Top mass updates from CDF: 1 – the dilepton template method October 19, 2007Posted by dorigo in news, physics, science.
A series of brand new results from CDF have been approved a month ago, and I feel enough time has passed to make it possible to describe the analyses here without hurting anybody’s feelings. I will be short here, and just give the updated results with a very quick and dirty description of the most important features of the measurements. These days I am a bit overburdened with deadlines, and this blog is the first to pay the price…
By the way, one thing to note. Among other things, I am presently spending some time browsing some textbooks for a course in particle physics I am to give next month: well, most books are from the early nineties, and they either report only lower limits on the top mass, or provide “indirect measurements” from electroweak fits which carry 30 GeV uncertainties. It is hard for me to escape from being awed at the contemplation of the giant steps forwards we have made with the Tevatron in measuring that quantity!
If I have time and energy (many, many units of ) I will complete this post with some commentary later on. For the time being, just enjoy the incredible precision CDF is obtaining in this once unknown parameter of the Standard Model.
The top quark mass determined from dilepton decays using mass template fits
This new result is a precision measurement based on the final state , and a total of 1.8 inverse femtobarns of proton-antiproton collisions provided by the Fermilab Tevatron collider. The so-called “dilepton” decay mode can be easily detected over backgrounds since “leptons” are defined as electrons or muons -objects the detector is optimized to detect efficiently and with high purity, while the tau lepton is much harder to isolate. Backgrounds are small because the presence of leptons removes all events due to strong interactions, which are the most frequent processes at a hadron collider: for the most part those are due to either electroweak pair production of two W bosons, with additional QCD radiation yielding the two jets; or to decays with tau leptons yielding electrons or muons, with QCD initial state radiation again providing the extra two jets. events where the W decays leptonically and one additional jet is mistaken for an electron or muon also constitute a significant, but still small, source of backgrounds.
The final state is clean, but rare: only 4/81, or about 5%, of all top-antitop decays feature the classic dilepton signature. This is something which is easy to determine. A W boson can decay to any of the following pairs with almost equal probability: , , , , . The “3” factors remind us that there are three species of each quark doublet, since these objects come in three different colors. Also, note that the final state is prohibited by energy conservation, since the top quark mass is way larger than the W boson mass. All in all, there are nine possible final states, all equally probable: they each get a probability of one ninth! And since W bosons cannot decay to anything else, each has a 11% branching ratio. Easy! But then, why 4/81 for the dilepton mode ? Well, just count: each W has to go to either an electron-neutrino or muon-neutrino pair, so a total of 2/9… Multiply probabilities to get composites, and you are done. The graph on the right explains the same concept pictorially – dilepton decays to electron or muons are represented by the green square at the lower right. [If you do not get it at a glance: Both the horizontal and vertical sides of the big square represent the possible W decay modes, and are divided into nine slices of equal width. The intersection of the slices represent areas proportional to the probability for a WW decay to yield any given final state. Oh, a further note: this plot is my own invention. I was probably not the first to cook it up, but I have indeed seen no instance of it in the literature before I started using it in presentations… If you saw it used before 1992, let me know.]
Now, not only is the clean dilepton final state rather rare – one such event is created in two hundred billion collisions: there is a further catch. This mode in fact features not one but two energetic neutrinos from W decay, and is thus unconstrained: we only measure the transverse component of the vector sum of the two neutrinos, so there is no kinematical closure. What that means is that the equality of top and antitop masses (1), the equality of the two W boson masses to 80.4 GeV (2,3), and the constraint that the total momentum transverse to the beam direction cancels (4,5: two components separately equal zero) provide in total five constraints, which are not enough to provide a unique solution for the undetermined six components of neutrino and antineutrino momenta: just as if you had five equations with six unknowns.
And then there is combinatorics: even if you had perfectly determined momentum for each of the six final state objects, you could match a lepton with a neutrino and a b-quark in four different ways (plus four for the other top). In reality, however, there are experimental techniques by which we can pick the most likely assignment, reducing the possible combinations.
With hundreds of man-years of analysis we have refined those methods, and we can now obtain from the measured momentum of jets and leptons alone a quite precise estimate of top mass for each event. I will not attempt a description of the refined technique called “neutrino weighting method” which allows that result, but just mention that if you plot the “neutrino-weighted” estimated mass for a sample of simulated top quark pair decays to dileptons, you obtain the distributions shown in the plot on the right, where different histograms refer to increasing values of the simulated mass of the top quark, from 150 to 180 GeV. These distributions are broad: they are not just simple narrow gaussians centered at the true top mass value. However, they still allow some discrimination between different top mass values.
What next ? Well, just a few fits of the mass distribution of 124 selected real events to a sum of a background template -obtained by mixing the various expected contributions from background sources, totalling events- and each in turn of the top signal templates shown above. Each of the different fits provides a different interpretation of the data, with a varying degree of likelihood – see the result for a top mass of 172 GeV in the plot on the left. In the end, a plot of the obtained values of likelihood as a function of the top mass used for he template provides a measurement of the top quark mass, as shown below (the fit has the top mass as a continuous parameter, but that is a detail I am glad to skip).
The result is:
A surprisingly precise determination from a final state “unsuited” for top mass measurements!
More details are available in the public page of the analysis.