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    Higgs Mass Limits: 130-210 GeV !!
    By Tommaso Dorigo | March 19th 2010 10:03 AM | 52 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...

    View Tommaso's Profile
    A brand new result in Higgs boson physics has been presented by my old-time CDF colleague Wei-Ming Yao at the Moriond QCD conference two days ago. It is the combination of CDF and DZERO limits on the Higgs boson, and it constitutes a significant advancement in our knowledge of the standard model.

    The result is simple to state in a single sentence, although it will take me several pages to explain it acceptably. The Higgs boson is excluded at 95% confidence level in the 130-210 GeV mass range, if there are four generations of matter fields.

    I can hear you thinking "Ah, here's the rub... Always some fine print." True, but although the conditional clause changes the picture significantly, I believe the result is still quite important. In fact, who said there should be three, and only three families of quarks and leptons ?

    Why three ?

    We needed two decades of investigations to find out that there are three families of quarks and leptons. It all started in 1974, when the second-generation charm quark was discovered at SLAC and Brookhaven; the search saw high points when a third-generation lepton was discovered at SLAC (a somewhat painful process, since the discovery took several years to be accepted as such) and when the third-generation bottom quark was discovered at Fermilab. The culmination point, and the (maybe temporary) end of the story was set when the top quark was discovered at the Tevatron collider in 1994, completing the third generation of matter fields and creating a pleasing, symmetrical picture.

    In the meantime, indirect investigations at LEP determined that there are only three types of light neutrinos. Through these data, supported by some ancillary indirect evidence, we convinced ourselves that matter in the universe exists in the form of three generations of quarks and leptons.

    So all known quarks and leptons, which share the property of having a half-integer spin but are otherwise quite different objects, can be arranged in a tidy scheme of three families, or generations. The first generation includes the up and down quark, together with the electron and its neutrino: these would at first sight appear to be sufficient to create the complexity of the universe around us. However, it is not so: even forgetting about the existence of antiparticles for each of those bodies, we have to come to terms that the universe would be quite different with a single generation of matter.

    You might argue that as long as we do not create energetic collisions we do not need to take strange, charm, bottom, and top quarks in account, and that even muons, taus, and their neutrinos are unnecessary. You would be wrong: strange quarks might make up a significant part of the core of neutron stars; cosmic rays produce second and third generation fermions day in and day out; and even the good-old protons contained in the fat molecules making up your buttocks contain quarks of the second and third generation of matter. You would be sitting on a different kind of ass if the proton was only made of up and down quarks!

    So there are three generations. Why not four, or five, or an infinite replica then ? Well, there are both theoretical arguments and experimental constraints that tend to let us think that three is indeed the magical number upon which Nature (the bitch, not the magazine) has apparently decided to base the construction of our universe.

    But theoretical predictions are always leaky, and experimental constraints can be circumvented. So indeed, one should take a "know-nothing" stand here, and be prepared to be surprised. Indeed, the CDF collaboration has found last year a nagging excess of a fourth-generation-like object with mass in the 450-GeV region, in a search performed by CDF colleagues, among them my five-times colleague John Conway (we are both members of the CDF and CMS collaborations; we are both members of the CDF Spokespersons Publication Review Group; we are both members of the CMS Statistics Committee; and we are fellow bloggers, too!).



    The figure above is the culprit: a few events appear to be compatible with the production of "top-prime" objects of 450 GeV mass. This is a two-sigma-like excess, and it is probably bound to be reabsorbed once more data will be added to the search; however, for the moment it is an interesting would-be signal, one to keep an eye on.

    Four generations and the Higgs boson

    While direct searches for additional fermions are underway, indirect searches are also progressing. A fourth generation of quarks and leptons would have a significant impact in several pieces of known standard model physics: virtual loops involving these additional particles could produce changes in branching ratios, modify couplings, and affect the rate of production of several subatomic processes.

    Higgs boson physics is not surprisingly one sector where one expects a large impact from additional quarks: the Higgs talks to all massive particles regardless of whether they are fermions or bosons, charged or neutral, green or blue. Indeed, a heavy quark changes the branching ratios significantly from the default picture: this can be seen from the figure below.



    This is an incredibly busy plot. Yet rather than busy I would call it "information-rich". It contains a huge amount of information on Higgs boson physics, and it would require me a series of postings to explain all of its features. Let me describe the salient points though.

    On the horizontal axis you find the unknown, hypothetical mass of the Higgs. On the vertical axisyou may read off the probability that one such particle will decay in a given final state. The different curves show exactly what is the probability of a decay into one of the possible final states, as a function of Higgs mass. Now, at "low" mass (say, below 120 GeV), the regular standard model Higgs would mostly decay to a b-antib quark pair (red curve) -the heaviest pair of fermions available. But here, with the increased chance of a quark loop, the gluon-gluon decay (dark pink curve) becomes dominant.

    At higher mass, instead, little changes: the preferred decay mode is the one involving a pair of W bosons. However, as you increase the Higgs mass further -say above 200 GeV in the graph above-, the possibility arises that you produce two fourth-generation objects: these decays "turn on" at Higgs masses equal to twice the new fermion mass. To compute the figure, the theorists had to assign hypothetical masses to all the fourth-generation fermions, and their guess was as good as yours would have been; so they chose values just slightly higher than the exclusion limits for each of the new fermions.

    Besides the presence of high-mass channels opening up, the reason why the probability of Higgs decay into one state or the other changes even at low mass if there is an additional pair of heavy quarks is that these quarks couple strongly with the Higgs boson (since the coupling is proportional to the mass of the particle), and thus the Higgs is likely to "split" into a pair of such virtual quarks. The latter cannot materialize as they are, though, because this would violate energy conservation: to be produced they require an energy larger than half the Higgs mass. Therefore they rejoin by closing a virtual loop. Before they do, however, they may emit all the available energy in the form of a pair of W or Z bosons, or two gluons. This suppresses the decay to fermions, while the gluon-pair final state gets a large increase.

    So the modification in the decay pattern is bad news for experimentalists! Gluon pairs are as rare as a rainy day in London. But this is not the end of the story... Invert the arrow of time in the process above, and you will also immediately realize how a fourth quark strongly increases the cross section of Higgs production. Let me explain why.

    At a hadron collider the Higgs is most readily produced from a pair of gluons. But the Higgs does not "couple" directly to the gluons (gluons have no mass). The production occurs via the creation of a quark loop, like the triangle shown in the graph on the right. Any quark may run in the loop, but the top quark dominates the proceedings, because quarks couple to the Higgs boson proportionally to their mass squared, and the square of the top quark mass is ten thousand times larger than that of the next-in-line, the bottom quark.

    Now, with a pair of fourth-generation massive quarks available for the virtual loop, the process becomes significantly more frequent: the cross section of Higgs production increases by a full order of magnitude! The contribution of the new quarks, if these are much more massive than the Higgs, is independent on their mass, because the rarity of the virtual loop is perfectly countered by the increased Higgs-new quark coupling. You can see that in the figure below.



    The rate of Higgs bosons (ignore the units on the vertical axis) produced at the Tevatron is plotted here as a function of the Higgs mass, for the case of three fermion generations and four fermion generations. The enhancement, shown by the dashed line on top, is almost a factor of ten!


    But We See No Higgs...

    Let us take stock. We have seen that a fourth quark would make the Higgs more likely to decay to gluon pairs in a wide range of masses. We have also seen that the production rate would increase tenfold. But we know that the rate of Higgs production cannot be large, lest we would have seen it already at the Tevatron! What gives ?

    It gives an exclusion. One may take the predicted yield of W boson pairs from Higgs production in the four-generations scenario, and compare with the maximum number of such decays that may be hidden in the CDF and DZERO data without having been spotted. If the former exceeds the latter, the model is excluded. Since the whole thing depends on the unknown mass of the Higgs boson, but it does not depend on the mass of the hypothetical fourth-generation quark, we get a simple plot with the Higgs mass on the horizontal axis: the one below.



    Here you may appreciate just how much would a tenfold cross section increase in cross section do: the Tevatron would have unmistakably seen such a thing! Indeed, a broad range of excluded Higgs boson masses is derived by taking the region where the excluded cross section (black line) lays below the blue one: from 130 to 210 GeV. These are the Higgs mass values where the limit is below the expected cross section.

    Also note that the cross-section of Higgs production, once multiplied by the branching fraction to W boson pairs, "peaks" at about 160 GeV: of course: the branching fraction to WW pairs is highest there. Finally, please take note of a fact: the blue and red curves, representing the predicted cross sections in a 4-generation scenario with infinite 4-generation-fermion masses, or in a scenario where these have a mass just above the existing limits, are almost coincident.

    Of course, I have made things easier than they are in the few paragraphs above: the search for this Higgs in the "four-generation" scenario has been re-optimized in order to take into account several nuisances. But the general picture is what matters.


    Concluding remarks

    I think the result I have described above is quite interesting. We give too much importance to the Higgs in the scenario where there is nothing else around; we also give a lot of stress to searches for supersymmetric Higgs bosons, when we really have to guess the value of dozens of parameters in order to pick a SUSY scenario; change these, and everything changes. I get dizzy when I think at the number of caveats and distinguos necessary to fully appreciate a SUSY Higgs search.

    Instead, here you get a real limit from a standard model scenario which just sees the addition of another generation of matter fields. Beware, the actual value of the mass of these new, yet-to-be-found objects does not affect much the limit on the Higgs mass. This is the most interesting thing in the whole analysis: bring the fourth-generation fermion masses to infinity, and nothing changes. Amazing!

    Further reading

    If you are serious about this, you may take advantage from the documents you will find in the public page of the Higgs group in CDF.

    I also recommend my own discussion of the search for a fourth-generation quark by CDF.

    A discussion of the latest Tevatron limit on the standard model Higgs boson (with three generation of matter fields assumed) is here.

    Four things about four generations are discussed in this post.

    Comments

    > But we know that the rate of Higgs production cannot be large, lest we would have seen it already at the Tevatron!

    Lest means "for fear that", not "or else". I've seen this abuse twice recently, no idea why.

    dorigo
    Thank you for the correction anon.
    Cheers,
    T.
    >This is the most interesting thing in the whole analysis: bring the fourth-generation fermion masses to >infinity, and nothing changes. Amazing!

    well, nothing changes only if these new particles get masses from the EWSB. I mean, doesn't make much sense bring this masses to infinity keeping at the same time the Fermi scale fixed; you would need to take very large yukawas and the theory would make no sense.
    Very nice post, though. I'm also wondering whether these searches say anything for a Higgs mass below the LEP bound.
    thanks.

    dorigo
    Hi anon,

    the infinite mass limit is just a simplifying assumptions -it saves you from having to pick at hand mass values for the four additional fermions. I agree with you in general.

    What do these searches say for low-mass higgses: nothing. These are searches for the WW final state (the other channels have not been included here yet). So we still have to wait for those, and for some more information at lower masses. But there, the gg coupling being so high in this model, I do not expect much sensitivity. Maybe we can reach 115 GeV, but I do not think we can go below that.

    Cheers,
    T.
    OK, so the obvious question: in your expert opinion, how long will it take for the LHC experiments to exclude 114-130 ??

    dorigo
    Hmmm Kea, a long time in the vanilla standard model; but in this 4-gen model it is a region at reach early on, despite the large branching fraction to gluon pairs strips everybody of sensitivity.

    I would say that by late next year the SM Higgs might well be ruled out in the whole interesting region, if we assume there are more than three generations.  But whether it will be the Tevatron or the LHC to do that, I am not sure.

    Cheers,
    T.
    Tree
    Wow, from  a cave man perspective...
     I just bookmarked your blog here (one of 4 total bookmarks), thank you for posting this, some of this is way over my head and I wont ask you to inform me of what is to you basics, I'll research, so I can come back and read this a few more times. Thank you for taking the time to present this here, and for some insights, that I'm going to have to let sink in some..... ;)
    dorigo
    Dear thunderchild,
    thanks for stopping by. No, the above is not "basic" in my perspective either. I sometimes fail to keep the discussion at a manageable level. But fear not, some of my posts are pretty understandable -hopefully without being boring.

    Best,
    T.
    Tree
    Dear Dorigo (I'll call you Tommaso if you call me Tree :),
     My pleasure to be here and read this, and if it that means reading it several times, and each time I read it more comprehension sinks in (and will even more when I google or search this site for many of the terms I am not familar with) that is not what I would call boring!!!
     Any time I dont understand something, it tends to captivate me, especially when it concerns more depth of understanding to be here in this universe, and just what that "really" means, the more I expand my awareness, the greater my overall awarenss of the universe becomes, and the better I can interact with it, by understanding as clearly as I can, just what "it" is.
     I'm facinated by this topic.
    Just as I am facinated at all we (humans) know, I am also facinated by how much we have yet to learn.
     "If" God is truth, then the more we learn the truth, the more we learn about God, so surely this is something he would want us to do?
      If I were to have a religion, it would be to know the truth, without bias, and with an open mind to letting the truth represent itself.
     I seek to understand the cosmos I live in, I cant do that well without understanding the implications of a fourth quark, to me the universe is all one, I cant understand a galaxy very well, without an understanding of this.
     Thank you again for the time presenting this information took you to do.... it means a lot to me!
    And want to keep reading it over and over and follow its leads, so it means (comprehension sinks in) even more.
     I am indebted to you for your time! I aim to make (not take) the most of it!
     
    lumidek
    Even though I would surely be happy to already see 130+ GeV for the Higgs excluded, for obvious superreasons, I must say: Jesus Christ, because of the "not so subtle" assumption, this is a truly redundant piece of research. ...

    There is surely no 4th light neutrino which can be seen from the Z decays. All the models I can think of would make it very strange for one generation of neutrinos to be comparable to the Z mass or heavier, while keeping others seesaw-light.
    So this is actually a much less realistic model than most of the "semi-realistic" top-down models.

    dorigo
    Hi Lubos,

    it is true that additional generations of neutrinos have to be heavier than 45 GeV, or not couple to the Z. But what reasons could we give from a theoretical standpoint for the heaviness of the top quark, thirtythree years ago ? Yes, I know that in 1982 the top was predicted to be heavy for super-reasons, but the fact that we see no reason for heavy neutrinos today is not, imho, so strong an argument.

    In any case, I am with Galileo: "io stimo piu' il trovar un vero, benche' di cosa liggiera, che il disputare lungamente delle massime questioni, senza conseguir verita' nissuna"....

    Cheers,
    T.
    lumidek
    Dear Tommaso,...

    as usually, your rhetorical question is not a rhetorical one because it has very good answers. Even in 1992, the top quark mass around 175-180 GeV was predicted by superstring models

    http://arxiv.org/PS_cache/hep-ph/pdf/9506/9506388v1.pdf


    It's actually a pretty well-understood thing in string model building that one generation should be heavy - it's something about the rank of the mass matrices etc. Even outside string theory, it's understandable that the same Higgs can't give you "qualitatively" higher masses because the Yukawa couplings would exceed one and would quickly run into a Landau pole.

    Because of the last sentence, the absence of lighter new generations is really determined empirically while the absence of heavier ones is determined theoretically.

    Moreover, I doubt that the model above would lead to the same result if the fourth neutrinos were heavy (heavy because of big Higgs couplings? do you think that they won't matter?). I think that the fourth neutrinos' lightness does affect the calculated bounds - and their assumption was that the neutrinos had to be similarly light as the three families. This assumption directly contradicts observations.

    Therefore, concerning your Galileo's quote, finding the truth on a trivial matter is, on the contrary, exactly what you want to avoid. The truth is that there can only be 3 generations similar to those we know. So whatever attitude you as a religious bigot want to promote, I am with Galileo, it's turning anyway.

    Cheers
    Lubos
    dorigo
    Hi Lubos,

    so in 1992 Alon Faraggi had predicted that the top quark was in the range 175-180 GeV, duh.  Let me be less than impressed: first of all, his prediction was wrong - the top mass is 173.1+-1.3 GeV, so over three sigma below his "central value". Second, Faraggi in the preprint you mention, dated 1995, explains that to be consistent the spectrum of sparticles assumed for the prediction has to be complemented with additional, "intermediate states", and these raise the prediction of the top quark mass to 192-200 GeV, which is now excluded at about 15 standard deviations.

    In 1992 the top quark was known to be heavier than 91 GeV from direct searches by CDF, but more importantly, the LEP experiments were already showing their first fits, which all pointed in the region above 120 GeV: to mention a few, Aleph (170+-60), Delphi (<215), L3 (193+-70) Schaile (150+-40). So anybody could really make that "prediction". I trust the honesty of Faraggi's work, but again, I am not impressed by the coincidence.

    Cheers,
    T.

    lumidek
    Please don't act as the most primitive anti-scientific barbarian. It's surely not the case that "anyone" could have made the prediction. The prediction was based on a calculation of couplings in a free fermionic heterotic string compactification and roughly 20 people in the world have ever mastered the art of calculating quantities in such a setup so that they could have done it. Tens of thousands of average physicists of your kind are 5 sigma below the ability to calculate such things so what you pretend to be possible is definitely impossible....

    Also, it is no "coincidence" that the guess was essentially right. No one has made any "strongly wrong" prediction of this number in string theory and the newer models simply do imply that the heaviest quark is in a very similar range. It does follow from string theory and yes, it's consistent with other arguments including RG flows of the top coupling to the high-energy scales. The fact that your pea brain is not enough to ever master string theory doesn't imply that there is anything wrong with stringy predictions of SM parameters.


    At any rate, it's meaningless to calculate detailed, "phenomenological" predictions of models that are known to be wrong. It may be interesting to play with four-generation models for theoretical reasons, if some of them exist, but it is totally nonsensical to pretend that such games are relevant for predictions of the experiment. It's just dishonest to hide the "not to subtle" fact that the model you present have nothing to do with the reality.

    I find the comparison of Faraggi's work and the work you are promoting stunningly qualitative. Faraggi's work was based on the most accurate, mathematically robust structure that just became capable to predict things such as quark masses. And his or their work also cared about every detectable detail about particle physics. The kind of physics you are promoting is a meaningless masturbation that brings completely random, mathematically unmotivated errors to the proper models of reality, it has no mathematical depth either, and when complaints that it disagrees with other known facts are raised, the idea is that one should ignore inconvenient experiments, too.

    It's essentially junk science whose value doesn't reach 0.01% of the value of this particular work by Faraggi.

    Faraggi's result is not unique, at that age there was a surge of "order 1" predictions yor the Yukawa coupling of the top. Some of them were related to the research for an infrarred fixed point of MSSM, but other results were independent of this quest.

    For instance http://www.slac.stanford.edu/spires/find/hep/www?j=PHLTA,B126,54 from 1983 predicts
    top-quark mass 50 GeV-190 GeV.

    Isn't your headline a bit misleading? It seems to say that the Higgs mass in in the range 130-210 GeV, rather than *not* in the range 130-210 GeV.

    dorigo
    Hi Thomas,

    oh, yes. But you know, being misleading is a common trait of headlines.
    Cheers,
    T.
    MarshallBarnes
    What I want to know is am I correct in thinking that this brings us closer to finding the Higgs boson?

    You see, there's this little matter of a $100 bet that I have with Stephen Hawking...
    Marshal,
    no, it does not make the higgs closer. And as far as bets are concerned,
    I have a $1000 out with G.Watts and J.Distler. But we just have to wait and see...
    Cheers,
    T.

    The top-prime objects which could explain the excess in the CDF search don't have to belong to a 4th *chiral* quark family just like the SM one. These new charge 2/3 quarks, if they exist, might well be non-chiral. In other words, left-handed and right-handed components of such quarks might well have the same SU(2)xU(1) quantum numbers. Actually, this option is preferred, since the electroweak precision tests strongly disfavor new chiral quark families, but non-chiral quarks are not problematic. Now, the mass term of non-chiral quarks does not involve the Higgs field, does not imply a strong coupling to the Higgs boson, and does not increase the GF cross-section appreciably. To summarize: there is no one-to-one connection between the CDF t-prime search excess and the increase in the GF production cross section. The fact that the second is now excluded (for the given range of Higgs mass) does not imply that the t-prime excess cannot be real.

    lumidek
    Slava, do you really believe this stuff about non-chiral families? If left-handed and right-handed spinors are given the very same/opposite SU(2) x U(1) quantum numbers, nothing would almost certainly stop these fermions' masses from being driven to the GUT scale or any other high scale.
    It would seem more accurate to claim that the vague excess may be viewed as a (very weak) evidence in favor of pretty much any new physics. The idea that it implies things like "non-chiral families" is just premature, isn't it?

    Your "Now, the mass term of non-chiral quarks does not involve the Higgs field, does not imply a strong coupling to the Higgs boson, and does not increase the GF cross-section appreciably."  is pretty much saying "I like effects that have no consequences."

    However, effects that have no consequences have disadvantages, too - not only by being less testable.  The tendency for such "everything goes" particles to get a huge mass is directly linked to their being unconstrained.
    >If left-handed and right-handed spinors are given the very same/opposite SU(2) x U(1) quantum numbers, >nothing would almost certainly stop these fermions' masses from being driven to the GUT scale or any other >high scale.

    Though, in the MSSM and many other SUSY models, Higgses come in vectorial representations and the mu-terms are not at the GUT scale. How do we live with this? Invoking the usual extra (ad hoc) singlets like in the NMSSM?

    Hmm but them, a fourth family of infinite mass (which you will never produce) has a different experimental profile that having only three families? It is sort of counterintuitive.

    ...because you then have additional lego pieces to put into your Feynman diagrams, even if you have to hide them in the end.

    Hmm I see, what happens is that "infinite" is about 1TeV.

    dorigo
    Hi Alejandro,

    well, what happens with a infinite-mass fermion is that it allows gluons to couple "directly" to the Higgs, because the triangle loop "shrinks" to a point. So it does change the whole picture, despite remaining unobservable directly.

    In any case, "infinite" for an experimentalist is just an approximation, no more than saying that the neutrino mass is zero, for all practical purposes (but not a fourth neutrino).
    Cheers,
    T.
    Tommaso:

    I realize you undoubtably inherited the plots from Wei-Ming, and I have no idea how he credited them in his talk, but I want to point out that at least two of your figures are from a paper I wrote with Tilman Plehn, Graham Kribs, and Michael Spannowsky.

    Lubos,

    I don't actually agree that a vector-like pair of fermions would have masses driven to the GUT scale (though I do agree that nothing in particular would argue for them to be light). But ordinary chiral symmetry allows one to set vector-like fermion masses to anything one likes and they remain technically natural in the sense of 't Hooft. While mysterious that they would be unconnected to a fundamental scale, this is no more unnatural than the electron mass being roughly five orders of magnitude below its natural value at the electroweak scale.

    Tim

    dorigo
    Dear Tim,

    I am happy that you point that out, and I would like to ask you to also link your preprint here.

    Perhaps I need to explain here that in general I do not give credit for plots of scientific results here, unless the results are brand new. A scientist should not be thanked every time his or her result is shown around, because once published, the result is owned by mankind, not by him or her alone.

    Please also note (but I guess you have already) that it is generally close to impossible to take a picture from the web and properly give the right credit. And scientific results have no copyright coverage.

    Cheers,
    T.
    lumidek
    Dear Tim,
    the lightness of the electron, of course, has some qualitative explanations in the realistic state-of-the-art string models. The first-order calculation, using cubic Yukawa couplings, gives zero (unlike the top quark and perhaps the whole 3rd generation), and the electron mass only comes from some higher-order effects - although the details what it means depend on the model.


    Of course that it's plausible that something like that would exist for the light non-chiral generations, or whatever else. I don't claim that such things can't happen. There can always exist new physics that makes natural what looked unnatural to start with.

    But I just think that it's a wrong approach how to choose "new possibilities". By Occam's razor, beings shouldn't be multiplied and proliferated unless it's necessary. I consider papers that just modify a random aspect of the established models in a random way, add a small mutation or an error unmotivated. This is the kind of cheap work that anyone can do under any circumstances. It's not exciting in any way. It's a bad type of phenomenology - both theoretically and empirically.

    Cheers
    LM
    New vector-like quarks with TeV-scale or slightly lighter mass are all over the place in models of composite electroweak symmetry breaking, like composite Higgs or Little Higgs etc. In those models, they have several roles to fulfill, like to cancel the Higgs mass quadratic divergence from the top, or to cancel otherwise large corrections to electroweak precision observables (in particular Zbb). And to fulfill these roles, they have to be around a TeV.
    It's technically natural, it's motivated, and it has observable consequences in Higgs boson physics, just not as dramatic as raising the GF cross section by an order of magnitude, but perhaps by 10%.

    dorigo
    I agree with what you say Slava, but vector-like quarks are not a small change in the standard model. Definitely not as small as the introduction of a fourth family. For that reason, the price to pay in "Ockham tokens" is high. I personally find it a stretch, while I would not be so surprised by a fourth generation of fermions.

    Cheers,
    T.
    "Even in 1992, the top quark mass around 175-180 GeV was predicted by superstring models"

    That's pretty impressive. And did those models predict an accelerating or decelerating expansion rate for the Universe?

    dorigo
    Huhm, I sort of detect some sarcasm here ;-)
    T.
    The 4th generation is consistent with electroweak precision tests only in a tiny region of its parameter space. The 4th generation top-prime and bottom-prime should be split by a small amount, because otherwise their contribution to the rho parameter would be ski-high and excluded. Nor should the splitting be exactly zero, because in this case the S parameter rules it out. It's not excluded, but it's unlikely. It would also mean that the top mass prediction from the early LEP data was a fluke, since for this prediction to work, there should be no other big sources of the rho parameter except for the top-bottom splitting (plus a smaller Higgs contribution).

    To an experimentalist, adding 4th generation may seem like no big deal, while the models with vector-like quarks may seem ad hoc. To a theorist familiar with those models and with the EWPT constraints, the situation is the opposite.

    I find the idea of 4th generation very interesting. Could someone please give some reference to experiments which established there are only 3 types of light neutrinos?

    lumidek
    Dear P, I wrote that there was experimental proof of 3 light neutrinos, so it's my responsibility to give you the reference. It's from Z-boson partial leptonic decays - the experimental result is by the ALEPH collaboration:
    N = 3.01 +- 0.15 (exp) +- 0.05 (theor)

    See the 1990 paper with hundreds of authors:

    http://scholar.google.com/scholar?q="z+boson+partial+widths"


    http://cdsweb.cern.ch/record/203580/files/199001198.pdf


    http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVN-4718PYH-D...


    dorigo
    Hi Lubos,

    it may not matter much to you, but the best reference is the PDG, which has an independent piece on the matter: http://pdg.lbl.gov/2009/listings/rpp2009-list-number-neutrino-types.pdf

    There, you learn that the result to point someone to is not the early one you quote, which has historical importance but lesser scientific value, but this one: N = 2.984+-0.082 .

    Cheers,
    T.
    lumidek
    Suddenly you know very well what I am talking about, Tommaso. 2.984+-0.082 etc. Just minutes ago, you would claim that there exists no experimental reason to think that the right number should be three and not four.
    Thank you both.

    Hi Tommaso,

    " Nature (the bitch, not the magazine)". I've noticed you like this quotation. I'm curious, what is the original form and who made it?

    Cheers,
    Martin

    lumidek
    Dear Martin,
    be almost sure that Dorigo put the two opinions - that Nature is a magazine and Mother Nature is a b-word - together himself.


    But he borrowed the disrespectful meme that Mother Nature is a b-word from his colleagues who also love to smoke lots of marijuana, from the International Cannagraphic organization, see

    http://www.icmag.com/ic/showthread.php?t=310


    These people smoke pot and pot and pot so it's not shocking that they fail to see how beautiful and unaccessible Mother Nature actually is. Tommaso is high all the time.

    Cheers
    LM
    dorigo
    Hi Martin,

    yes, it is my own cooking. And I always use it in its original form. I think it dates back to a post I wrote four years ago.

    Cheers,
    T.
    Hi Lubos,

    I don't think that your link points to the origin of "Mother Nature is a bitch".
    I have heard that regular consumption of substances containing THC leads to apathy. I'm sure that maintaining a website interesting enough to get you to comment on and smoking canabis are incompatible.

    Cheers,
    Martin

    lumidek
    Of course it does, Martin. The discussion thread is called "mother nature is being a bitch". Read more carefully, please.
    Concerning your second point, I agree. I also think that Dorigo has a secretary who is not an addict and who is actually inventing postings like these ones while he is only predefining or adding the important big claims such as that Berlusconi is evil and the number of generations is four. ;-)
    Hi there,

    since it was discussed before: the LEP limit is actually weakened slightly in this model. The reason is that
    the decay H -> glue glue is enhanced, and therefore the main search channel at LEP, H -> bb, becomes
    weaker. This was shown in Fig. 5 here:
    http://arxiv.org/abs/0811.4169

    Cheers,
    Sven

    "the lightness of the electron, of course, has some qualitative explanations in the realistic state-of-the-art string models. The first-order calculation, using cubic Yukawa couplings, gives zero (unlike the top quark and perhaps the whole 3rd generation), and the electron mass only comes from some higher-order effects - "

    I think it should be mentioned that the idea that the first, and maybe also the second, generations get their mass from radiative corrections --- as a mechanism to explain the fermion mass hierarchy --- goes back to Weinberg, and was developed subsequently by Glashow and Georgi and many other authors. So, that mechanism doesn't originate in string theory.

    Tommaso,

    Since you asked, a link the arxiv version is:
    http://arXiv.org/abs/0706.3718
    I don't actually mind that you use plots without attributing them, though my junior coauthor is still a postdoc and in need of a job, so I do consider it somewhat of a personal responsibility to point out his hard work, at least.

    I agree that on the web attributing images is very slippery, and I doubt you are particularly unusual in how you handle this issue. Some (and I am familiar only with a very few) scientific forums (such as, say, Cosmic Variance) do seem to do a reasonable job, however, so there are different approaches out there. I could take CDF's route and embed authorship into the image itself, but it doesn't seem worth the trouble. If I'm not even willing to take that step, I certainly accept that the plots I make may lose causal contact as they propagate.

    I managed to find Wei-Ming's slides online and he did indeed responsibly report where he got his plots from. I appreciate his good scholarship; it is one thing to discuss a plot on a blog, but in a professional presentation, sloppy research (in the literal sense of the word) is just unacceptable.

    Lubos,

    I am somewhat familiar with the stringy constructions, thanks for mentioning them. I don't think we really actually disagree on any points. My personal attitude is that right now we have a lot of "facts" within particle physics that are begging for a more fundamental theory to explain them, be it directly from string theory or from some other physics which may lie between us and Planck scale.

    Regards,
    Tim

    lumidek
    Dear Tim, I am not in any real disagreement with you, either. ;-) By the way, 4 would be a great number of generations in string theory because there are many really simple 4-generation string models. :-) I just happen to care about the evidence, probably more so than Tommaso. Cheers, LM
    Sorry for the double comment. Please feel free to remove one of them...

    Tommaso,
    thanks for the (usually) very interesting post. Aa a layman, am I wrong in arguing that this resarch is more about limits on the possibility of 4 gens than about limits on the HIggs mass, since the former is in my view a far wilder speculation?

    dorigo
    Hi Filippo,

    well, for sure 4 generations are on less firm ground than a standard model Higgs boson; however, the limit says nothing about the former, but something about the latter in the presence of the former. If you however are sure that the Higgs exists, then P(4)=P(4|H)P(H)/P(H|4) from Bayes theorem... Draw your own conclusions ;-)

    Cheers,
    T.