UPDATE: what a difference a small typo makes! In the report below I claimed that the CDF top mass measurement was yet to be stripped of the record of being the most precise in the world, given that the total uncertainty on the mass was 1.01 GeV, while the newest CMS result has a total error of 1.07 GeV... I however realized this morning that the total CDF uncertainty of the quoted measurement is 1.10, not 1.01 ! So the CMS result mentioned at the bottom of this article is indeed the most precise single measurement in the world of the top quark mass !


The top quark is the heaviest known elementary particle, and its mass is a fundamental parameter of the standard model, one which is important also to determine the phenomenology of new physics models such as Supersymmetric ones. No wonder that since the top quark discovery in 1995 all experiments who have had a chance to measure the top mass have struggled to do so with all available means.

Measuring the top quark entails first of all isolating samples of data containing a sizable fraction of top pair-production events, and then using the measured characteristics of the final state particles emitted in the decay of the quarks to gauge the value of the mass of the two decaying objects.

Two words: production and decay

The production of top quark pairs proceeds through the mediation of the strong interaction: it is a quantum chromodynamical process. At the Tevatron the most fruitful reaction that results in a pair of top quarks is the collision of a quark-antiquark pair (one quark from the proton and one antiquark from the antiproton, typically, although not exclusively), which then annihilates into a gluon; the gluon then materializes the top quark pair.

At the LHC, on the contrary, the most frequent mechanism for producing top quarks is the collision of two energetic gluons. The gluons "fuse" into another one, which then produces the top quark pair just as before. While in 1.96 TeV proton-antiproton collisions the rate of production of top quark pairs is of about one in 10 billion collisions, at the LHC in 7 TeV proton-proton collisions the rate is of about 2 in a billion: roughly twenty times larger odds!

Since the Tevatron and the LHC experiments have currently analyzed datasets of similar size -of the order of 5 to 10 inverse femtobarns have been used in Higgs boson searches published this summer by CDF and DZERO on one side of the Atlantic and by ATLAS and CMS on the other side, for instance- one would believe that the most precise measurements are certainly those produced at the LHC, due to the higher statistics of top quarks available there by now. But that is not so: it is systematic uncertainties that dominate the total error in the most precise top mass determinations by now, and the smallest systematics are those of experiments that have run longer and have perfected their calibration procedures, so this gives the advantage to the Tevatron (one further factor is the large pile-up of the LHC collisions, which messes up a little the measurement of jet energy there, but we won't get into that detail here). Just barely, as you will see below.

I should not forget to mention the phenomenology of top quark decays: they almost always decay (in an incredibly short time, a trillionth of a trillionth of a second) into a W boson and a bottom quark, so that in a pair-production process one expects to have two W bosons and two bottom quarks. The W bosons may then decay (they too do so in a trillionth of a trillionth of a second or so) each into a lepton-neutrino pair (either electrons, or muons, or taus) or into a pair of quarks.

The top-antitop final state is then classified according to the number of electrons or muons it contains (taus are left aside because of their more difficult experimental signature): if there are no electrons or muons the final state is dubbed "all-hadronic", and has a total of six hadronic jets coming from the quarks emitted at high energy from the decay of the heavy objects; this final states arises 45% of the times. If there is only one electron or muon (from the decay of one of the W's), then the event also features four hadronic jets (two from the bottom quarks and two from the other W boson), and the final state is then called "single-lepton": this arises in 30% of the cases. If, finally, there are two electrons, or a muon and an electron, or two muons, then there are just two hadronic jets (from the bottom quarks), and the event classifies as a "dilepton" decay: this only happens 5% of the times, though.

Now, if you browse through the many measurements of the top quark mass produced since 1995, you will find that typically the analysis of events classified in the single-lepton category has been providing the best measurements. That is because the final state is an excellent trade-off between the rate of signal events and the purity of the selectable event samples. In fact, an experimental signature with an energetic lepton and four jets is produced relatively rarely, mostly by a process called "W plus jets" production. That is the main background to top quark pairs in the single lepton category.

The dilepton and all-hadronic final states have instead respectively a very clean signature but too small signal rate, and a dirty signature with the highest rate. The nasty multijet QCD backgrounds have in the past prevented the all-hadronic final state from competing with the single-lepton decay mode in top quark measurements. Instead, it is the scarce number of signal collectable in the dilepton final state what has prevented those samples from providing precise top mass measurements.

Matters are changing now that statistical uncertanties are not the dominant source of error any more, but this is too long a discussion, worth another post. Instead, let me now go back to discuss the status of the most precise measurements of the top quark mass which are available on the market as of end of September, 2012.

The race to the top

A look at the public web pages of the CDF and DZERO experiments will reveal that their latest and most precise measurements of the top quark mass (which are probably going to be final, since the experiments are now so heavily undermanned that only a small selection of physics measurements will be attempted) have accuracies in the GeV ballpark. Since the top quark weighs about 173 GeV, that means accuracies of less than a percent.

CDF, for instance, quotes as its most precise result the determination obtained from a measurement using 8.7 inverse femtobarns of 1.96 TeV proton-antiproton collisions, employing data in the single lepton category and with an in-situ calibration of the jet energy measurement (basically they use the mass of jet pairs coming from the W boson to simultaneously determine the jet energy scale, using the fact that we know the W boson mass to 0.02% accuracy nowadays). The result is 172.85 +- 0.52 +- 0.49 +- 0.84 GeV, where the first uncertainty is due to sample statistics, the second is due to the jet energy calibration, and the third is the sum of other systematic uncertainties. If you add things up in quadrature (not entirely appropriate, but let's forget about these details) you get a total uncertainty of 1.10 GeV.

DZERO's most precise measurement, again in the single-lepton decay mode, is based on just 3.6 inverse femtobarns of collisions, and uses a matrix-element method with an in-situ jet energy calibration. The top mass is measured as 174.94 +-0.83 +-0.78 +-0.96 GeV (again respectively statistical, jet energy scale, and systematic uncertainties are quoted) which is a total error of 1.49 GeV.

The two experiments, to tell the truth, have also combined their most precise measurements of the top quark mass in a paper published in time for ICHEP this year. The combination results in a top mass of 173.18 +- 0.94 GeV, which is a sub-GeV uncertainty. A great legacy from the Tevatron!

And what is going on at the LHC then ? at ICHEP, also CMS and ATLAS have produced a combination of their top mass measurements, most of which used only a small part of the total statistics of data available at the time (10 inverse femtobarns of proton-proton collisions, shared equally between 7 TeV 2011 data and 8 TeV 2012 data). The result of the combination shown in July in Sidney was a top mass of 173.3 +- 0.5 +- 1.3 GeV: a total uncertainty of 1.4 GeV which is over 40% larger than the Tevatron average. Worth mentioning is that in this average the most precise single measurement was the one by CMS in the muon plus jet final state (172.6 +- 0.4 +- 1.5 GeV), carrying a total uncertainty of 1.6 GeV in total. ATLAS lagged behind with a measurement of 174.5 +- 0.6 +- 2.3 GeV.

Like any other record, however, the precision of the Tevatron top mass determination is bound to yield, but for how long will it hold up ? Both ATLAS and CMS are now using larger datasets to measure the top mass, but most importantly they have improved their calibration techniques, to reduce systematic uncertainties that are already dominating the total error in the numbers quoted above.

So CMS this month produced a new determination of the top mass based on single lepton events which is just barely more precise than the previously most precise single measurement, the CDF single lepton one. The measurement, based on 5 inverse femtobarns of 2011 data, is of 173.49 +-0.43 +- 0.98 GeV, which makes a total error of 1.07 GeV. When this result gets combined with other CMS determinations at the next winter conferences, it is expected that the CMS-only average of top quark mass determinations will become the most precise single-experiment result in the world. In the meanwhile we may also hope that other, even more precise measurements will appear. But it is not time to write off the Tevatron results yet.

To summarize, the most precise measurements available today are:

CMS, single lepton, 5.0/fb at 7 TeV: 173.49 +- 1.07 GeV

CDF, single lepton, 8.7/fb at 1.96 TeV: 172.85 +- 1.10 GeV

DZERO, single lepton, 3.6/fb at 1.96 TeV: 174.94 +- 1.49 GeV

ATLAS, single lepton, 1.0/fb at 7 TeV: 174.5 +- 2.4 GeV

I expect ATLAS will soon improve their result, which is admittedly a bit outdated now that the experiment is sitting on over 15 times more data than what was used in their currently best measurement of this important standard model paraleter! Will they beat the CMS result ? We will know very soon, I bet.