The Top Quark Mass

Recently I’ve been reading a new book, The Evidence for the Top Quark, by a philosopher of science named Kent Staley. It’s a combination of a history of the CDF collaboration’s work leading up to their claim to have discovered the top quark, together with an extensive discussion of issues in the philosophy of science raised by the different methods used to analyze the data. The book is very topical since last week the D0 collaboration published an article in Nature claiming a new, more accurate, mass for the top quark based upon a re-analysis of their data from Run I of the Tevatron, which lasted from around 1992-96. The old analysis of the D0 data gave a top mass of 172.0 +/- 7.1 Gev, the new analysis gives 179.0 +/- 5.1 Gev. Combining the D0 data with the CDF data, the old analysis gave 174.3 +/- 5.1 Gev, the new 178.0 +/- 4.3 Gev.

Measuring the top quark mass is quite tricky since there are not a lot of events to work with and one needs to precisely measure the energies of jets. If a linear collider ever gets built, it would allow much more precise measurements. Knowing the top quark mass accurately is very important for the following reasons:

1. In the standard model one can try and use precision measurements of the electroweak parameters to observe the effects of higher loops including the Higgs and get a prediction for the mass of the Higgs. This crucially involves the top quark mass, since that is the strength of the top-Higgs coupling and the top quark couples far more strongly to the Higgs than any of the other fermions. With the latest D0 value for the top quark mass, one now expects (95% confidence level) that the mass of the Higgs is less than 237 Gev. For more details see websites at CERN and Fermilab.

2. In the minimal supersymmetric extension of the standard model there is an upper bound on the mass of the lightest neutral Higgs, a bound that depends strongly on the top mass. There’s an explanation of this on Jacques Distler’s weblog. With the newest value for the top quark mass one expects that the Higgs mass should be below 140 Gev in the supersymmetric case.

There are a few funny things about this report from D0:

1. It was published in Nature rather than the more conventional Physical Review Letters. Nature is not where high energy experiments normally announce their results and this appears to be an attempt to get wider publicity than is usual for such a result. For some comments on this, see David Harris’s weblog.

2. The new method of analysis is similar to one discussed extensively by Staley in his book: the “dynamical likelihood method” due to Kuni Kondo. Ten years ago the CDF collaboration was rather skeptical of this method and decided not to use it, basically seeing it as too complex to be reliable. Have they changed their minds? Will CDF re-analyze its Run I data using this technique too?

3. Much is made in the paper and the associated Fermilab press release that this result changes the “best estimate” of the Higgs mass from 96 Gev (which is excluded by LEP results) to 117 Gev, which isn’t. While this sounds impressive, it would be a lot less so if you do what you are taught in high-school physics and quote error bars with your numbers. As mentioned above, while it is true that the new result is that 117 Gev is “most likely”, it is also true that a very wide range of values is almost equally likely. A more sensible but much less impressive way of saying things would be to just say that at 95% confidence level the Higgs mass has to be between about 50 and about 250 Gev.

Update: The D0 Nature article is now at the arXiv.

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7 Responses to The Top Quark Mass

  1. John Martin says:
    On above site I give formula for the field structures of particles and atoms. The particle formula is based on the mass of the electron as this is the most accurately known particle mass. This indicates that a mass of 174GeV is the correct figure for the top quark.

  2. D R Lunsford says:

    Peter, the reason your b-log is so well received is very simple – the topic is physics as it once was practiced, with excursions into math for variety. You seem to me to be close to unique in having a mathematician’s sensibility and depth combined with a physicist’s common sense. It really shows in all your writing.

  3. Peter says:

    Glad to hear you enjoy the weblog and thanks for the encouraging words. I’ve been surprised how much attention it has gotten.

    The string theory situation is a rather weird one and the public discussion of the theory has been almost all coming from its promoters. I hope I’m redressing that situation a bit, and that people will look at both sides of the story and make up their own minds.

  4. raj says:

    FWIW, I am not a physicist by profession (although I did undergrad and graduate work in physics many years ago, and continue to follow some of the literature), I wanted to let you know that I enjoy your blog very much. I am particularly interested in your criticisms of string theory. It has gotten such hype in the popular press, but I have yet to see anything that appears to make sense about it. I read Brian Greene’s book and, although I found it interesting (particularly the first quarter, relating to quantum mechanics and general relativity), I hate to say it but it did seem more than a bit unpersuasive.

    Regardless, I do enjoy the blog, and I would encourage you to keep it up.

  5. Peter says:

    Hi Thomas,

    A good recent reference for all this is chapter 5 of some lectures by Sally Dawson, hep-ph/0303191.

    In the SM there is no tree-level restriction on the Higgs mass. However, increasing the Higgs mass requires increasing the quartic Higgs coupling, and perturbation theory breaks down if this gets too large. For perturbation theory to be valid the Higgs mass can’t be more than a few hundred Gev.

    In the MSSM you have to introduce a second Higgs field (otherwise the anomaly from the superpartners of the first one are uncanceled). You can show that, at tree level, the lightest neutral Higgs should have mass less than that of the Z. Taking into account one-loop effects the upper bound goes up. It depends on the extra parameters in the theory (e.g. tan \beta, the ratio of vacuum expectation values of the two Higgs), but overall it has to be less than 140 Gev.

  6. Thomas Larsson says:

    Is a light Higgs compatible with the ordinary standard model?

    I have seen somewhere that the tree-level prediction from the SM for the Higgs mass is m_H = m_Z = 91 GeV; that’s the same with or without SUSY. The big difference is that the uncertainty in the radiative corrections is much smaller with SUSY, so the upper bound gets much tighter. So a light Higgs wouldn’t really be a proof for SUSY, but the absense would be a proof against it.

    OTOH, I have seen an argument by Frank Wilczek that a light Higgs would be problematic for the ordinary SM, but I don’t remember the details.

    The discovery of sparticles at the LHC would be a proof SUSY though, and would be a pretty strong indication that the string line of though is on the right track. But that doesn’t seem to be too likely, does it?

  7. D R Lunsford says:

    Tony Smith’s analysis:

    He gets these numbers as ratios of volumes within Shilov boundaries (as I understand it).

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