I wonder how interesting can be to an outsider to learn that the mass of the sixth quark is now known to 0.38% accuracy, thanks to the combination of measurements of that quantity performed by the CMS experiment at CERN. In fact, the previously best measurement was the one recently published by the DZERO collaboration at Fermilab, which has a relative 0.43% accuracy. "So what" - you might say - "this 14% improvement does not change my life". That's undeniably true.

The perspective can be a little different if we consider that the precise measurement of the mass of the top quark, the heaviest known elementary particle, has been one of the main goals of the Tevatron experiment in Run 2, an endeavour on which were spent several hundred million dollars and ten thousand man-years of research. Due to well calibrated detectors and years of experience, CDF and DZERO have been leading the field on the measurement of this important standard model parameter in the past; but that bit, too, has now been stolen by the CERN experiments.

One further reason for being interested in the new measurement by CMS is that there is now a rather odd tension between the best Tevatron measurement and the best CERN measurement of the top mass: while CMS measures now M_t = 172.38+-0.66 GeV, DZERO earlier reported M_t=174.98+-0.76 GeV. Even admitting that no correlation exist between the systematic uncertainties in the two determinations, we are facing a 2.6 sigma discrepancy. In other words, there is a chance in about 250 to observe such a difference if the two experiments are measuring the same physical quantity.

The above is not to say that the top quark mass is different in the US from what it is in Europe: that would be a rather annoying fact, almost as annoying as having to think in feet inches and pounds here and meters and kilograms there. No: the answer is most likely hiding in the detailed evaluation of systematic uncertainties in one of the two measurements. But which of the two ? Well, if we compare the two results with the ones -less precise, but still quite a good reference point- obtained by CDF and ATLAS, we learn that the CMS result is in good agreement with them, while DZERO is the one far off. So the blame falls most likely on the DZERO experiment. This is just an indicium, of course, but it carries some weight.

Anyway, let us go back to the CMS combination for a moment. The result, which you can find described in detail in the public note just published by the experiment, comes from combining the measurements that CMS obtained from the study of different final states of top pair production and decay: the "single-lepton" one, the "dilepton", and the "all-hadronic" one. These three names describe the way top pairs present themselves after the decay of the tops into W bosons plus b quarks, the further decay of W bosons into quark-antiquark pairs or lepton-neutrino pairs, and the hadronization of all energetic quarks into as many collimated jets of hadrons.

When one W boson decays to quarks and the other to leptons one gets the "single lepton" final state, featuring a lepton, a neutrino (causing missing energy in the detector) and four hadronic jets; when both Ws decay to leptons one gets the "dilepton" final state, featuring two leptons, two neutrinos (more missing energy) and two hadronic jets; and when both decay to quarks it is the "all-hadronic" final state what arises, which features six hadronic jets and no leptons nor energetic neutrinos.

In reality there are a total of 8 different determinations that CMS produced analyzing its 7- and 8-TeV datasets of proton-proton collisions collected in 2011 and 2012: you can see them listed in the two graphs below. The first reports the numerical inputs, the second lists them with associated bars that describe the total weight of each input in the combined weighted average.

The combination may indeed be called a "weighted average" - that's what it is - but the weights are not simple inverses of the respective variances of the individual determinations: the various systematic uncertainties affecting the 8 measurements are of course at least in part correlated among each other, and the accounting of the partial correlations is a bit tricky, although after all not conceptually too complicated. In the end, you can see that the input which contributes the most to the average is unsurprisingly the 2012 lepton+jets determination, which is the most precise one if taken individually.

And now what ? Well, I believe CDF might produce a further improved measurement in the future; ATLAS will surely do the same. Eventually, by analyzing LHC Run 2 data and combining all inputs, we will nail down the top quark mass to less than a couple of hundred GeV. Going further with these direct methods would probably be silly, as we know that the top quark is not an "asymptotic state": despite being a heavyweight the top does not exist as a free particle, as it is a coloured object and quantum chromodynamics forbids the existence of free coloured states.

Hence, the mass of the top quark -the one we can derive by looking at its decay products- carries a uncertainty which is neither statistical nor systematic: it is an uncertainty of a third form, whose source is the ill-defined nature of the quantity being measured. The precise value of the top quark mass as measured by its decay products does not exist, in that sense, as there is a uncertainty in its definition which is of the same order of magnitude of a constant of quantum chromodynamics called "Lambda_QCD", which is indeed of the order of 200 MeV.

Another way to look at this is to consider that when a top quark decay, it transmits its colour to the decay products; but this colour needs a corresponding anti-colour to nullify in the final, "asymptotic" states: so there has to be at least a pion (the lightest particle made of quarks) that is partly produced by the decaying top and partly by the remnants of the hadron collision that produced the top quark. The mass of the pion is of the same order of magnitude of the uncertainty I was discussing above (140 MeV, to be precise).

To go further one must change one's objective: the "true" top quark mass, arguably, is the parameter which directly enters the Lagrangian of the theory. That number can be determined by other means - for instance, by scanning the cross section of top pair production in electron-positron collisions. But that will require us to build a 350 GeV electron-positron collider: not in the cards yet.