CPT Violation In The Top Quark Mass ?
    By Tommaso Dorigo | March 17th 2011 05:57 AM | 42 comments | Print | E-mail | Track Comments
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    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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    The CDF collaboration sent to the preprint arxiv a new paper a few days ago. In it, they report on a measurement of the mass difference of top and anti-top quarks. The result would not be worth discussing in detail, if it did not show a 2-sigma discrepancy which might be the first hint of a CPT violation. So let me discuss it here.

    "CPT" is an acronym for a symmetry of Nature that is generally believed to be absolutely conserved. Such properties of matter are best tested at a microscopic level, where things behave "simply" -if you understand quantum mechanics. Each of the letters in the acronym refer to a different symmetry operation one may act on elementary particles (as well as more complex systems): C stands for "charge conjugation", and it is the operation consisting in changing the electric charge of every body. P stands for "parity inversion", and it corresponds to a mirror transformation: particles in a mirror will appear to move in the same direction, but their spin will be inverted. T stands for time inversion, and corresponds to inverting the flow of time in particle motion and reactions. If you invert the time coordinate, a forward-moving particle will look like its own anti-matter counterpart moving backward, so if you act on a system with the combination of charge conjugation and time reversal you get back your original system moving backwards, but it will look like its mirror image. Acting on a system with the successive operations of C,P, and T should leave the physics of the system invariant.

    So what does this have to do with the top mass ? Well, quite simply, all particles must have the same mass as their antiparticle counterparts if CPT is a conserved symmetry of nature. Since top quarks are created in pairs in proton-antiproton collisions, one can try and measure separately the mass of top and antitop quarks, to verify whether they do look the same.

    Of course the same game can be played with any other elementary particle! However, remember that the top quark is the best measured one, due to its large mass. But electrons and muons are certainly much, much better measured. So one must hypothesize that the large mass of the top quark makes it special as far as a potential CPT-violating effect is concerned.

    The analysis concentrates on single-lepton final states of top quark pairs from a sample of 5.6 inverse femtobarns of 2-TeV proton-antiproton collisions collected by the CDF experiment in the course of the last 10 years. The charged lepton (an electron or a muon) provides a trigger for the collection of the events, and a first background discrimination. Events are selected to contain in addition a significant amount of missing transverse energy (a signature of the escape of a neutrino from the W boson decay which also produced the charged lepton), and four hadronic jets. The decay chain, in fact, involves the top pair going into two W bosons and two b-quarks; while one W boson decays into the lepton-neutrino pair, the other produces two hadronic jets. The two b-quarks yield the other two jets to complete the "W+ 4 jets " signature. The figure above hopefully clarifies what I mean!

    CDF divides their candidates into ones where zero, one, or two jets were "tagged" as containing a signature of b-quark decay. This division produces three orthogonal samples with quite different background content, and improves the overall sensitivity of the analysis.

    Usually, when measuring the top quark mass from top quark pair events candidates, one employs a kinematic fitter that assumes that the top and antitop quarks are equal. A modification of the fit releasing this constraint (but keeping in place others including the equality of W boson masses to the PDG values) allows to extract the top and antitop mass separately.

    The figures on the right show the difference in the best reconstructed mass of top and antitop candidates for non-b-tagged and b-tagged events. The darker shaded curve shows the background component. The red line is a fit which assumes a difference of 4 GeV in the top and antitop masses, while the blue one is the hypothesis of no CPT violation.

    A likelihood fit to the data returns a mass difference of top and antitop quarks of -3.3+-1.7 GeV, which is an almost two-sigma difference of the top and antitop masses; the difference is then not significant. also worth noting is its size, which is of 5%, a huge value. If CPT is violated in the mechanism that gives mass to top quarks (whatever this may be),  this is a very large effect. According to Guido Altarelli (giving his summary talk at NEUTEL as I write), this mass difference "is unrealistic".

    What to say... It would be fantastic to step into such a unexpected effect just by accident. That is: the physicists who have performed this analysis spent a long time making it a precise measurement and deserve our full respect, but the search seems to me a bit like the one of the drunkard who searches his watch under the street lamp, because it is too dark in the place where he believes he really lost it!


    Nice results!
    Just to make things clear: it's the blue line which corresponds to the hypothesis of no CPT violation on the plots (you wrote "red" twice).

    Daniel de França MTd2
    So, maybe the Top is its own antiparticle, and the anti particle is actually its mirror, like Marni says? This is the 2nd time an apparent violation of CPT is seen,besides that one of the neutrino.
    Looks pretty subtle to me for the sum total of ten years of collisions. A very minor omitted detail in the background could expand the error bars enough to make a null hypothesis fit. Similarly, I could imagine, something like failure to accurately predict a correct amount of CP violation by using a slightly erroneous experimental constant for the CP violating phase somewhere in a the b decay chain turning what would otherwise have been an unremarkable 1.5 sigma anomaly into more notable 2 sigma territory.

    Also, I think it is appropriate in general to be more wary of a two sigma deviation in someplace you aren't looking for anything special than it is in someplace that you have reason to think, a priori, should be atypical. Two sigma effects should show up as a matter of random chance in one out of twenty experiments merely as statistical flukes. If you look at all of the "baseline" results of Tevatron over the last ten years in every possible way, something is inevitably going to go outside the two sigma error bars even without CPT violations. Presumably, in shorter data runs the top-antitop mass deviations were too small to be considered statistically significant, or the result would have already been announced.

    The only thing that makes a top-antitop mass discrepency even worth seriously considering relative to a statistical fluke hypothesis is the existence of a similar discrepency in the MINOS data comparing neutrinos and antineutrinos (although that isn't replicated in other neutrino mass estimation experiments).


    This is a fascinating topic and I am sure that Kea, Lubos and others may have different opinions on how to interpret these results. Here is my take:

    The CPT theorem holds strictly for local and Lorentz covariant field theories that obey the usual spin-statistics connection. It is, however, likely that either a) heavy flavor physics or b) physics beyond SM could deviate from conditions required by the CPT theorem. But this does not automatically imply breaking of Lorentz invariance which MAY NOT be directly applicable to either a) or b) in its conventional formulation. Same applies to other consistency requirements of QFT such as unitarity, renormalizability and absence of anomalies.

    In my view, the bottom line is that recently reported mass and charge asymmetries between top and anti-top, as well as the neutrino asymmetry reported at MINOS, may not be at odds with Lorentz symmetry as we understand it today.



    It's interesting that the background model in the nontagged plot is not perfectly symmetric.

    I agree and the hard working experimentalists do have my respect, but this doesn't increase my confidence. The masses are not precisely known, and there could be any number of other explanations for this that do not require the assumption of the basic symmetry.

    Sorry, I meant basic symmetry being violated.

    I think that the interpretation chosen by this paper is shameful sensationalism. Paying attention to 2-sigma deviations is bad enough, but using 2-sigma deviations to "disprove" one of the most important principles of the discipline is a really bad taste.

    Whoever had the idea to interpret their inability to measure the masses of tops and antitops more accurately in this far-reaching way should be ashamed.

    YES! I think this guy has it nailed!

    Thanks, Sean! The truth ultimately always prevails although it can take some time.

    Ttoday, D0 have released a preprint in which they squashed the nonsensical sensationalist CDF hints on CPT violation:

    The mass difference in GeV is 0.8 plus minus 1.8 stat and 0.5 syst - so it's as zero as you can get.

    YES! I think this guy has it nailed!

    Hi Lubos,
    I suspect you didn't actually read the paper.
    I didn't find a single sentence of the paper where they claim that this result "disproves" anything. If I missed it, please point me to the exact line.
    The most bold sentence that I found is that it deviates at 2 sigma level from the CPT-symmetry expectation. What is your criticism, exactly? That they should have written "it agrees at 2 sigma level with the CPT-symmetry expectation"? Whomever is able to read until that point in the paper also knows that the two statements are the same.

    I must also add that I can't understand the criticism in some of the comments above for looking for an effect that "cannot" be there.
    I find healthy to look for deviations even when you have no reason whatsoever to expect a deviation; I understand in general the criticism that, with finite resources, these must be prioritized, but this is a particularly uncontroversial case because data are anyway available as a by-product of all the rest of the Tevatron program, and performing this study doesn't require any other cost than a few months of salary of just two people (*).
    There are several instructive historical examples of important effects that could have been observed before, because the data for their discovery were already available or easy to produce, but none of the "owners" of the data had considered to look for that particular effect (or, even worse, had actually stumbled into a 2-3 sigma deviation and paid no attention, remodelling the background or inflating the systematic uncertainty to take it into account and therefore unwittingly hiding it under the carpet.)

    (*) their number and identity can be seen here:

    Dear Andrea, what I find offensive is your arrogant suggestion - included to the very title, and much of the abstract as well as paper - that you have measured a nonzero difference between top and antitop masses.

    To deduce what are the masses of the particles from your measurements, you effectively have to use some quantum field theory at one level or another. Quantum field theory implies that the mass difference is zero. So the most accurate measurement is to do nothing and to conclude that the difference is exactly zero.

    In this sense, the most outrageous sentence about your paper is the last sentence, one that your measurement of the top-antitop mass difference - which is a whopping 3.3 GeV according to your paper - is the "most accurate" measurement of the quantity.

    This is just bullshit. The most accurate measurement of the mass difference, done with a clever definition of the mass, is 0.000000 +- 0.000000 GeV, and you have presented no real evidence that this is not the case. Your result is a striking sign of the immense inaccuracy with which you measure the mass of the heaviest quark, so it's really disingenious for you to claim that you've just produced the most accurate result.

    You have produced one of the most *inaccurate* results for this quantity ever written down.

    It is healthy to look for whatever effects but it is totally unhealthy to publish papers claiming to have measured effects that almost certainly don't exist, without having any real evidence for such claims.

    You should have verified that you don't have any 5-sigma deviation, and because you don't, you use use the obvious identity mass(top) = mass(antitop) as a method to make your other measurements more accurate. In other words, you should have used the top-antitop average mass, 172.5 GeV, as the actual input to use for other measurements. You failed to do all such things which really indicates that most of your mass measurements depending on the matter-antimatter difference are likely to have similar 3.4-GeV-like errors, too.

    You have surely nothing to boast about in this context, so it is irritating that you apparently do.


    Hi Lubos,

    > your arrogant suggestion - included to the very title, and much of the abstract as well as paper -
    > your measurements,
    > you effectively have to use
    > about your paper
    > your measurement
    (...a few other tens of istances...)
    > You have surely nothing to boast about in this context, so it is irritating that you apparently do.

    I surely have nothing to boast about in this context, because -ehm- I am not one of the authors. I didn't even sign the paper. Actually, I belong to a *competitor* collaboration.
    Of course you are not expected to know anything about me before answering. Nevertheless, it would have been nice if you had assumed that my comment was not interested at all, and was only motivated by correcting what I find wrong.

    Like, for example:

    > This is just bullshit. The most accurate measurement of the mass difference, done with a clever definition of the mass, is 0.000000 +- 0.000000 GeV

    Sure, and for example there was no need to measure the W mass at LEP2, after having measured the Z mass with such a high precision at LEP1, given that the Standard Model yields a very precise prediction for the MW/MZ ratio.
    Nevertheless, people did, and still do. There are countless other examples I could choose.

    > You should have verified that you don't have any 5-sigma deviation, and because you don't, you use use the obvious identity mass(top) = mass(antitop) as a method to make your other measurements more accurate.

    This identity is in fact used in most (probably all) papers by all the groups at Tevatron and LHC who aim at measuring the top mass.
    Here we agree: if there is an indication for a systematic effect, this must be understood, whether it is new physics (which is important per se) or a funny detector effect (which is important because it screws up all other measurements).
    But in my humble opinion they report their finding in a honest way (including the title, the abstract and the conclusions): they measure an experimentally defined quantity, the one declared in the title, which is expected to be 0 in our model of reality, and they communicate to the world what is the outcome of the test of this hypothesis.
    Do I understand correctly that your argument is that the title should be something like "Test of the hypothesis of top-antitop mass equality"?

    Dear Andrea, a prediction for M_W / M_Z is just a prediction of one specific model - the Standard Model - that we quantify at various approximation schemes and that - as we know - eventually has to break down somewhere. So assuming that M_W / M_Z may be something else than the theorist's first guess is reasonable.

    On the other hand, the identity of the mass of a particle and its antiparticle is the universal property of all relativistic quantum field theories and their stringy extensions. It follows from the CPT theorem that is equally universal. It's just insane to compare a particular numerical guess about the ratio of two random but inherently different quantities with a fundamental discrete symmetry of Nature.

    Great that you agree because if it's a detector effect - and chances are 95% (because it's two sigma haha!) that it is a detector effect - then the detectors are systematically treating matter differently than antimatter, and it means that different things should be recalibrated differently. For example, the calorimeters may overestimate the energy of some particles going through them and underestimate others. These are the things that serious experimenters should look into when they get such inaccurate results - instead of dreaming about disproving the CPT theorem.

    You ask: "Do I understand correctly that your argument is that the title should be something like "Test of the hypothesis of top-antitop mass equality"?"

    No, you don't understand me correctly at all. I don't think that those folks have managed to test the equality. The only thing they tested was the accuracy with which they may measure masses of different particles - and the answer is that the accuracy is extremely lousy. Regardless of the lousy "absolute" magnitude of the error - 3 GeV is a lot - one may also discuss whether the "two sigma" is large or small. Well, the size of "2 sigma" is exactly the place where one can say that he doesn't have a result in either direction - neither the direction that it works, nor in the direction that it doesn't work. It's the ultimate uncertainty, and when one gets a 2-sigma deviation, he may be unlucky but it just means that the power of his result is zero - it is not capable of shifting people's opinions in either direction.

    One can still publish such a paper but it's important what the conclusion from this result may be. It's surely not "we have said something about the CPT symmetry or the top-antitop mass difference" because this result says nothing about it in either way. They could write a paper about "Estimating the inaccuracy of the Tevatron-measured heavy quark masses". Yes, not too many people would care but that's exactly how it should be - because those folks have found nothing that someone should care about, so any other result is inevitably an artifact of dishonest hype.


    Thanks for the post! Well, I guess this lends some credence to the recently discussed idea that antineutrons and neutrons have distinct masses. Now, perhaps it is time for a combined significance analysis for the top quark, neutron, neutrino and other CPT violation evidence.

    I can't believe you wrote this while listening to Altarelli! Obviously you are an excellent multi-tasker, but even so, Altarelli's talk deserved special attention. And what's with the drunkard? Are you suggesting that the watch is over with the neutrinos, or what? In physics, drunkards smash their watches and the little pieces get spread all over the place.

    Bonny Bonobo alias Brat
    Interesting observation Kea.
    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at
    gotta love those watch analogies.
    If the level of intoxication is great, the watch may still be on his wrist.
    It might be the last place he would look.


    Knowing how abstract my analogies can be, let me clarify.
    In regards to the quest of mass differentiation with 5.6 inverse femtobarns, wouldn't your view be impared with this amount of data, yet wouldn't it be solid enough to warrent a continued or extended search at 1.96 TEV?

    Perhaps given more time (7.5) their will be no need for the street light as the little pieces catch the first glimpses of a sunrise.
    It is stated; that it is consistent with the recent result from DO..

    Instead of criminalizing experimentalists who just represent the results of their analysis theoreticians might enjoy playing with thoughts without taking any pro con attitudes.

    CPT theorem after all applies to QFT in Minkowski space. In this framework C has no geometric interpretation whereas P and T have. Maybe something is lacking from the picture.

    In TGD framework situation changes since M^4 is replaced with M^4xCP_2: C involves complex conjugation in CP_2. This purely geometric aspect of C implies much richer structure making possible purely geometric breaking of C in the framework of zero energy ontology assigning to elementary particles time scale which is macroscopic as the size of the causal diamond assignable to the particle (for electron its scale corresponds to .1 seconds which defines fundamental biorhythm, corresponding length scale is that of Earth). One could think spontaneous breaking of C in geometric sense as something analogous to spontaneous magnetization inducing breaking of CPT by giving to particle mass a small C and CPT odd contribution.

    This might relate also to the poorly understood mechanism for the generation of matter antimatter asymmetry and perhaps also to CKM mixing. Maybe matter antimatter asymmetry could be seen as the analog of chiral selection in living matter in the sense that P is replaced by C.

    For possible manner to understand breaking of CPT along these lines see the posting at my blog.

    In FIG. 1 of the paper,
    delta m_reco is shown as having a slight discrepancy for both tagged and nontagged.
    However, in the other two plots in the same FIG. 1,
    delta m(2)_reco shows no comparable discrepancy for either tagged or nontagged.

    The paper says:
    "... To increase the statistical power of the measurement,
    we employ an additional observable delta m(2)_reco from the assignment that yields
    the 2nd lowest Chi2.
    Although it has a poorer sensitivity, delta m(2)_reco provides additional information
    on delta Mtop and improves the statistical uncertainty by approximately 10 per cent ...".

    Does the lack of comparable discrepancy in delta m(2)_reco indicate that
    maybe the assignments used for it might be more physically realistic
    than the assignments used for delta m_reco ?

    Can you give a nice clear explanation of the physical differences between
    the assignments used for delta m_reco and for delta m(2)_reco ?


    A key difference between the D0 and CDF analyses is:

    The D0 analysis does not assume the average value of top-antitop quark mass to a particular value, while the CDF analysis assumes that the average of top-antitop masses is 172.5 GeV. In D0 analysis, MC samples generated over a two-dimensional grid of top-antitop masses between 165 to 180 GeV were used to calibrate the analysis.

    In other way: The D0 analysis measures the mass of top-antitop separately (measurement of two parameters) while the CDF analysis measures the mass difference of top-antitop assuming the two masses averaged to 172.5 GeV (measurement of one parameter).

    An argument I will put against the CDF analysis is: the value of 172.5 (or 173.1, or whatever the current average value of top mass) is measured *using* the assumption that top-antitop quark have equal mass. How valid is using that value when determining the mass difference is a matter of subjective debate, as Reverend Thomas Bayes has taught us. For me, were I going to do top-antitop mass difference, I will definitely not use any assumption regarding the average value of top-antitop mass.

    If there is a 2-sigma discrepancy in the mass difference, which must surely be zero, what can we conclude about the 3-sigma deviation in the forward-backward top-antitop asymmetry so much talked about these days?

    Daniel de França MTd2
    Maybe both things are related. A difference in decay would result in slightly different mass interpretations.

    I wouldn't go as far as Lubos in qualifying the intent of the report as being "dishonest". But what I find objectionable is its bias towards theories seeking to disprove Lorentz invariance. It ought to be well understood by now that Lorentz invariance is an EXACT symmetry of Nature, despite persistent attempts to prove otherwise by Kostelecky and others.

    Has anyone read this yet (including the paper linked)? I've given it a quick look at, but I'm too tired at the moment to give it a thorough examination. Really just wanted to share this, as this could be very interesting (and unexpected!).

    Ervin, they are doing no such thing. You should not equate an apparent violation of CPT symmetry with Lorentz violation. The answer is simple: particles that we usually call antiparticles are not actually antiparticles.


    I am unclear about your reply. This is why:

    1) Reference [4] in the CDF report links to D. Colladay and V. A. Kostelecky, Phys. Rev. D 55, 6760 (1997). This paper (and many others by Kostelecky) clearly link CPT violation to breaking of Lorentz symmetry.

    2) The CDF report unambiguously considers anti-top as being the anti-particle of the top.


    Ervin, if you insist in trying to understand Kea, remember she uses anti-logic. You're welcome.

    Hi all,

    I apologize for not having been able to participate in the interesting discussions of this thread so far. Let me say I would have not added much anyway. Motl's objections have been well rebutted by Giammanco. I can only add that the technique used to determine a mass difference have, indeed, been used to measure as precisely as possible the top mass _assuming_ mtop=m_antitop, as is routinely done. The data are enough to provide a check of that assumption, and it was nice to check it. If this 2-sigma effect disturbs anybody, sorry, but this is what the data say.

    I hope I will be more present in future lively discussions! Apologies to all.

    Tommaso: I don't see a rebuttal to the claim that the two particles are not being accuractely distinguished. As for myself, I am disturbed by the 2 sigma result. What bugs me is that its considered acceptable to use such scant evidence to make dramatic insinuations about the fate of CPT. And make no mistake about it, by referencing "well motivated" extensions of the standard model, this is exactly what they seek to do. It seems to me some humillity and caution should be used when we attack the foundations of the models from which so many other measurements are drawn. Do we believe with 95% confidence that we're this screwed up?

    Dear Sean,

    dogmas are against scientific progress. CDF was in the position of measuring better than previous experiments the possible mass difference of top and antitop pairs. This is sufficient justification for doing it.

    One shouldn't pay too much attention to the theory references in such a HEP paper. After all, these are professionals who allow the stringers and loopies to dictate hiring in Theory. And if they call the 'antitop' an antitop - well, that's because it's traditionally called an 'antitop'. The result most certainly does not preclude alternative explanations, as the experimentalists perfectly well know.

    Hi Tomasso,

    I think you need to revisit your descriptions of the C, P and T transformations. CPT is not the identity...

    And my sincere apologies for misspelling your name.

    You are right Rhys, I wrote a stupid thing. I modified it, please let me know if it makes more sense now.
    Dear all,
    as usual, thanks Tommaso for giving a clear description of rather complex analysis, and in general for your nicely selected highlights. I would like here to make a couple of very simple points. First, stressing a two sigma deviation in the text, or not doing it at all once you observe such an effect, does not make any substantial difference. The effect is there and it takes a fraction of a second to the reader to estimate it her/himself. Given that two sigma effects happen by definition in 5% of measurements where the systematics are very small, there is no surprise here. Also, D0 measures the opposite effect, so after all there is no reason to get excited.
    If someone wants to complain about the subjective choice of calling this a "2-sigma deviation" rather than a "2-sigma agreement", he should also realize that this is objectively not a "claim", but a measurement like any other, and the most precise in its context. Tommaso knows this very well, but it seems like it's not clear to some of the comment writer.

    The second point is actually to Tomamso regarding the drunkards: we are all drunkards here! We want to recover excitement in particle physics - the watch - and we can only look for it where data - the light - is. This is what we humbly do, and we all try to do it to our best. Good luck to all my colleagues in finding the watch!


    Your points are well taken. It looks like some of us have prematurely jumped to conclusions and CPT invariance stands unshaken, at least for now.



    Hi Tommaso,

    Actually, I think your descriptions of P and T are still wrong.
    (Even though you are right that P is 'morally' the same as a reflection, it is technically easier to discuss the actual P transformation, (t, x, y, z) -> (t, -x, -y, -z), so I will assume that).

    P reverses the momentum of a particle, and flips its helicity. So a left-handed electron travelling in the positive z-direction becomes a right-handed electron travelling in the negative z-direction (i.e. the 'spin' actually stays in the same direction). Note that left-handed electrons interact with W and Z, whereas right-handed ones don't -- the weak interactions violate P in a serious way.

    T reverses the momentum of a particle, but does not affect its helicity. It also interchanges ingoing and outgoing states. It does *not* replace a particle with its anti-particle, in any sense.

    C replaces particles with oppositely-charged particles, as you say.

    (If you think about the above, you see that in the standard model, C and P cannot even be defined as separate operations. The combination CP can, but that doesn't mean it is conserved -- it is violated by the physical phase in the CKM matrix.)

    So, for example, CPT changes an incoming left-handed electron, travelling in the positive z-direction, to an outgoing right-handed positron, travelling in the positive z-direction. An easy experimentally relevant example: CPT invariance says that the amplitude for an electron-neutrino to oscillate to a muon-neutrino is the same as the amplitude for an anti-muon-neutrino to oscillate to an anti-electron-neutrino (when energies, distances etc. are the same).



    Tommaso, I think it would be fair if you wrote, because of the new D0 paper on the subject, another blog post in which you would admit that you were completely wrong, I was right, and it was wrong to hype this nonsensical "evidence" for CPT violation.