Plot Of The Week - The Upsilon Puzzle
    By Tommaso Dorigo | October 28th 2009 03:54 AM | 32 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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    My statistics page depressingly shows that a large fraction of readers who visit this site do so for an average of 30 seconds. Maybe they were looking for something different, or maybe they do not like the content offered here. In any case, I have decided that my long, detailed articles about particle physics are not exactly meeting the demand of the audience. I am not going to change my writing style because of that, of course, but I will try to also offer some thirty-seconds physics bits here, every once in a while. So let me make a dry run, using a recent result by the CDF collaboration. The clock may start.

    Upsilon mesons are fancy subatomic particles composed of two b-quarks tightly orbiting each other. Three such states, of different mass, can be copiously produced by the Tevatron proton-antiproton collisions and efficiently detected by the CDF experiment when they decay. Here is how they look like, once their mass is reconstructed from the energy of the two muons they yield when they decay:

    CDF used the decays of the (1S) resonance to measure its polarization -a quantity describing the angle between the direction of the particle motion and spin. The polarization is reduced to a number alpha variable between -1 and 1, which is shown in the vertical axis in the figure below, while the horizontal axis shows the transverse momentum of the produced particles. Also shown is the determination of the polarization obtained by the competitor of CDF, D0. The two results are utterly inconsistent!

    What is even more interesting is that theoretical predictions (from a non-relativistic QCD model) disagree with both results: below you can see the comparison of CDF data with theory. From 8 to 17 GeV there is agreement with CDF and disagreement with D0, above 17 GeV the opposite occurs.

    Ok, you can stop the clock. More than thirty seconds, huh ? Well, I took some liberty here, since I think these results are really interesting! For more information, please visit the web site of the CDF Y polarization analysis.


    Are you sure the short-time visitors aren't actually search-engine spiders?

    Yes, these are real visitors.
    Tommaso, many times I click on your page to see if there is new physics content. When there isn't, my average stay is on the order of 2 seconds and will thus contribute to the average time in a manner inconsistent with your conclusion =)

    A naive question. I thought the polarization is independent on pT. How do we convert |costheta_star| to alpha? Thanks

    Hi Anon,

    the polarization depends on Pt (or at least, there is no reason it should be constant) because the production of Y(1S) proceeds through different mechanisms, each of which has a different helicity structure, and each of which has a different Pt production spectrum. So the sum of the various processes should have a Pt dependence.

    Alpha is defined as (s_T-2s_L)/(s_T+2s_L), where s is the cross section and T,L are transverse and longitudinal indices. The distribution of the emission angle theta* of the positive muon in the Y center of mass frame, with respect to the motion of the Y in the lab frame, is dN/dcos(theta*)=1+alpha cos^2(theta*).

    Hi Tommaso,
    why non-relativistic QCD was used for theoretical predictions? Because of just to make it simple to calculate (I realise it is)?

    No, no. It's not exactly a simplification, but rather a theoretical description of the production processes, based on assuming a factorization of the mechanism creating quark-antiquark pairs and the ones responsible of binding them into a colorless stable state. The latter part is governed by the calculation of matrix elements which do not require a relativistic treatment. At least that's what I remember about the whole thing. Bear in mind that it has had some successes in predicting other phenomenology of quarkonium in the past. Cheers, T.
    Yeah, maybe it's so. But why I asked is: first, I compared momentum (which is even larger than p_T ) with mass and resulted with relativistic case; second, I've treated how I can get b-quark from first generation quarks and noticed that due to large mass difference (even if transition is not direct but proceeds more gradually) velocities should be relativistic anyway to get energy from. Maybe these facts have negligible influence on helicity.

    Hi Quantense,

    the production of b-quark pairs proceeds through a quantum chromodynamical interaction. As you correctly note, b-quarks do not exist in the proton so they are produced in pairs, from the splitting of a gluon. The two quarks weigh a total of about 9 GeV, and the combined momentum is often not large (the Upsilon has a very soft production spectrum, as you may also infer from the error bars in the points in the graphs above). The pair is indeed "relativistic", in the sense that it carries a momentum of comparable order to the rest mass. What is non-relativistic, however, is the relative motion of the two quarks. Since binding occurs depending on the relative motion and not depending on absolute motion, what matters is the former. The relative motion of the two b-quarks produced in a gluon fragmentation is typically non-relativistic, and one may parametrize the binding probability in terms of the relative velocity (non-relativistic), helicities, colour, etcetera.

    Come on, don't tell me that you don't understand what the timing means. A "lasting visit" is between the first click on a page (when the counter is activated) to the last one. So when someone only opens 1 page, which most people do, he contributes 0:00 to the average time (even if he reads the page for 2 hours). If you have SiteMeter, I would suspect that you could figure it out.
    Aha, no Lubos, thank you for the hint. I had not stopped to think on this. Do scrolling down a long page generate a click ? Anw no, I do not have sitemeter, there is a statistics page handled by ScientificBlogging here.
    Dear Tommaso, I think that the mechanism must be pretty general even for different software arrangements. I believe that even Scientific Blogging  only generates one signal if the user opens one page (the signal probably occurs as long as the user loads the page - presses enter), and the only possible length to attribute to such a signal is zero.
    In particular, it sounds almost inconceivable that Scientific Blogging is interactively monitoring - like a Big Brother - whether the user scrolls up/down a page.

    To reduce your optimism, serious blogs still have something like 1:48 of the average time spent,

    That does help, thank you.
    You can also see that the average visit of large blogs such as Instapundit or DailyKos

    is reported to be 0:00 by SiteMeter. That apparently means that a visit is interrupted, or cancelled in this counting, once 100 additional visits appear after it. Because 100 visit take a minute and most people don't manage to click quickly - or because SiteMeter simply gives up the remembering of all the visits of such large blogs - the result is zero.

    The B-physics already looks pretty messy.

    That's an excellent description.   Our actual average (using the server logs and not javascript tools like Sitemeter or our own) spent is over 6 minutes per visit - quite high compared to ordinary sites and our average pages per visit is just under 9 - also very high.

    Outside server logs, which would take far too long to compile on the fly for users, I haven't found an accurate way to see time spent on the site.    
    Hi Tommaso,

    Thanks a lot for your clarification about mechanism of the process. Actually I suspected the role of relative
    b-quarks motion to be prevailing important here.

    Please don't give up writing long (or short) articles. I come to your site slightly more than once a week, look at what paragraphs are recently added, click through if I'm interested (physics, Italian politics, travels, not so much chess), and read for a long time. The physics articles are of great interest to me. As for the site ratings, if Samuel Clemens were alive today, he'd probably change his comment to "lies, damn lies, statistics, and web statistics".

    Thank you for your input, Mark. No, I am not giving up, of course. But I sometimes wonder what fraction of readers actually read the whole thing, when I write my longer pieces. I guess something between 5 and 10%. Of the rest, a good 50% seeps through, and 40% plain leave after a couple of paragraphs. This is just my hunch -it does not use any accurate means of monitoring. I still think it valuable to talk to that 5-10% of interested readers, but of course one must try and reach a larger audience if possible, so some adjustments are at times required.
    Hey Guys, I just wanted to say I am not a scientific person. I do not work in a science related field. Any scientific formulas that are used is complete gibberish to me, yet I find science fascinating and your site is one my favorite sites to read on a daily basis, and makes me appear much smarter to my friends and family than I actually am.

    Michael Galltielli

    Anon, if you read us, they are right -you are smart.

    You are essentially correct that a non-relativistic version of QCD is used to compute the properties of the Upsilon as a bound state of b quarks because it is simpler. In this case, it takes an intractable problem and makes it seem approachable. The reason that is so is that it allows us to take what would look like an infinite set of terms we would need to measure to determine the properties of the b quarks in side the Upsilon, and orders them by their velocity. Since the b mass is large enough that alpha is << 1 (well, about 0.3 or so), the velocity works as an expansion parameter, which reduces the infinite set to a few coefficients which one can measure. That means we can fit them from some observables, and then start predicting further measurements based on them. If there was an infinite set, we would never have enough measurements to get to the point where we can start predicting.

    Dorigo is correct that the production is in fact treated relativistically, and only the relative motion of the b quarks in non-relativistic.

    Non-relativistic QCD (NRQCD) is the modern underpinning of our understanding of Upsilons, charmonium, etc. It's close cousin, heavy quark effective theory (HQET) has been even more instrumental in understanding systems with one heavy and one light quark.

    Dear anon, darn it, it is in cases like these that I hate anonymity the most. Why not disclose your name here? There is no argument, just a beneficial discussion... You might be a reader with good acquaintance with wikipedia, or a student in theoretical physics, but you might also be one of the leading experts in the field, and were the latter the case, I would be happy to start asking you questions myself on the subject. In fact, this blog sometimes does allow me to open a discussion channel with people in the know on some relevant theory aspects of particle physics, and I am always thankful of that added bonus. But unless I know who you are, this is not possible. It sucks! Cheers, T.

    I am the anonymous poster previously. I signed my name to the bottom of my post, simply forgot to add my name in the "name field". I have always found science interesting with particular interest in both physics and astronomy, as well as general science education, However I am mere telecommunications technician by trade, with a hidden passion for literature, writing, and science. Although I like to consider well informed, I can never claim to have more than a basic understanding of any scientific field. . However I do like to read something more advanced than Popular Science. Your site is a great read, even if I might need "wikipedia" to help me understand some of what is written. You, Josh Witten and Kimberly Tyree are m favorites, but in reality all the regular writers here are quite good.

    Thank you again

    Michael Gallitelli

    Michael Gallitelli mentioned (as Anonymous) nonrelativitistic quark models as being usefully acccurate,
    you Tommaso said that you "... would be happy to start asking ... questions ... on the subject ...",
    I will mention an aspect that seems interesting and hope that some experts might commment here:

    The nonrelativistic quark models assume that, internally to composite particles, the component quarks move slowly and have constituent masses,
    relativistic QCD assumes that quarks have current masses and move more rapidly the lighter they are, with lighter quarks moving at relativistic velocities.
    A puzzle is that the nonrelativistic quark models seem to be realistic even for the lightest quarks (up and down).

    A conjectural resolution to the puzzle might be possible using Bohmian quantum physics, in which the kinetic energy of confined fermions is transformed into the potential energy of the Bohmian quantum field,
    that even the lightest confined quarks would move slowly because their kinetic energy would have been transferred to the Bohmian quantum field potential energy.
    (see Bohm's Hidden Variable paper II (Phys. Rev. 85 (1952) 166-93,
    reprinted in the book Quantum Theory and Measurement by Wheeler and Zurek (Princeton 1983) especially at page 387)

    Tony Smith

    Toby, the wrong I think you have me confused with the other anonymous post --- but some other anonymous mentioned the quarks. I merely professed a liking of the website. I apologize for the confusion.

    Hah Michael, I will admit you left me somewhat perplexed. I mean, for an outsider explaining in detail the problems which lead to NRQCD being a good way to predict the phenomenology of quarkonium, better than I could do it, was a bit too much :)
    Just another example of why being anonymous on the web causes confusion.
    Hi Tony,

    Actually I'm a little bit surprised about your conjucture, because I believe QCD (and SM) to be sufficiently OK for the most of HEP processes (at least like this, but there's quite big probability I'm wrong). And the question was how to use it properly and how to expain experimental results (which do not agree even with each other). But anyway you are using non-standard ways and I like it very much. But do you think you are trying to find the limit of QCD validity in the right place? Maybe here we just should use ordinary tools?


    Quantense, I agree with you that the SM and QCD are good things,
    it seems that the nonrelativistic quark model NRQM is also a good (i.e. pretty much realistic) thing,
    I would like to see how the relativistic QCD and nonrelativistic NRQM can be reconciled.

    The Bohm Potential might explain the different interpretations of velocities of quarks confined inside composite partices (most prominent in up and down quarks)
    that leads to the next issue:

    the relation between constituent and current masses (also most prominent in up and down quarks, with constituent masses around 300 MeV but current masses of only a few MeV).

    The current accepted view seems to be that "... Constituent quark masses model the effects of dynamical chiral symmetry breaking, and are not related to the quark mass parameters ... of the QCD Lagrangian ...".
    (from the Particle Data Group Review on Quark Masses, updated February 2008 by A.V. Manohar and C.T. Sachrajda)
    some have looked more closely at "the effects" leading to constituent quark masses, such as Nambu-Jona-Lasinio (NJL) and related models. For example, in hep-ph/9702219 Mishustin and Scavenius "... studied ... dynamical generation of the constituent quark mass ... within the linear sigma model and Nambu-Jona-Lasinio model ...".

    My query is about relationships between relativistic QCD and models such as those related to NJL,
    that might improve physical insight into how each of them with respect to sea vs. valence quarks, sea gluons, etc.

    Also, I should confess that I have a personal affinity for some NJL-related models related to the work of Yamawaki et al (see arxiv 0907.5277 etc).

    Tony Smith

    I'm the anonymous poster to which Dr. Dorigo referred. I have to confess I was somewhat perplexed by Mr. Gallitelli's posting, but that was quickly cleared up. I have changed my moniker to "Anonymouse" to be slightly more individual. I can't be bothered to be more creative than that, Sorry. To answer your question, I am conversant, but not truly an expert in NRQCD or HQET. I'm happy to answer questions as I can, and if it is beyond me, I'll just own up to it.

    Mr. Smith is a little confused with what is meant by "NRQCD". The nonrelativistic quark model he has in mind is usually called just "the quark model" or sometimes "the constituent quark model". It is very true that it seems to "work better than it ought to", but it is based on a picture where the (nearly massless) up and down quarks are dressed up with a cloud of gluons, and the constituent quarks get massive as a result. It's an interesting and effective picture, but it is more or less impossible to relate it in a controlled way to ordinary QCD. It's easy to see that QCD does something like this, but there is no well-defined mapping from QCD to the constituent quark model. As such, one can't honestly say its predictions are from QCD. They're just reasonable approximations, and we don't really know how crude those approximations are. NJL lives in a similar framework -- it makes it clear why spontaneous symmetry breaking is something we expect a theory like QCD to produce, but it is not a rigorous derivation of it from QCD.

    NRQCD deals exclusively with bottom and charm quarks, whose masses are much bigger than the scale of the strong interactions. They truly are non-relativistic (in the sense of current quarks). Unlike the constituent quark model, it is rigorously derived from QCD, and we can think of its predictions as being firmly connected to the Standard Model itself.

    I agree with the statements of Anonymouse that:
    "... NRQCD ... is rigorously derived from QCD ...[for]... quarks, whose masses are much bigger than the scale of the strong interactions ..."
    "... the constituent quark model ...[and]... NJL ...[do not have]... a rigorous derivation ... in a controlled way ... from QCD ...".

    What I am trying to ask is:
    Whether any experts out there know of any theoretical work that now might be going on to try to establish such derivations from QCD ?
    Would such work be regarded as a useful line of inquiry ?

    Tony Smith


    As far as I am aware, there is no effort in that direction. It could be useful, but since it is unclear how to proceed, it is not considered very promising by most theorists.

    The constituent quark model is not even well enough defined from a quantum field theory point of view to make it obvious what one would be looking for. In fact, it may be that is inconsistent with QCD at some (small) level, making it impossible to do better.

    I dont think that it is so relevant to measure the average time of visits.
    1. I check a few newspapers, but I open them all at once and check them some time later on. So my average time there might be a few hours, even though the real time is actually between a few seconds and a few minutes.
    2. Sometimes I check if there is anything that interests me. Some things in this blog dont, which doesnt mean they are bad, they are just for someone else. That takes it a few seconds.

    If a student is in your class (or any physicist at a seminar, for that matter) it doesnt mean that he (or she) is listening. Its the ones asking questions that give you the true measure of their interest.