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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


1. Big Vlad - November 8, 2008

These sorts of posts are the reason I come to this blog. Will there be a part III ? I’m looking forward to you telling us what is in fact behind the muon excess 🙂

2. tripitaka - November 9, 2008

Yes! Bring on part III

3. Jester - November 9, 2008

Tommaso, you mention these two muon systems: CMU and CMP. I heard that if one takes into account only the CMP muons (which are presumably less contaminated by punch-throughs) then the excess disappears. Is that true?

4. carlbrannen - November 9, 2008

This should be written up as an article for a general physics magazine like Physics Today. I would add a note on the bubble chamber photo that the reason the incoming track disappears is because the results of the tracks are neutral particles (lambda and kaon if I recall) which do not leave a track of charged particles. This is, of course, obvious to you but might not be so to a general audience.

5. carlbrannen - November 9, 2008

And the same principles, neutral particles don’t leave tracks and so disappear, also applies to modern particle detectors.

6. Hatim Hegab - November 9, 2008

T, you never fail to amaze me with all these amounts of knowledge and info you have. How could you know all these things you post? I wish I can have the privilege of meeting you someday, here, at Fermilab.

7. dorigo - November 9, 2008

Hi all,

Vlad, Tripitaka:

yes, I think there will be a part III, a part IV, and a part V. I hope I have the time to write those! Thank you for your note.

Jester, yes and no. CMP muons (we call them “CMP-only”) do not have a CMU stub. That means either that the muon was not CMU-fiducial, or that we simply found no hits in the CMU we could associate with the CMP track. CMU-fiduciality means that the track, extrapolated to the CMU chamber, would miss the sensitive detector volume (yes, the system is not totally hermetic). So a CMUP muon is the cleanest, and a CMP-only and a CMU-only are more background-ridden. Now, are CMU-only better or CMP-only better ones ? It depends on momentum. Since a muon cannot reach the CMP if it has less than 3 GeV of momentum, a 2.5 GeV CMU-only muon is perfectly ok, while a 5 GeV CMU-only one which is CMP-fiducial is suspicious. A 2 GeV CMP-only muon is all background, a 5 GeV one… it depends on whether it was CMU-fiducial or not. Complicated, ain’t it ? Throw in the fact that we do not know the trajectory of soft muons very precisely, because by the time they cross the calorimeter they have undergone multiple scattering which can have altered their position by even 10 centimeters, and you get a messy picture! In any case, you just inspired me to make a post explicitly on this very issue.

Carl, your point is an excellent one. I wrote the post in a rush and it shows (no links, inaccuracies, typos). I will correct it as I find the time to do so.

Hi Hatim, welcome back! Well, I do know a few things about CDF. And what I do not know, I make up 😉 It will be also my pleasure to meet you, next time I travel there. Should be this winter…

Cheers all,

8. Jester - November 9, 2008

Tommaso, it’s anyway less complicated than theories explaining the CDF anomaly 😉 But i didn’t find the answer to my question, so let me repeat/rephrase it: Does the excess you find depend on whether you look at CMU-only muons, CMP-only muons, or CMUP muons?

9. dorigo - November 9, 2008

You are right, I did not answer your question, only part of it. My fault.

Ok. First of all, we have a two-CMUP muon trigger: those are CMUP by construction, and backgrounds are small. One cannot release trigger cuts, so we have to live with those. But when we search for additional muons, we do with an .or. of the three categories: CMU, CMP, CMX, with as loose transverse momentum cuts as possible: 2 GeV. That is, we collect “looser” muons. This results in finding four times as many additional muons in “ghost” events than in normal ones.

The attempt at tightening the cuts and asking for CMUP additional muons results in a much smaller efficiency, and so a much smaller set of extra muons. But the excess remains: four times as many CMUP muons are found in ghost events than one would expect. So in this respect, there seems to be consistency.


10. dorigo - November 9, 2008

… to be clear, what I answered in #7 above was to the question “are CMP muons cleaner”, which was not your question…


11. FNesti - November 9, 2008

Dear Tommaso,
thanks for your clear notes!

Just two (simple?) questions:

– First: at the risk of being simple minded – if I understand it right, single soft muon events are not even recorded, ok? Therefore this excess may well be accompanied by single leptons – unobserved. However, given the overabundance of the double ones, these could be even much more (depends on physics of course). Is it possible to give any upper bound on them (even crude) and look for any excess? I suppose the answer is no… but let’s be optimistic.

– An other thing: Is there somewhere a distribution of impact parameter according to muon order? This should be doable, and interesting; for example, should one assume that all ghosts come from a single displaced vertex, or they seem to come from subsequent displacements?


12. dorigo - November 9, 2008

Hi Fabrizio,

there is a single muon trigger in CDF, with a (I think) 8 GeV Pt cut. I need to give a look at the trigger tables though, because I haven’t checked it recently. But if it is not 8 GeV it is 9 or so. In any case, not too “soft”, but not hard either. However, the search for heavily displaced muon tracks in that sample has not been carried out yet in Run II data.

It has, instead, been done in Run I data. Guess what: there is an excess of both additional electrons, and additional muons, with very low invariant mass – quite like the distributions in the present paper. The Run I analysis did not concentrate on very high-impact parameter tracks, however: it had not occurred to anybody back then that there was such a source of background. Giromini did study that lepton excess, and came up with a very controversial analysis, which saw the light only a few years later with few authors. It is reported here, and the paper is here.

As for impact parameters: there are distributions in the paper of the impact parameter correlation for pairs of muons traveling in the same “jet”. The correlation is found to be very small, compatible with the fact that these objects appear to be produced by a cascade, and not by a single decay.


13. FNesti - November 9, 2008

Thanks Tommaso,
yes the Giromini paper reports 8GeV as the minimum Pt for the ‘hardest’ lepton, the one defining the lepton-jet. Still I do not understand if lower energy leptons (alone) are not recorded, or just they made a cut (for flavour purity?).

Anyway, I saw the bump .. very interesting.


14. island - November 10, 2008

These last few posts are why I endure your politics, Dorigo… 😉

Great stuff, and I am curious about low energy leptons too.

15. dorigo - November 10, 2008

Hi FNesti,

there are trigger-level cuts, made online during data acquisition. These cannot be made looser, or the data aquisition system would drown in dead time. A single muon trigger Pt cut cannot be loosened below 8 GeV. A dimuon trigger can have much looser cuts, 3 GeV.

Then there are offline cuts, which are made to select a sample with reasonable purity. For muons, cutting below 2 GeV would gain little real muons -those who by chance lost less than that in ionization during the passage through the calorimeter. Cutting below 3 for CMP muons amounts to the same thing.

And no, generally b-quark purity cannot be increased much by tightening Pt cuts. That is, it can, but it is not advantageous.

Is that what you were asking ?


16. carlbrannen - November 11, 2008


If you ever get to thinking that your readership doesn’t understand physics, you might try recalibrating your sensors by reading the comments on this article on the muon jets that quotes you and Not Even Wrong at length.

17. Philipum - November 11, 2008

Hi Dorigo,

I am Philippe, working as a postoc in the ATLAS experiment. I have been studying the CDF multi-muons a bit since last week : I have read the paper as well as your fantastic posts about it. I have just one question to ask you for the moment : do you know why the paper does not show any calorimeter-based information ? I am very curious to see distributions of, e.g., jet energy or missing transverse energy for the ghost events : do you know if such plots exist ?

18. dorigo - November 11, 2008

Hi Carl,
well, I think most readers here do know something about physics. And most of those that do not are not scared to get to know something, at least.

Hello Philippe,
congratulations for your wonderful, idle detector 😉 (I am in CMS 😦 )…
The paper is a bit hard to digest, perhaps because the review process was hampered in some ways. I do know the answer to your question. The authors disregarded calorimeter information, finding it inessential for their studies. During the review the calorimeter info was analyzed in more detail, but found not providing additional insight. However, it is true, some more detail would have been a good idea. The publication stands on its feet even if incomplete (no electron study, no study in additional datasets, no information from calorimeter discussed in detail) because it is a warning about past measurements involving muons with no SVX information (b xs measurements turn out high, X_d also, and other biases result from including in one’s data those muons). If it was a direct claim for new physics, it would be a crippled one. Instead, it is a first warning that CDF sees this effect and is investigating it further. That, at least, is the way I see it.


19. Not Even Wrong » Blog Archive » Short Bits - November 12, 2008

[…] the CDF anomaly, Tommaso Dorigo has started a series of detailed posting on the analysis here and here. Matt Strassler has a new paper out about this, including some discussion of possible […]

20. Philipum - November 12, 2008

Thanks Dorigo. So, the ghost event do not seem to exhibit striking jet characteristics.

The paper is a warning about inconsistencies in past measurements, with ghost events as a plausible solution. My next question is the following : have the same inconsistencies (b cross sections, X_d etc.) also clearly been present with measurement made by the the D0 experiment ? If yes, is it not a strong indication that ghost event are going to be seen in D0 as well ?

21. dorigo - November 12, 2008

Hi Philipum,

D0 measures the correlated bb production to be in agreement with NLO QCD when b’s are tagged by secondary vertices, and higher than NLO when b’s are selected with soft muons, exactly as CDF does.

The numbers are R=1.1+-0.3 in the first case and R=2.3+-0.7 in the second.

More detail about the CDF measurement and a summary can be found here.

This might be taken as an indication that the muon excess is due to a systematic effect not coming from detector modeling or similar instrumental effects.

To me, the difference between 1.1+-0.3 and 2.3+-0.7 is just what it is: 1.2+-0.7, or 1.7 standard deviations. The same significance of the LEP II Higgs signal. Neither convinces me of anything, although both are suggestive. I would not call the D0 result as a strong indication that they will also find ghost events, any more than I call the LEP II result a strong indication of the Higgs sitting at 115 GeV.


22. Philipum - November 12, 2008

Hi Dorigo,

Thank you for your answer, everything is clear now. Let’s wait for more detailed CDF studies and for an eventual confirmation by D0.

I have a clear memory of the LEP II Higgs “signal” : I was a summer student at CERN at that time, it was quite exciting ! And I agree with you, the indication was not strong. Actually, I still believe that the Higgs does not exist :o)


23. Xerxes - November 12, 2008

Why does the signal drop below the expected background at low-d (in the last figure)? Is that a known systematic?

24. dorigo - November 12, 2008

Xerxes, the two distributions of impact parameter are very different. They are allegedly constituted by different processes. While the red one is due to a mixture of QCD processes, the black one contains an excess which cannot be easily accounted for by those components.


25. Henry Deith - November 13, 2008

Hi Tommaso, could you define “minimum ionizing”? I’m a bit confused about what is meant by this.


26. dorigo - November 13, 2008

Hi Henry,

a charged particle is minimum ionizing in a certain range of momenta, depending on its mass. Ionization depends on a formula called “Bethe-Bloch”. The ionization energy loss has a broad minimum in a wide range of momenta: it is very large for slow particles, then minimum, and then it grows slowly due to some relativistic factors in the BB formula.

Hope it helps… I do not recall having a post about this, maybe I will write one soon.


27. Some notes on the multi-muon analysis - part III « A Quantum Diaries Survivor - January 1, 2009

[…] muons, CDF, new physics trackback 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 […]

28. 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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