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Post-diction effects: the top mass example December 17, 2006

Posted by dorigo in personal, physics, politics, science.

My last post about deceiving details in the scientific presentation of data stimulated Tony Smith into suggesting that a similar effect to the one I described in the post was at work when the top quark mass was still unknown to most – but the first hints that it was sitting at around 180 GeV were starting to leak out of CDF.

I remember that time. It was the beginning of 1994, and I was attending my year of military duties as a civil servant in a cooperative where I worked with boys with psychiatric problems. I used to visit the Physics department about once a week, and I too started to hear from my colleagues in CDF the first news about the top being heavy – when most still believed it had to be at about 140 GeV of mass. The latter, at least, was the value preferred by most electroweak fits.


Ten years later I made an update to a plot I had done in 2002 for a Frontiers in Physics conference in Frascati; it is shown above. Beware, it is quite busy! In it, you see both experimental and theoretical information on the mass of the top quark as a function of time. The lower blue areas shade out top mas values excluded by direct searches, first at electron-positron colliders and then at proton-antiproton colliders. The upper green area is instead excluded by theoretical information. More precise fits to electroweak parameters allowed to “determine” the unknown value of the top quark mass as early as in the late eighties: that information is shown by the red line with yellow band. Finally, CDF and D0 determinations are shown by points with error bars. 

Now, Tony’s point is that the red line had a jump towards 175 GeV or so just about at the time when the first information on the top mass was coming from kinematical fits to the first events collected by CDF in 1993-94. I think he is right, but let us take a more analytical standpoint, an d look at all the data at face value. You can get very detailed information by visiting the particle data group web site, http://pdg.lbl.gov . In it, you can browse the archives on past editions of the “Review of Particle Properties” just back to 1995. So let’s have a look at what they were publishing for the top quark back then.

There are a large number of indirect determinations of the top mass listed in the review. If we start from 1990, and first look at LEP ones only, here is what we get:

  • OPAL 1991 – 100+70+24-52-11 GeV
  • L3 1991 – 193+52-69 +-16 GeV
  • ALEPH 1992 – 170+42+21-55-14 GeV
  • ALEPH 1993 – 174+27+17-32-22 GeV
  • L3 1993 – 152+36-46+-20 GeV
  • OPAL 1993 – 91+-46+-9 GeV
  • ALEPH 1994 – 184+25+17-29-18 GeV
  • OPAL 1994 – 132+41+24-48-18 GeV
  • L3 1994 – 158+32-40+-19 GeV
  • DELPHI 1994 – 115+52+23-82-24 GeV
  • DELPHI 1994 – 157+36+19-48-20 GeV

Taken at face value, these determination send a rather homogeneous picture – no real “bias” can be inferred from them. However, the devil is always hidden in the details. Indeed, each of these numbers comes with notes in the PDG review. From the notes, one learns about a few assumptions made in producing the estimates (such as the value of alpha_s used in the fits, the range of variability of the Higgs boson mass, and -most important- the kind of measurements used and those not used in the fits). One really starts thinking that to get a clearer picture it would be really necessary to read all the papers describing these results.

Other notes:

  1. Aleph seem to have gotten the top mass right from the start. However, they publsihed in 1993 a paper when they only gave an upper limit at 228 GeV to the top mass, while their central value is hidden in the paper: 50+-70 GeV! One thus learns that to get the limit they used experimental input on the CDF lower limit, then at 91 GeV… That analysis by Aleph was based on the width of the Z boson to b-quark pairs, a parameter that gave the LEP experiments some headache back then. I wonder if all other determinations by Aleph on the top mass used or not that particular measurement in their averages.
  2. Opal were always consistently low in their estimates of the top mass.
  3. L3 bounced around a bit, but one sees no real hint of the “bias” we are talking about here.

So that is the LEP panorama. But LEP was not alone in the business: others used LEP results as well as other determinations of electroweak parameters (SLD, but also neutrino scattering experiments) to make more “global” fits. Let’s look at these revue determinations:

  • Ellis 1990 – 127+24-30 GeV
  • Decamp 1990 – 120+-40+-20 GeV
  • Langacker 1991 – 124+28+20-34-15 GeV
  • Hioki 1991 – 145+47-48 GeV
  • Gonzales 1991 – 119+39-45 GeV
  • Schaile 1992 – 150+29+20-34-22 GeV
  • Renton 1992 – 137+22+18-25-22 GeV
  • PDG 1992 – 150+23-26+-16 GeV
  • Ellis 1992 – 120+27-28 GeV
  • Delaguila 1992 – 112+22-23 GeV
  • Banerjee 1992 – 123+33-38+-19 GeV
  • Quast 1993 – 147+22+17-26-22 GeV
  • Passarino 1993 – 146+18-19+-17 GeV
  • Montagna 1993 – 102+35+19-32-18 GeV
  • Ellis 1993 – 132+20-22 GeV
  • Blondel 1993 – 143+19-18 GeV
  • Novikov 1994 – 161+15+16-16-22 GeV
  • Montagna 1994 – 174+11+17-13-18 GeV
  • Gurtu 1994 – 177+-9+16-20 GeV
  • Ellis 1994 – 140+21-22 GeV

These other “global” fits give a more concrete picture of the situation in the years 1993-94. One must keep in mind that in 1993 the lower limit from experimental searches by CDF and D0 was growing almost by the day, and indeed some of the determinations above suffer from having incorporated that limit in their fits. Others were just influenced by the results, but until late 1993 nobody had real information on the “real” value of the top mass from direct determinations at the Tevatron (see plot above, where the light blue shading shows a consistent increase in the lower limit at 95%CL from CDF and D0 in those years). Indeed, before 1993 no determination was above 150 GeV, while from 1994 on all results seemed to align close to 170 GeV.

Can we cast doubt on the good faith of these scientists ? For sure not. They did their homework the best way they could. If some used the experimental lower limits in their fits, they did mention it in their papers, and that is perfectly legal. More subtle is the case when they chose not to use the lower limits: in that case, a involuntary bias might have been at work. The same can be said of the determinations published in early 1994, when the leaks from the Tevatron about the top mass were hard to avoid.

What is the bottom line ? I think there is nothing wrong in the way we do science in particle physics – the interplay between experimentalists and theoreticians is sane and fruitful. It is important, however, to keep a critic eye open when looking at results. That’s for sure!


1. Alejandro Rivero - December 17, 2006

I think that there are other versions of your plot around; perhaps by Quigg, who does nice plotting job too; I can not remember now.

Another historically interesting point is the age previous to the plot. I supposse that starting from Zichichi’s suggestion of a third lepton, some teams should have conjectures about the bottom and the top. When did the top mass started to increase up to two orders of magnitude beyond the tau mass? It was not an steady process. There is a paper published by Tony in the eighties (the only one I have found actually in the library in Cambridge and not in the internet), as contribution to a meeting on Clifford Algebras, and there the expected mass of the top is about 40 GeV, while Tony boldly predicts the 120-140 GeV… it is amusing if you think that at these times he was outsider because he was predicting a higher mass, and now he is outsider because he is predicting a lower mass.

But another interesting point is that not only Tony’s, but all the models of GUT theories were done in the age of low mass. At the first hints of high mass, supersymmetry claimed the new land because of a result of Ibanez, that a huge difference between the mass of top and the rest was a good trick, when combined with renormalisation running, to get the mexican hat for the Higgs. That was about 1981-83. But they really did not need a gap of two orders of magnitude, did they?

To me, the big consequence of the gap is that the top can not build mesons. I am pretty sure that if this fact had been known in the age of the dual model, string theory would be very different today.

2. dorigo - December 17, 2006

Yes Alejandro, Tony was caught in the crossfire apparently🙂

About the top, you raise two good points of which I am aware. Let me stress here the no top hadrons point: from heavy quark effective theory we know that the splitting in mass between B** and B mesons is independent on the heavy quark mass. It is 450 MeV, and since the width of the top quark is predicted to be a cubic function of the top mass, one easily gets what the situation is for a heavy top: top mesons merge and act coherently, and what is left of them is a broad excitation curve. I have no idea how early this could be speculated… HQET is not an old theory itself.

As for the Ibanez paper of 1982, it is another interesting thing seldom quoted. Indeed, a heavy top was predicted back then as a way to prevent radiative corrections in the MSSM from spoiling the SU(2)xU(1) breaking. I do believe he was hinting at a 120 GeV top if I remember correctly.

Quigg did a similar plot in 2000 indeed. Mine dates back at 2002, when I decided I wanted a version where “points with error bars” were reserved to direct determinations of the top mass…


3. Tony Smith - December 17, 2006

Another early heavy Tquark prediction was in 1983, when Joe Polchinski (with Wise and Alvarez-Gaume in Nuc. Phys. B221 495-523) found, in the context of “Minimal Low-Energy Supergravity”, that
“… The renormalization group equation … tends to attract the top quark mass toward a fixed point of about 125 GeV
It also puts an upper bound of 195 GeV on the mass …”.

As I mentioned in a comment over on Cosmic Variance, it is sort of ironic that Polchinski is now a strong advocate of superstrings, which seem to me to have less predictive power than his 1983 techniques,
and it seems even stranger to me that back then he did not claim the high Tquark mass as a prediction, but abandoned it when CERN announced a 40 GeV Tquark.

For instance, the book “Unification and Supersymmetry” by Mohapatra discusses the paper by Polchinski et al and then says:
“… The recent discovery of the t-quark in the mass range of 40-60 GeV therefore rules out the simple-minded analysis carried out here. …”.

Tony Smith

4. Alejandro Rivero - December 17, 2006

Hmm I think that there was some estimates before HQET. Fabiano 1998 tells that “It is conventional wisdom” and refers to some russian papers in 1987 and 1988 (Fadin and Khoze) plus a PLB by Rubbia in 1992. An intermediate paper is Physics Letters B Volume 181, P 157-163, of 1986. It is very explicit about the bounds but -in a first examination now- it does not risk to suggest it should apply to the top, just “very heavy” quarks perhaps from other generations. So it seems that really they waited until the nineties before taking the courage to tell that the top does not bind.

Last year I found all this mess very atractive because it implies that the pseudoscalar mesons are in total six of +1, six of -1 and 13 neutral (not 12, to my regret). If strings theoretists had know of it back in 1974, I think they had argued for superstrings in a very different way; after all, each of these mesons is the start of one of their Regge trajectories, and if the count coincides with the number of degrees of freedom of the leptons, I strongly doubt they had resisted the temptation of claiming susy. But not having a clue about the peculiarities of the third generation, they changed instead to Planck mass scale and the joys of, they say, quantum gravity.

5. Alejandro Rivero - December 17, 2006

Btw, Ibanez & al papers in the 81-85 period constitute the TopCited research on particle theory from Spain. Only a hep-th paper from Garriga and Tanaka, on the Randall-Sundrum bussiness, has recently surpased them in citations for single papers, but I’d said they still head the list as research group (I am not sure about what it implies for theoretical physics in Spain as a whole; but it must be stressed that some of our high people are adscribed to international institutions)

6. dorigo - December 18, 2006

Alejandro, the speculation about PS mesons is interesting… Too bad for the extra neutral one! As for the speculations about string theorists, hmmm. Maybe we could construct a Meta-String theory, which governs the behavior of string theorists and predicts their physics output, given a (possibly useless) clue on the organization of the particle spectrum.
To clarify what I have in mind, take a string theorist S in a state x,
S(x). A new-particle operator NP[] acts on S(x) producing a new speculation on the physical world W = NP[S(x)]. Then one could think of higgs-mass operators HM[] with a similar behavior. And of course you can combine operators with a suitable set of formal rules.
The name of the game is to find an operator X such that by acting on S(x) it produces the null state :))


7. Alejandro Rivero - December 18, 2006

No worry about the extra neutral, I am sure a good mathphys will have a dozen tricks to orthonormalise it out (U(3) to SU(3) and so on). The real problem comes in the quark sector where, while the counting extends to q=-1/3 diquarks easily, we have things as the (uc) diquark killing the joy, having q=+4/3. It is not even a prediction because you can not arrange them into a new fermion.
In any case, my point is that the theory building methodology frozen itself during the seventies, and in any case early eighties to include Witten et al. insights. Since then, the neutrinos are massive and the top mass is in the electroweak vacuum range, but theoretical modelling has not even able to incorporate these insights in a fundamental way. They cope with them but they do not incorporate them.

8. dorigo - December 18, 2006

Yes, things really froze apparently… We could call it “the big chill” of theoretical physics. But I think things are thawing! Woit’s and Smolin’s book have not gone unnoticed, and string theory starts to be overstretched… The good thing about low points is that you can only raise from them.

9. James Graber - December 18, 2006

Hi Tomasso,
Thanks for the chance for a trip down memory lane.
Let me tell you about the day Carlo Rubbia *did not* announce the discovery of the Top quark at a meeting of the American Physical Society in Washington DC. I think it was about April 1985 or 86, right after his Nobel prize.

The rumors that he was going to announce the discovery of the Top quark were very strong. Even I, who have no connections to the particle physics community, had heard all about it. For the only time in over thirty years, I even took my wife to the APS meeting to hear the historic announcement. The medium-large hotel balroom auditorium was packed.

In fact, one of the first questions he got in the question period was along the lines of “We know you’ve discovered it. When are you going to announce it?” As I best remember, he answered by saying something like “There is an accumulation of events near 33GeV. We’re not sure yet if these are a signal of a new particle, or merely a bunch of noisy events caused by heavy flavors”.
The audience laughed.

That day Carlo wore a loud plaid sports jacket. They were then somewhat in fashion and I had one, too. My wife thought then and still thinks they are horribly tasteless. To this day she calls them “Nobel-prize-winning jackets”

Carlo was scheduled to speak for about 40 minutes, but he spoke for over an hour, using more than 120 slides and talking very rapidly. My wife hardly understand a single word, but she got the heavy flavors joke and remembers that he kept talking about “the p-bar-p and the b-bar-b.”

Prior to this, I remember the unexpected discovery of the charm quark at the shockingly heavy mass of 3 GeV. (When it was not found around 1 GeV, people gave up looking for it.) Then the bottom quark was found around 9 GeV. I predicted to myself, based on nothing more than the geometric series 1,3,9,27 that the top quark would be found around 27 GeV, but I think serious people at first thought it would be lighter than that. Later, I think, they were sure it would be found below 40 GeV, and there were lots of rumors about that bump at 33GeV.

Please remember that I am not a particle physicist, and I couldn’t even play one on TV; it’s been a long time; and my memory could be faulty. But that’s what I remember.
Jim Graber

10. dorigo - December 19, 2006

Hi James,
I myself find hoping that masses follow numerology at times… But the complexity of the physical world is what makes it so fascinating after all.
Rubbia went further than showing a sports jacket at a seminar and muttering something about a pile of events. They published their results one year thereafter… But I would not blame him too much about it: Monte Carlo simulations were far from perfect those days, and in particular, QCD emission of jets in the production of W bosons was totally not understood. Perhaps they were overconfident with their simulations, but that is a minor sin… I way prefer a incorrect claim out in the press than a potentially groundbreaking result being kept for review for years, as happened in CDF in Run I.


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