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A look inside the Tevatron Mtop combination March 10, 2008

Posted by dorigo in physics.

They say that people who follow the law and people who eat sausage should not ask how these are made. If you are going to trust the top mass average just released by the Tevatron Electroweak Working Group, you should instead educate yourself on what is behind it: the reason is that it is in fact a very instructive case study of a combination of different measurements of the same quantity.

Before I try to do my little bit to discuss some details of the Tevatron combination, there is one outstanding -if a bit silly- preliminary question to answer. Is it the same quantity, after all, the one we are averaging ?

If you studied Measurement Theory in your undergrad courses, you will surely remember that one of the most easily overlooked sources of systematic uncertainty in a measurement is frequently the ill-defined nature of the quantity one is attempting to determine. As an example, take a determination of the g constant. g is the downward acceleration of a body on the surface of the Earth due to the latters’ gravitational field. Depending how you measure it, you might find different values, which could be significantly at odds with one another. What is downward, for instance ? And what is the Earth’s surface ? If downward is defined as the direction of the center of the Earth, one needs to keep in mind that the Earth is not spherical; one instrument could be more sensitive to this feature than another.

A quark is an elementary particle, but elementary does not mean “simple”. The top quark decays in a time so short that it does not have time to emit radiation – both a good and a bad thing if you want to measure its mass, because if the absence of radiation helps you “picture” the quark decay and measure it well from its decay products, on the other hand the shortness of its life demands you to assume a lifetime to model the probability of exhibiting one particular mass value. Here is an example of how the imprecise definition of the the mass -given a unknown lifetime \tau, or unknown width \Gamma_t = 1/\tau–  is usually treated as a systematic uncertainty: experimentalists will just bracket the lifetime within reasonable bounds, and check the variation of their results on the variable assumption on \Gamma_t.

[As a side note, there are further issues with the top quark mass, connected with the nature of QCD, but let us forget about those… They will be an issue only when we will reach a 200-300 MeV uncertainty in the top mass, maybe at a 500 GeV linear collider…]

As I opened this bracket on what is it that the Tevatron experts are averaging, however, I was thinking of something more basic than the imprecise definition of the top mass: not the unknown value of \Gamma_t, but the quite exotic speculation that the top mass might not be one single value. I heard it claimed several times in the past, mostly at dinner tables, with a glass of alcoholic beverage in hand, that there was a intriguing “jet effect” in the top mass measurement. Indeed, by putting side-by-side different determinations of the top mass based on different final states, one observed that as the number of jets in the final state increased, so did the measured top quark mass. The effect has never been large enough to cause more than a shrug of shoulders in who, like me, believes that statistical fluctuations are a necessary player in experimental physics. However, it is nice to have a look at the situation today, for a start. 


The graph above shows the Tevatron average of the top quark mass in three bins, corresponding to the dilepton, single lepton, and all-hadronic final state of top pair decay. In the dilepton decay you have two b-jets and two leptonic W decays; in the single-lepton decay you have two b-jets plus two more from a W; and in the all-hadronic decay you get six jets. The graph shows the present state of the “effect”. As you see, a straight constant fit to the three points produces a very nice \chi^2 (2.27/2), and the effect is a non-issue.

Ok. Now that we have put the issue of a dependence of the top mass on the final state behind our back, let me discuss the averaging of 12 different results obtained by CDF and D0 in Run I and Run II. First of all, those 12 results are only a small selection of the determinations that the Tevatron experiments have produced in the last 14 years – from the “evidence” paper by CDF in 1994 (quoting M_t = 174 \pm 16GeV based on the analysis of 19 inverse picobarns of data) to this winter’s precise results obtained with 110 times more statistics. The selection leaves out a few results that have too much correlation with those included, or ones whose inclusion would have added no statistical power to the combination. Alas, it also excludes one of those I was a main author of – it but includes many more I have contributed to, fortunately.

The list of 12 included results is best shown graphically. Please see the plot below:

 topmass average 08

Marvelous display of science, is it not ? As you see, there are determinations for all final states by CDF both in Run I and Run II data, while D0’s determinations in the all-hadronic final state have been left out. Included, instead, is one measurement which is quite different from all others: it is the last, quite wide, error bar, which is obtained by fitting the decay length distribution of b-quarks in top-decay b-jets. The decay length of b-quarks is in fact a function of the b-quark boost, which is in turn a function of the top mass, since the latter decays to two bodies in the process t \to W b, and there is an approximate linearity between top quark mass and the energy -and then the boost- of the produced b-quark. The measurement is valuable because it only uses tracking information, unlike all others, and is thus subjected to very different systematic uncertainties. Most notably, it is totally unaffected by the jet energy scale uncertainty, the single largest source of uncertainty of most if not all other determinations.

The combination of the 12 results above is not just a weighted average, of course. The authors took in consideration several sources of systematic uncertainty, and accounted for the cross-correlation of each result with the others. In particular, the treatment of the systematics due to the jet energy scale is exceedingly accurate: there are no less than six different factors related to the measurement of jets energy by the two experiments; some of these are totally uncorrelated, and some are partly or fully correlated, through the assumptions on the fragmentation properties of light-quark jets, those of b-jets, the decay properties of the latter, and other modeling issues such as out-of-cone energy. It is also to be noted that CDF measurements in Run II using the in situ calibration of the jet energy scale through the fitting of the hadronic W signal in the top pair decay no longer include an external constraint from the jet energy scale determination in QCD samples, since that input is no longer contributing appreciably to the uncertainty.

The last comments were a bit too technical for such a long post, I gather. What I still need to do is to mention a few of the heroes of these many excellent measurements. Really, too many people have contributed to making top mass measurements the trademark of the Tevatron, and it would take a week to mention all of them duly; besides, I have no notion of who are the principal actors in D0 and so I have to avoid discussing that side of the coin. I only want to cite two CDF colleagues here: Lina Galtieri and Doug Glenzinski.

Lina has been in CDF ever since the sun rose on that orange building, and she is one of the most striking examples of continuity and devotion to top quark physics in our experiment. She is a professor at Berkeley and has directed her group in Run I and Run II to top physics for two decades. I think she is one of the few people to whom CDF owes more than the other way around.

Doug is one of the members of the TeV Electroweak Working Group. He joined our experiment in 1999, and he has directed the effort of CDF in top quark physics for several years. He is now the physics coordinator in CDF, and several of the successful measurements in the top sector by CDF have his fingerprints on them.

Finally, I have to apologize to the many brilliant D0 colleagues who are behind the D0 measurements shown in the plot above. I can only invite any one of them willing to discuss the subtleties between their top mass measurements to contribute here with a guest post…


1. Tony Smith - March 10, 2008

Tommaso mentioned “… something more basic than the imprecise definition of the top mass: …
the quite exotic speculation that the top mass might not be one single value.
I heard it claimed several times in the past, mostly at dinner tables, with a glass of alcoholic beverage in hand, that there was a intriguing “jet effect” in the top mass measurement. …”
attacked the significance of such a “jet effect” by comparing the Tevaton average T-quark mass results as follows (numbers approximately read off from Tommaso’s graph):

dilepton – 2 jets – 170 GeV
single-lepton – 4 jets – 172 GeV
all-hadronic – 6 jets – 177 GeV

and saying that the straight-line fit gives a CHI2 (2.27/2) indicating that “the effect is a non-starter”, I guess in the sense that everything is within a reasonable statistical range of 172.6 +- 1.4 GeV value of the new CDF+D0 combination. Since only the all-hadronic 177 GeV is very far from 172.6 (compared to 1.4 GeV error bar), and all-hadronic uncertainties are relatively pretty high, I do not disagree with Tommaso’s conclusion from that graph
my position is that the T-quark “mass might not be one single value” in that the T-quark (in connection with interactions with the Higgs, which itself may be described as a T-quark condensate) might have 3 states:

low – around 130-145 GeV or so
medium – around 172 GeV, the state so precisely measured by DCF and D0
high – around 220 GeV

The “jet effect” that seems to me to support my 3-state view is based on detailed study of individual events, something that can be buried in the statistical analyses more fashionable nowadays.

For example, consider the 1997 UC Berkeley PhD thesis of Erich Ward Varnes and the D0 event Run 84676, Event 12814 (e mu) in which there were 3 jets instead of the 2 jets that are normally expected in a dilepton event.
Varnes plotted the mass as about 170 GeV if all 3 jets were included,
but also as about 130 GeV if only 2 of the jets were included.

To me, that indicates that a T-quark was produced in the 170-GeV state and quickly (by one jet) decayed to the 130-GeV state which then decayed by conventional 2-jet dileptonic decay.

That event is only one of many that can be similarly explained in terms of the 3-state T-quark model.
Unfortunately (in my opinion) such detailed event data is not routinely made available, as it is not needed for currently fashionable work that is carefully looking at the 172-GeV T-quark state, but ignoring the other two.

I will also note that my initial motivation for the 3-state view came from comparing the early semileptonic histograms by CDF and D0, both of which not only showed a peak at the 172-GeV T-quark state, but also a peak at the 130-145 GeV T-quark state, something the Tommaso described as being of 4-sigma significance.

Tony Smith

PS – I prefer to call it the Truth Quark, since I think that Truth and Beauty are like Charm and Strange, and in the old days my favored terminology was used by a lot of particle physicists, but nowadays the sterile conformity of rigidly enforced consensus has almost completely eradicated the use of Truth and Beauty with respect to Quarks,
which is itself a term that extinguished at least two (probably more meritorious historically) competing terms:

due to George Zweig. According to the book The Second Creation by Crease and Mann: “… Caltech theorist … George Zweig duplicated the quark model exactly at almost the same time. He called the quarks “aces” … he was at CERN … and … had to publish … in … Physics Letters … the editors would hear none of it … Despite heated argument, Zweig never published his long, careful article on aces … It was all right for someone of Gell-Mann’s stature to advocate the … notion … Zweig … having no reputation to protect him … was denied an appointment at a major university because the head of the department thought that he was a “charlatan”. …”.

Ceng Zi
due to Liu Yao-Yang, who was actually the first (around 1960) to invent what is now known as the quark model. His paper was rejected by a Chinese journal. After the publicity of Gell-Mann’s rediscovery, the editors apologized for rejecting the paper, but nowadays not so many people know the name of the true inventor/discoverer of Ceng Zi (now mostly known by the term quarks).

PPS – Tommaso links the “jet effect” with “alcoholic beverage”, so maybe I should say that my favorite such beverage is Strega (however, mostly after dinner, rather than “at dinner tables”).

2. Andrea Giammanco - March 10, 2008

I think it’s misleading to call it “jet effect” (it could be called “lepton effect” as well), but this misleading name makes me wonder if anybody ever checked whether the result, channel by channel, is stable against the number of extra-jets.
I mean: in the di-leptonic channel, is the mass the same when the number of jets is 2,3,4, etc.?

And can you please list those measurements making use of the Matrix Element technique?
As far as I know, this has its impact mostly in the dileptonic measurements. And some time ago I noticed that ME analyses tended to give the lowest values (but I don’t know if it is still the case with the newest ones).
Maybe there is some very subtle bias related to the technique? After all, it is the technique with the maximum model dependence.
If, as you mention, there is the possibility that we are measuring two different things, any model dependence will introduce biases in favor of one or the other.

3. Tony Smith - March 10, 2008

Andrea Giammanco asked “… in the di-leptonic channel, is the mass the same when the number of jets is 2,3,4, etc.? …”

No. That is the point of the example in my comment from the Varnes PhD thesis. The event had mass around 130 GeV if considered as a 2-jet event (throwing away as background the lowest transverse energy jet of the three jets in the data) but had mass around 170 GeV if considered as a 3-jet event.
As Varnes said in Chapter 8 of his PhD thesis:
“… there are six t-tbar candidate events in the dilepton final states … Three of the events contain three jets, and in these cases the results of the fits using only the leading two jets and using all combinations of three jets are given …”.
Note that in those early days D0 (about which Varnes wrote his PhD thesis) had only a few dilepton events, so it was relatively easy to look in some detail at each event individually,
which is an approach that is not so common with higher luminosities and numbers of events.
My fear is that individual event characteristics, possibly key to understanding New Physics (not only my 3-state T-quark model, but also possibly other New Physics), might be missed by LHC if its data is amalgamated into statistically easy-to-manage analysis,
with such detailed individual event data being overlooked.

The reluctance of LHC management to release all data for analysis by outsiders reinforces my fear. See for example the adverse reaction to the open-data proposal by Tao Han described by JoAnne Hewett on her CV blog at

Tony Smith

PS – There being only 6 dilepton events in Figure 8.1 of Varnes’s PhD thesis, it is reasonable for me to discuss each of them, so (mass is roughly estimated by me looking at the histograms) here they are:

Run 58796 Event 417 ( e mu ) – 2 jets – 160 GeV

Run 90422 Event 26920 ( e mu ) – 2 jets – 170 GeV

Run 88295 Event 30317 ( e e ) – 2 jets – 135 GeV

Run 84676 Event 12814 ( e mu ) – more than 2 jets – 165 GeV
– highest 2 jets – 135 GeV

Run 95653 Event 10822 ( e e ) – more than 2 jets – 180 GeV
– highest 2 jets – 170 GeV

Run 84395 Event 15530 ( mu mu ) – more than 2 jets – 200 GeV
– highest 2 jets – 165 GeV

To me in terms of 3 mass Tquark states
high around 220 or so
medium around 170 or so
low around 130-145 or so
those look like

Run 58796 Event 417 ( e mu ) – direct 2-jet decay of medium

Run 90422 Event 26920 ( e mu ) – direct 2-jet decay of medium

Run 88295 Event 30317 ( e e ) – direct 2-jet decay of low

Run 84676 Event 12814 ( e mu ) – decay of medium to low
then 2-jet decay of low

Run 95653 Event 10822 ( e e ) – direct 2-jet decay of medium
with small background other jet

Run 84395 Event 15530 ( mu mu ) – decay of high to medium
then 2-jet decay of medium

I wish that comparably detailed event data would be available for LHC dilepton events.

4. CDF/D0 Combined Top Mass Result « Imaginary Potential - March 11, 2008

[…] They’ve changed from last year to which is a total uncertainty of 0.8%. Tommaso Dorigo has a really nice post on the individual measurements and combined uncertainties that went in to the result. There’s […]

5. dorigo - March 13, 2008

Hello Tony, Andrea,

I am sorry if I have not answered your interesting comments above… I was traveling to the US and now I am still quite busy. Let me just pick from your comments at random.

Tony, my remark on alcohol was totally a joke… However, it is true that as measurement techniques have improved and statistics has enlarged, the possibility to miss a state with a much different mass has not decreased, because the two effects work one against the other. I still do not believe it, though 😉

Andrea, your point is a very good one. Nowadays, most high-precision results on Mtop are obtained with matrix-element techniques. I think your suggestion on the amount of extra radiation affecting the results should be looked into – I believe it has been studied, but fetching the documentation is not trivial.


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