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    Free Quarks ? Don't Be Fooled!
    By Tommaso Dorigo | November 7th 2011 08:16 AM | 41 comments | Print | E-mail | Track Comments
    About Tommaso

    I am an experimental particle physicist working with the CMS experiment at CERN. In my spare time I play chess, abuse the piano, and aim my dobson...

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    These days I am preparing a three-hour course of statistics for particle physicists which I will give at a winter school in a couple of months. This stimulating task forces me to find nice and simple examples of good and bad applications of basic statistics. Stuff with high didactical value, and hopefully also entertaining.

    For today, I am happy with a simple illustration of why to be a physicist you need to know basic Statistics. The example is of course based on a real analysis in particle physics. It is based on a claim made in 1969 by McCusker and Cairns that they had observed the track of a special charged particle in a bubble chamber exposed to energetic air showers. The track appeared to ionize the gas of the chamber less than half as much as what it should have: 110 droplets along a unit-length path instead of 229.

    Ionization is (well, was) measured in bubble chambers by counting with a microscope the number of droplets along the particle path. These droplets form by condensation around the points where the incident particle scatters with the gas of the detector.

    The figure on the right, taken from PRL 23 (1969), page 658, shows a bunch of parallel tracks caused by a shower of charged particles from a energetic cosmic ray. Among the tracks there is one which is much fainter than the others (I leave you to guess which one it is): that is the one which McCuster and Cairns claimed to be due to a fractionally charged particle.

    The question one must answer, in order to start fiddling with the idea that the track in question is due to a free quark or some other exotic thing produced in the very high-energy interaction in the atmosphere, is how likely it is that one observed, among 55,000 tracks, one track with 110 or fewer droplets per unit path length, when the average expected number is 229 (the latter determined by studying the total sample of tracks).

    I can hear some of you radiating confidence as you think: "Ah! A simple problem in Statistics... The number of droplets is a Poisson variable, since the Poisson distribution describes the probability of finding n events in a given time, if these occur independently from a constant rate process". Very good then: what you have in mind is the formula

                    P(n) = [mu^n e^(-mu)]/n!


    where mu is the average number in the given time (or given path length, in our case). If for a track we observe n=110 when mu=229, we may ask "What is the probability that a track produces less than 111 droplets, if the expected number of droplets is 229?". The required probability is the sum of P(n) with n running from 0 to 110, and the result is P(n<=110) = 1.6 x 10^(-18).

    Okay, then if we have 55,000 of these, the total probability to observe one or more of these is P(>=1 weird track in 55000) = 1-[1-P(n<=110)]^(55000), which is in the whereabouts of 10^-13. One in ten thousand billions! That must surely be a fractional-charge particle ! We are surpassing the five-sigma "observation-level" significance head, shoulders, and tail here.

    Hmmm, not so fast.

    If you are a good physicist, you know that a single scattering of a charged particle off a nucleus in the vapour of the chamber produces more than a single droplet. In fact, this number is four, on average. The droplet production is itself a Poisson process. Fine, so we have two separate Poisson processes - particle scattering, and droplet formation. Does it change the picture ? No, if you are a good physicist who does not know squat about Statistics.

    If you have at least a good hunch of basic Statistics, however, you know that what you are describing is not a simple Poisson process, but a compound Poisson process. And the two are rather different things. The fact that scatterings yield an average of four droplets in fact dramatically increases the likelihood of tracks with small droplet multiplicity: by using the correct distribution function of the compound Poisson (where now mu=4, lambda*mu=229, and N is the number of scatterings):



    If we then ask what is the chance to have seen at least one such low-ionization track in the 55,000 sample, the probability is now 1-(1-P')^(55000), which is a striking 92.5% ! Ooooops! We should have rather been surprised to NOT have observed such a low-ionization track!

    The summary of this example is simple to spell: You may know your detector and the underlying physics as well as you know your ***, but if you do not know basic Statistics you are going to be fooled !

    The McCusker and Cairns PRL article soon received its due rebuttal [R.Adair and H.Kasha, PRL 23, 1355 (1969)].  For an evidence of quarks, one would have to wait five more years...

    Comments

    Vladimir Kalitvianski
    I know that the ionizing power is energy dependent so you have to prove that you speak of the same energy particles. Otherwise comparing the track densities is meaningless. I do not know anything about stability (dynamics) of the tracks either. It should be unambiguously described.
    dorigo
    Hi Vladimir,

    all charged particles except electrons above some energy reach a regime called "MIP", for minimum-ionizing particle. In these conditions their energy loss is quite similar. The particles recorded were in the core of high-energy showers, and all in the MIP regime.

    As for "stability" of the tracks I do not know what you refer to. A track is a trajectory, and as such it has a direction and a curvature, but no dynamical properties. If you are talking about the collection of droplets, if you need a description of the way droplets condense along charged particle paths I suggest a book on tracking detectors... There are no stability concerns that I know of.

    Cheers,
    T.
    Vladimir Kalitvianski
    Thanks, Tommaso, for your answer. Yes, I meant droplet formation, growth, and disappearing dynamics.

    As to the charge "measuring", it is better done in magnetic fields.

    So your explanation of a thinner track is a rare statistical fluctuation. Then, more frequent fluctuations must be present amongst those 55000 tracks too.
    vongehr
    So your explanation of a thinner track is a rare statistical fluctuation. Then, more frequent fluctuations must be present amongst those 55000 tracks too.
    That is exactly what crossed my mind. In other words, the argument of
    the chance to have seen at least one such low-ionization track in the 55,000 sample, the probability is now 1-(1-P')^(55000), which is a striking 92.5% !
    is unconvincing if there is only one such track and not at least many more in a continuum of ionization track densities. As it is presented now, it seems somebody stopped arguing once he had the result he needed. But the argument is not finished. If this is the only track of low density, the probability is certainly not 92.5%!
    dorigo
    Indeed, there must have been exactly 27500 tracks with lower-than-average ionization. But the data we have, from the short article I quoted above, is that they found one low-ionization track, what was its specific droplet density, and what was the expectation value for that. I do not venture to speculate what the authors have done with the rest of their data.

    In general, however, please note that the fact that one expects four droplet per interaction is just a model. As such, it approximates things. Not all tracks have the same ionization, as mentioned above, and not all scatterings are equal.

    What do we get from those observations ? We get that the fixing of mu=4 and using a double Poisson is in itself a poor description of the physics. But it is a much better description than the original one. Since the original claim of free quarks, and the calculated exceedingly low probability, was done with a poor statistical model, while a distinctly better model (although arguably still not perfect) finds no statistical significant effect, the argument is over: if one wanted to resurrect the observation one would have to do a better homework.

    Cheers,
    T.
    vongehr
    they found one low-ionization track ... and what was the expectation value for that.
    So you are charging scientific misconduct rather than bad statistics? Surely if they found a whole continuum of lower density tracks, they should not have portrayed this one as special, even without doing any statistics. Assuming they were not cheating, the ones presented were the only ones found (sure they would have been proud to present more if they have had them). The expectation value for that is one in gazillions.
    dorigo
    Sascha, don't be pathetic. I am using the only hard facts available to me to extract statistical inferences, and I am not charging anybody of anything. You are making wild assumptions of all kinds. Please refresh your memory on what is the scientific method.

    Cheers,
    T.
    vongehr
    And another insult. "Pathetic". Thank you TD. I could have called your 92.5% pathetic, but hey, that would have been an insult, right. What is it with you two southern Europe guys here thinking you can insult other people and at the same time be all pissed off claiming others like me or Lubos are insulting if they plainly point out your mistakes? Oh right, that is your version of the scientific method.
    The Stand-Up Physicist
    I don't want to step into any kind of cat fight, but I would recommend on writing style to avoid any sentence containing the clause "like me or Lubos". I may have to issue a retraction on this little comment.
    whitepanther65
    Nice post, Tommaso. Actually it's the first time I learn something from a Science 2.0 blog. But I must add I am really a newbie, so I think there will be more possibilities in the future to learn useful things.
    dorigo
    Thanks Paolo. There's always stuff to learn in the folds of this site. Many smart writers, and readers too ;-)

    Cheers,
    T.
    vongehr
    "it's the first time I learn something from a Science 2.0 blog"
    Wow - you surely like to insult people a lot in your comments and articles. Some people who cannot bear hardness of hard science arguments claim I do, but you are just here a short while and have insulted so many people already with under the belt throws, I am a saint compared to that. Maybe you like to tone it down a little?
    Bonny Bonobo alias Brat
    Ionization is (well, was) measured in bubble chambers by counting with a microscope the number of droplets along the particle path.
    Thanks for this great educational article Tommaso. I read recently here and here that bubble chambers are no longer just history, that they are being rebuilt and resurrected to aid in the search for dark matter :- 
    The Tevatron collider shut down at the end of September, but Fermilab physicists are still active in the ongoing search to directly detect dark matter. To aid in the research they're resurrecting bubble chambers and fixed target experiments dating back to the 1970s. ANALYSIS: Where is Dark Matter Hiding? Bubble chambers are basically vessels filled with superheated liquid to detect particles moving through it. A new experiment underway aims to achieve better calibration for the bubble chambers used in the Chicago land Observatory for Underground Particle Physics (COUPP) experiment, located 350 feet underground in a Chicago tunnel. It's called the COUPP Iodine Recoil Threshold Experiment (CIRTE), and it's designed to improve the sensitivity of the COUPP detector.
    There are lots of different experiments, using a variety of approaches, designed to search for dark matter particles, with some promising -- if hotly debated -- preliminary results. But bubble chambers were nearly extinct in the field before COUPP leader Juan Collar hit upon the notion of using them to search for dark matter. They're great as neutrino detectors, too. In 2007, COUPP installed a new germanium-based neutrino detector 330 feet below ground in the sewers of Chicago, renting this unusual lab space from the city. The design was modified to detect WIMPs instead of neutrinos.
    Bubble chambers sound like fun things to experiment with, though maybe a bit slow, and I love the pictures, however I couldn't help wondering if fire extinguishers all over the world containing iodotrifluoromethane are also all inadvertently acting as unrecognised bubble chambers, without the digital cameras in situ, after reading this part? 
    COUPP's "detector" is a glass jar filled with a liter or so of a fire-extinguishing liquid (iodotrifluoromethane). When a WIMP hits a nucleus of one of those atoms, it triggers an evaporation of a small amount of that liquid, producing a tiny bubble.It's initially too tiny to see, but it grows, and that growth can be recorded with digital cameras."The bubbles in the fluid are slow enough that high-speed cameras will capture the changes through continuous still shots. We're making the world's most boring movie," Peter Cooper, the Fermilab physicist heading up CITRE, told Symmetry Breaking.
    My article about researchers identifying a potential blue green algae cause & L-Serine treatment for Lou Gehrig's ALS, MND, Parkinsons & Alzheimers is at http://www.science20.com/forums/medicine
    dorigo
    Hi Helen,

    yes, bubble chambers are not dead - I was thinking at HEP when I wrote that. They are very beautiful detectors, the only ones that allow a visualization of the physical reactions without the need of computer reconstruction (emulsions also might be argued to provide the same feature, but that's another story).

    Cheers,
    T.
    Bonny Bonobo alias Brat
    They are very beautiful detectors
    What about the fire-extinguishers Tommaso? Are they also acting as bubble chambers?

    My article about researchers identifying a potential blue green algae cause & L-Serine treatment for Lou Gehrig's ALS, MND, Parkinsons & Alzheimers is at http://www.science20.com/forums/medicine
    dorigo
    I don't think so - the bubble chambers work under special pressure-temperature conditions, they are filled with a superheated liquid, which enables the droplets to form.
    Cheers,
    T.
    Vladimir Kalitvianski
    You confuse me. If it is a bubble chamber, it is bubbles that are formed, not droplets. If it is a vapor chamber (unstable over-saturated vapor), it is droplets that are formed.
    Bonny Bonobo alias Brat
    I just wondered because this article at a physics lectures site says :-
     'you can have a superheated liquid at room temperature (20oC) like the CO2 in a fire extinguisher. Liquid CO2 at 20oC has a vapor pressure of 100 atmospheres (100 kg/cm2! To contain that we need a strong steel container. If the valve is broken off, the awesome flashing of liquid to gas makes the cylinder into a rocket that can penetrate a wall! Video:'
    My article about researchers identifying a potential blue green algae cause & L-Serine treatment for Lou Gehrig's ALS, MND, Parkinsons & Alzheimers is at http://www.science20.com/forums/medicine
    Halliday
    Helen:

    Technically, the liquid CO2 in a fire extinguisher is not a superheated liquid, until "the valve is broken off".  The distinction is that not only is temperature involved (20°C), but pressure as well.

    Superheated liquid means that you have a liquid under temperature and pressure conditions where the phase diagram for the material indicates you should have a gas.  So, for the given temperature and pressure, one should have a gas, but, instead, one has arranged things (very carefully) so as to have a liquid instead.

    (Of course, there are also cases where one may wish to go the other direction—with a supercooled gas, say.  One may also have supercooled liquids, and superheated solids.)

    David
    Bonny Bonobo alias Brat
    Thanks David, so what about a pressurised fire extinguisher filled with the same fire-extinguishing liquid, iodotrifluoromethane as used in the COUPP detector? Will it occasionally be behaving like a bubble chamber as electrically charged particles pass through it or only when and if the fire extinguisher valve is broken off?
    My article about researchers identifying a potential blue green algae cause & L-Serine treatment for Lou Gehrig's ALS, MND, Parkinsons & Alzheimers is at http://www.science20.com/forums/medicine
    Halliday
    From the description you quoted in your previous post, the material, in the bubble chamber, must be in a superheated state (otherwise, the bubbles will collapse, rather than grow).  So, if this is correct, then no:  Such fire extinguishers will not be acting as "bubble chambers".  Even when one uses the fire extinguisher, thus lowering its internal pressure, one is highly unlikely to reach a superheated state (too much perturbation occurring, and too many nucleating contaminants, typically).

    Technically, even "if the fire extinguisher valve is broken off" one still doesn't have a superheated liquid state, but an almost explosive vaporization (boiling) of the liquid into a gas, all due to the decompression one has instigated.

    David
    vongehr
    This stimulating task forces me to find nice and simple examples of good and bad applications of basic statistics.
    Well, since your example above is not convincing, what about this one: Corrupting Bayesian updating and entering a prior of P = 0 (for example: Orthodoxy demands FTL neutrinos are impossible, period!) in order to kill all experiments' significance to squat? That is a very simple example of "bad applications of basic statistics".
    dorigo
    You are off-topic Sascha. Can you discuss anything else than neutrinos these days ?

    Cheers,
    T.
    vongehr
    You are off-topic Sascha.
    Did you or did you not ask for examples of bad fundamental statistics? You know that my official work is mostly on statistics, right? Well, probably not, since you do not care about critical people. So let me tell you, even my PhD was on nontrivial cluster collision statistics and since then I have published on several different issues where people in Nanotechnology use bad statistics.
    Can you discuss anything else than neutrinos these days ?
    These are my four recent articles (not counting the blog entry): On AI personal assistants, on a book about the IPCC and climategate, on ecological problems due to cats, and on the physical basis of influence from the future. You are welcome to read my articles. Why don't you inform yourself first before being dismissive?
    whitepanther65
    From my point of view, there is another reason why this article is important: it underlines the fact that data, by themselves (or a figure like the one commented here), do not "speak" to us. In order to interpret experimental data we always need tools (like statistics for instance) and models (like a model for droplet formation for instance). In other words, I think that sometimes it is very hard to distinguish "theory" from "experiment": they both conspire to give the final interpretation.

    I have one question: does your analysys imply that also the probability for higher inonization  tracks is increased if one takes into account the underlying droplet formation process?

    Cheers Paolo

    PS I have been unable to spot the fainter track in the image :(
    dorigo
    Hi Paolo,

    yes - basically having a compound Poisson "spreads" the PDF to higher and lower values of the total number of droplets.

    The faint track is the seventh from the right, or the fourth from the left.

    Cheers,
    T.
    rholley
    How they did things in the old days: here are some pensioned off apparatus at DESY – “C” is their original bubble chamber.

    Robert H. Olley / Quondam Physics Department / University of Reading / England
    dorigo
    Nice pic Robert!
    Cheers,
    T.
    In what sense are top quarks not "free quarks" if they hadronize? Is the point that we do not observe them direclty, and instead only observe their decay products?

    typo correction "if they don't hadronize"

    dorigo
    Hi Ohwilleke,

    indeed, the top quark is the only quark that lives its life free of QCD infrared slavery. The price to pay for this luxury is that it lives a very short life!

    It is the width of the top quark (the inverse of its lifetime) what guarantees that the top quark does not hadronize before decaying: G_t is 1.5 GeV, while Lambda_QCD is 0.2 GeV. So the scale of its lifetime is one order of magnitude shorter than the scale of time needed for QCD interactions.

    But saying that the top quark is free does not lead us very far. QCD still applies. Yes, we cannot observe them directly, because we do not have cameras with a 1/10000000000000000000000000 sec shutter...

    Cheers,
    T.
    Vladimir Kalitvianski
    Due to what interaction does the top quark decay? Weak? Strong (QCD)?

    If it decays before interacting with other quarks, it is (top quark) a rare fluctuation rather than a fundamental brick of nature.
    dorigo
    Weak, Vladimir. Strong interactions cannot modify the flavour of a quark, because they are insensitive to it.
    Cheers,
    T.
    I am a bit puzzled by your formula for P(n). Did you mean:

    P(n) = [mu^n e^(-mu)]/n!

    dorigo
    Oh goddamnit, I must have been drunk!! :)

    thanks, fixed.
    Cheers,
    T.
    Nice catch... I believe the same happened in OPERA, where the proton extraction functions were averaged, and the information on its -horizontal- spread was washed away.

    A nit: it is not clear whether it is a cloud chamber or a bubble chamber picture. A cloud chamber uses supersaturated gas a bubble chamber uses supercooled liquid, no?

    Your statistics discussion is interesting, but I would bet on an expansion cycle effect, i.e. a left over from the previous cycle. bubble chambers are certainly cycled and I expect cloud chambers would also have been, a clean film so to speak. It could also be an effect of the time distribution of the shower, mgcht have been a late track or the first one, when the expansion was starting .Back in the 70's I worked a lot with bubble chamber pictures and do vaguely remember ghost tracks

    dorigo
    Hi Anna,
    yes, it is a cloud chamber, actually. Apparently, the authors measured the width of the track and it is consistent with the width of the others, so it is unlikely a ghost.

    Cheers,
    T.
    Awesome article T. Keep the coming...

    dorigo
    Ela re Ale3, 8a prospathsw. Ta leme suntoma, 8a er8w sto CMS week...
    Geia,
    T.