In the past few weeks the Tevatron and LHC experiments have updated their results on some of the most important Standard Model parameters. Of these, notably the top quark mass is one where the Tevatron is still doing slightly better than the LHC, due to the longer running time of the CDF and DZERO experiments, which allowed for a more precise calibration of the jet energy scale - the largest systematic uncertainty in this kind of business.

I have updated you on the matter tangentially in the previous two posts, where I discussed the overall compatibility of top and W boson masses with the Standard Model predictions, where the latter depend on the now well-known mass of the Higgs boson. Here instead I want to focus briefly on the top quark mass.

Following its first spotting in 1994 by CDF and the definitive observation by CDF and DZERO in 1995, the top quark has been the subject of a huge effort at the Tevatron: being the only collider which could produce that particle, it was of paramount importance to study it as well as possible there. Furthermore, the top quark is a very special particle, endowed with properties that naturally offer precise tests of the Standard Model predictions.

On the other side of the Atlantic ocean we had to wait until 2010 to start studying the top quark in detail, with the LHC collisions. ATLAS and CMS have since then amassed large samples of almost-pure top pair events, as well as large signals of single top production. With those samples, ATLAS and CMS have now reached the precision of the Tevatron experiments.

It is the purpose of this article to examine the quality of the most precise measurements, explaining what is their limiting factor at the moment. However, since I have mentioned quite a few facts of which the general reader might be unaware, without giving a proper explanation, let me first give a itemized list of simple facts and explanations.

A few basic facts about the top quark and its mass measurement

• The Tevatron collider is a facility built in the eighties, and then upgraded in the late nineties, to collide protons with antiprotons at the center-of-mass energy of 1.8 TeV (then 1.96 TeV). Collisions were obtained in the core of two experiments along the ring -CDF and DZERO - in 1987-88, then 1992-95, and then from 2002 to 2011 following the machine upgrade. The total integrated luminosity acquired by the two experiments have been of about 11 inverse femtobarns each: that corresponds to about 600,000 billions of collisions in the core of each detector.
• The LHC, which hosts two general-purpose collider experiments (ATLAS and CMS) as well as two more specific experiments targeting b-quarks (LHCb) and heavy nuclei collisions (ALICE) has operated since 2010 at the CERN laboratories of Geneva. Colliding protons with protons at the total center-of-mass energy of 7 TeV, and then 8 TeV, the LHC has delivered in total about 25 inverse femtobarns of proton-proton collisions to CMS and ATLAS, corresponding to about 2,000,000 billions of collisions.
• The top quark is the heaviest known elementary particle. It is one of the six known quarks, which are the constituents of atomic nuclei along with the carrier of the strong interaction, the gluon. The top quark weighs an equivalent 180 proton masses, and it is not found in ordinary matter: to produce it we need collisions that convert the kinetic energy of the projectiles into its mass.
• I mentioned above the special properties of the top quark. Indeed, the large mass of the top quark makes it different from the other five known such bodies: once produced in energetic collisions, the top quark decays in an extremely short time, less than a trillionth of a trillionth of a second. Because of the shortness of its lifetime, the strong interaction is unable to act on the top quark; in turn, this implies that we can measure properties of the particle without the hindrance of strong interactions, which would otherwise make it impossible to study it as a free particle, and e.g. spoil our ability to detect its polarization at production by examining the angular distributions of its decay properties.
• The top quark decays by the electroweak interaction by emitting a W boson and turning into a bottom quark. The W boson in turn can very quickly decay into either a lepton-neutrino pair (either a eν, or a μν, or a τν) or a pair of lighter quarks (up-antidown, or charm-antistrange).
• Since the largest fraction of detected top quarks are produced in pairs (they are simpler to identify, and pair production is also more frequent than single production), the signature of the event contains two b-quark jets - produced when the b quarks fragment into a stream of collimated hadrons - and two W bosons. The W bosons yield either two lepton pairs, or one lepton and one quark pair, or two quark pairs. There are therefore three corresponding topologies in the final state: "dilepton plus dijet", "lepton plus jets", and "all jet" (also known as "all hadronic"). Because the W boson decays one ninth of the time into each lepton pair, and two thirds of the time into quark pairs, the relative frequency of occurrence of the three topologies is of 4/81, 8/27, and 4/9 (where we are omitting tau leptons in these three categories).
• I also mentioned above, as I will below, the "jet energy scale" systematic uncertainty. This is relevant in the measurement of the top quark mass because we measure the top mass by the energy of its decay products, and these always include hadronic jets. To measure jet energies, we need to carefully account for the total energy we detect in our detector due to the iassage of all the particles contained in the jet. However, a number of physical phenomena concur to make this a very tricky business; the biggest problem is that we do not have a copious "reference signal" with which to calibrate our energy measurement. A long, tedious and painstaking effort is required to understand the detector elements and their response to low-energy particles. Besides the longer experience with their detectors, a factor favouring CDF and DZERO over ATLAS and CMS on the business of the jet energy measurement is also coming from the running conditions of the LHC: being a higher-luminosity machine than the Tevatron, the LHC produces tens of independent proton-proton collisions in the course of a single crossing of the proton bunches inside the detectors, as opposed to just a few collisions produced at the Tevatron. Each collision, albeit "soft" when compared with a top quark pair production process, contributes soft particles that "pollute" the energy measurement in the detectors. Algorithms that account for these additions with great care of course are routinely employed and are part of the calibration procedure of the jet energy measurement, but they contribute some smearing that results in some added headache to experimentalists at CERN more than they did at the Tevatron.

The measurements

Let me start with CMS. In the public page of the experiment we find a link to a  recent publication discussing the measurement obtained in the "all-hadronic" final state (i.e., one with only hadronic jets in the final state of the top pair decay) contains the nice graph below, which already contains some important comparisons.

As you can see, there are four independent measurements by CMS that have been averaged, accounting for all correlated and uncorrelated systematics.  The CMS combination is the fifth bar, which is M_top(CMS) = 173.54 +- 0.33 +- 0.96 GeV. This is a total error of one GeV, and as you can see the dominant error is systematical, and three times larger than the statistical one. If we look into the individual sources of systematic uncertainty, indeed we find that the largest single contribution is the jet energy scale, contributing e.g. +-0.97+-0.49 GeV in the all-hadronic measurement which is the focus of the paper linked above; here the two jet-energy-scale-related uncertainties are coming from generic jets and from specific issues connected with the measurements of b-quark-originating jets, which have a peculiar phenomenology that needs to be accounted separately for a tidier job.

Another thing worth noting from the graph above is that they still refer to datasets of up to 5 inverse femtobarns of proton-proton collisions. In other words, CMS has not thrown in all the available statistics yet. The logic is along the lines I already mentioned: the datasets have already a lot of statistics, so that the dominant uncertainty is anyway systematical; calibrating properly the new data, and accounting from the larger number of interactions per bunch crossing of the latter part of the LHC data takes time. On the other hand, this also says that once all the data will have been used, CMS will be likely able to further reduce their total uncertainty.

In the publication above we also get the most precise single published result on the top mass by CMS, which comes from analysis of the single lepton final state, in the 2011 7 TeV dataset. The result is M_top = 173.49 +- 0.27 +- 1.03 GeV, which is a total error of 1.06 GeV.

As for the Tevatron, what you see in the graph above is already a combination of the CDF and DZERO results. The graph however does not contain the most up-to-date result, which includes more measurements and has a better precision. The latest result for the top mass Tevatron combination is instead detailed in a recent arxiv posting, and is M_top(Tevatron) = 173.20 +- 0.51 +- 0.71 GeV, which is a total error of 0.87 GeV, and thus overall better than the CMS average by about 13%. However, this is already a lab-wide combination! Since a LHC-wide combination of the most recent top quark mass measurements is not available yet (the last available one is based on 2011 results, 173.3+-0.5+-1.3 GeV, and is less precise than e.g. the most precise CMS measurement alone), it is best to compare the individual results of each experiment.

The last CDF average of the top quark mass I can find is detailed in a conference note, but is two years old. It lists M_top(CDF comb '11) = 172.70 +- 0.63 +- 0.89 GeV, which is a total error of 1.09 GeV. Also worth noting is that since then CDF published a very precise measurement based on the single lepton topology and 8.7 inverse femtobarns of data; that result is M_top(CDF sl. '13) = 172.85 +- 0.71 +- 0.84 GeV, which is a total error of 1.10 GeV.

As far as DZERO is concerned, their latest combination linked from their public results page quotes M_top(DZERO '12) = 174.94 +- 1.49 GeV, which is way less precise than other combinations discussed so far; as for the single most precise result produced by DZERO, this comes from a lepton-plus-jets result of 3.6 inverse femtobarns of data, using a matrix-element technique for the measurement. This is quoted as M_top(sl, me '11) = 174.94 +- 0.83 +- 0.78 +- 0.96 GeV, where the last two numbers refer to jet energy scale systematics and other systematics, respectively. If one adds in quadrature, that is again a total error of 1.49 GeV.

The last player in this game is ATLAS. From the public page of the experiment I found many results, but no ATLAS combination. ATLAS has two recent results which are of almost equal precision: this one, obtained from 4.7 inverse femtobarns of data at 7 TeV in the dilepton topology, at M_top = 173.09 ±0.64 ±1.50 GeV, and this one, using a three-dimensional fit technique in single-lepton events again from 7-TeV collisions, at M_top = 172.31 ± 0.75  ± 1.35 GeV, where here the first error includes statistical fluctuations and jet energy scale together. In the first case the total error is 1.63 GeV, the latter is a total error of 1.54 GeV.

To summarize, the four experiments can be compared using their most precise individual results on the top quark mass (bearing in mind that this comparison is temporary, and that it is a rather idle game - we are comparing results from different apparata using different datasets taken under different running conditions, so we do not really learn much!):

CDF: 1.10 GeV total uncertainty
DZERO: 1.49 GeV total uncertainty
CMS: 1.06 GeV total uncertainty
ATLAS: 1.54 GeV total uncertainty

so the winner of this particular contest is CMS, but by a narrow margin. If instead we compare experiment-wide averages, we can only do this meaningfully for the following three:

CDF: 1.09 GeV
DZERO: 1.49 GeV
CMS: 1.00 GeV

Finally if we take a snapshot of the lab-wide averages, the Tevatron wins:

Tevatron: 0.87 GeV
LHC: 1.00 GeV

where for LHC I have used the CMS average in the absence of an updated LHC one.

One note at the end of this long busy post: if you are aware of more recent measurements on the top quark mass (at the date of August 5th 2013), please let me know - I will be happy to update the piece (and I will be grateful, since this information will in some way make it through into a presentation I am going to give at a conference in a month or so!).