charged tau-pion is same as the lifetime of the possibly existing new particle. The neutral tau-pions and their p-adically scaled up variants with masses coming as powers of two would correspond to the three states proposed by CDF collaboration: mass predictions are consistent with the proposal of CDF. The decays of these neutral pions to 3 pions almost at rest explain the jet like structure.

The remaining challenge was to estimate the production cross section. A brief article summarizing the details of the calculation of the tau-pion production cross section can be found from my homepage. Here is the abstract.

The article summarizes the quantum model for tau-pion production. Various alternatives generalizing the earlier model for electro-pion production are discussed and a general formula for differential cross section is deduced. Three alternatives inspired by eikonal approximation generalizing the earlier model inspired by Born approximation to a perturbation series in the Coulombic interaction potential of the colliding charges. The requirement of manifest relativistic invariance for the formula of differential cross section leaves only two options, call them I and II. The production cross section for tau-pion is estimated and found to be consistent with the reported cross section of about 100 nb for option I under natural assumptions about the physical cutoff parameters (maximal energy of tau-pion center of mass system and the estimate for the maximal value of impact parameter in the collision which however turns out to be unimportant unless its value is very large). For option II the production cross section is by several orders of magnitude too small. Since the model involves only fundamental coupling constants, the result can be regarded as a further success of the tau-pion model of CDF anomaly. Analytic expressions for the production amplitude are deduced in the Appendix as a Fourier transform for the inner product of the non-orthogonal magnetic and electric fields of the colliding charges in various kinematical situations. This allows to reduce numerical integrations to an integral over the phase space of lepto-pion and gives a tight analytic control over the numerics.

See also the this and the earlier postings in my blog.

17. Matti Pitkänen - November 18, 2008

A little addition. The plot for differential production cross section for taupion is here.

18. That crazy leptonic sector: multi-muon model-making « High Energy PhDs - February 16, 2009

[…] reading on the multi-muon anomaly is still Tommaso’s set of notes: part 0, part 1, part 2, part 3, part 4. An excellent theory-side discussion can be found at […]

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