One, I started my career in experimental HEP with searches and measurements of the top quark properties, and the mass was one of the parameters I spent quite some time working on.
Two, I do believe that the top quark mass is outstandingly interesting in a varied landscape of standard model measurements. The top quark is a unique particle - the heaviest-known elementary fermion, or if you prefer the heaviest elementary particle we know altogether. It is unique for a number of reasons; and its mass is a very important parameter. One of the reasons for that has been underlined in 2012 when it was discovered that the combination of Higgs and top quark masses makes our Universe walk on a thin line dividing stability from possible collapse.
Three, I have spent my whole career in experiments that have led the pack of competitors in the competition for the most precise measurement of the top quark mass. CDF has produced both the first and the most precise top quark mass measurement from 2 TeV proton-antiproton collisions; and then CMS has taken over with its most precise measurements after 2010.
So I think the above does justify why I am interested in knowing very precisely the mass of this particle. But beware - here I have been neglecting to point out a very important detail: the top quark mass is an ill-defined quantity. In fact, it could be taken as a very clean example of situations where you have statistical, systematical, and "definition errors" all playing a role - the latter becoming more important as we improve the former two.
You may think that when you reconstruct the mass of the top quark by measuring the energies and momenta of jets and leptons you are nailing down the parameter that enters the Electroweak Lagrangian density - the equation that governs the rules of electromagnetic and weak forces among fermions and force carriers. But you would be wrong: what you are measuring is instead something different - what we have come to call the "Monte Carlo mass". This is the mass one can reconstruct with observed final state particles, by comparing the energies of the latter with a Monte Carlo simulation (or several ones, differing by the input mass in the simulation). Having direct access to the Lagrangian parameter is no easy matter, and the ill-defined nature of the quantity you are measuring plays a role in the total uncertainty.
I think the topic is too complex to make justice of it here - even assuming I could do a decent job. So rather, let me just tell you what is the present status, after the Moriond 2016 conference has drawn to a close and ski slopes have been cleared of skiing physicists. Unfortunately, the 2016 winter conferences have not brought dramatically new results: the top mass measurement with the highest precision is still the CMS one shown below (and reported here), in red.
Will we get to know this parameter with much higher precision soon ? Not a chance. The higher statistics of Run 2 LHC data will help, but systematic uncertainties (and the precise definition of the measured parameter) are starting to be the dominant factor. Or I should rather say "have become already": the systematics uncertainty in the CMS measurement is almost four times as large as the statistical one, meaning that more data may help only if they help constrain the former rather than the latter. And typically, while statistical uncertainties scale down with the square root of the integrated data, systematical ones scale more frequently with a smaller power, like x^1/4. So to halve them you are required to throw in 16 times more data. Sort of.
Nonetheless, this remains a fascinating topic. Electron-positron colliders producing top quark pairs will allow us to measure the top quark "pole" mass -a better-defined quantity- with higher precision by scanning the production rate as a function of beam energy (see graph on the right), but it will take a while to construct them. For now, we'll have to wait for the slow improvements that the LHC experiments will offer. Maybe this summer.
Comments