Toward a 2.3/fb W mass measurement August 21, 2008Posted by dorigo in news, physics, science.
Tags: CDF, systematics, w mass
I looked with pleasure today at a few plots in the public web page of the CDF W mass measurement. They excellently describe the statistical power of the data collected so far by the experiment, and provide a clear hint that the next W mass measurement by CDF will make all previous determinations of this quantity grossly outdated, to say the least.
The W mass measurement is one of the most complicated analyses at a hadron collider. I would actually venture to say it is the most complicated one, and threaten anybody who wishes to challenge that judgement that I will use the argument “you object because you do not understand it well enough”, and proceed with showing why that is the case.
The reason why a measurement in HEP is more complicated than another one, in my opinion, is largely due to the potential of the data. When one has few events to study, statistics seriously limits the possible precision which can be obtained on any observable quantity derived from them, and a detailed study of systematics effects is useless. When one instead has to deal with huge statistics, the problem becomes that of understanding the systematic effects which affect the measurement, reducing them to a size comparable with the statistical uncertainty. If systematic uncertainties themselves can be studied with large samples of data, the level of understanding, and thus the level of detail of the studies, has to increase.
In the case of the W boson mass, the analysis was already extremely complex in Run I, when CDF had 100 inverse picobarns to study, and a few tens of thousands of good candidates of both the and the decays. I remember that in 1999 Andrew Gordon, a Harvard University graduate student who was doing the electron W mass measurement, took two years to try and figure out why the E/p distribution of electron tracks indicated one W mass value, and the reconstructed mass pointed to another one which deviated by four standard deviations from the former. Gordon was one of the brightest students that ever walked the corridors of the CDF trailers, and yet the puzzle went unexplained. Or so I remember (anybody out there reading this, who know the solution?).
You might be wondering what the heck I am talking about. Well, let us see if I can explain it in a paragraph. Measuring the W mass from decays requires you to set the scale of the electron energy measurement. Setting the scale means, literally, converting a given signal read in the electromagnetic calorimeter -a phototube output- to a precise energy measurement in GeV. From the latter, the W mass is easy to extract. Well, easy… But let me focus on the scale now. There are two ways to determine precisely the scale of electron signals. One is to take a high-Et electron, measure its momentum in the tracker, and impose that the E/p distribution has the same shape expected from a tuned Monte Carlo (which must know everything about the amount of material traversed by the track, about internal QED radiation, about delta rays… You name it). By tweaking the energy measurement until an agreement of the shape with MC is reached, one determines the energy scale. The momentum, incidentally, is very well determined with other means, which do not interest us here.
I said one paragraph, ok let’s have two. The other method to set the scale of the e.m. calorimeter is to use the decay: we know very well the mass of the Z boson, so a direct reconstruction of the Z peak from those events allow to tune the energy scale such that the Z mass distribution agrees with what is expected. Mind you, the peak does not come exactly at the Z mass value you find in the PDG (91.19 GeV, as measured by LEP): it comes out lower, because of parton distribution functions, internal QED radiation, and other effects. But with a good Monte Carlo simulation, those effects can be constrained, and the scale is determined well. How well? It depends on the statistics. There are fewer Z boson decays to dielectron pairs than there are electrons with which to determine the E/P distribution, so the Z mass tuning is intrinsically less powerful a method than the E/P.
Anyway, I was discussing the new results by CDF, which are based on 2.3 inverse femtobarns of proton-antiproton collisions. That is a huge number of W boson decays! The process has a cross section of about three nanobarns, which means 3,000,000 femtobarns. You multiply by 2.3/fb and you get 7 million electron W events! This statistics is huge, and the accuracy which is required in understanding systematic effects is seriously challenging the CDF experts who are trying to produce a new world’s best W mass determination.
Let me remind you here, incidentally, that the W mass is now the most important input in the electroweak fits which attempt at constraining the mass of the Higgs boson in the Standard Model. See here for a short review of the current status of affairs.
Now, what I wanted to discuss in this post -which has become way longer than I wished- was just a couple of plots, which show the behavior of high-energy electrons as they cross the CDF detector.
The plot above shows, for 2.3/fb of data, the Z boson mass reconstructed with electron energy deposits in the calorimeter. The shape is not exactly easy to describe analytically (it is a Breit-Wigner resonance shape convoluted with a gaussian resolution smearing, convoluted with PDF of quarks and antiquarks in the proton, and smeared with other small effects), but to a quick glance it looks roughly a gaussian peak.
Now look at the plot below, which shows, for the same data, the Z mass reconstructed by using the track momentum measured in the tracker, for those same electrons. What is going on ?
Before you start thinking that the tracker measures momenta less well than the calorimeter measures energy, let me get this straight: the momentum in the tracker is measured with better accuracy -and in fact, that is the reason why setting the energy scale with the E/P distribution, using the momentum as a reference, is a valid method. The reason for the odd-shaped curve is bremsstrahlung: high-energy electrons traveling in the material of the CDF tracker emit soft photons, which can be collected and measured in the calorimeter, but are instead lost in the track measurement. For that reason, the Z mass distribution above has a long “radiative” tail to lower masses.
Now, look at the E/p distribution itself (see below). In absence of QED radiation, this would be a distribution peaking at one, with no tails at high values. Instead it does show a long tail, which is exactly the reason for the low-mass tail in the Z mass distribution above. Incidentally, look at the agreement with the simulation in the plot: amazing match! The residual systematic uncertainty coming from setting the energy scale with the E/P distribution, on the future W mass measurement, amounts to barely 5 MeV!
And finally, a plot showing the W transverse mass distribution, which is obtained by using the electron energy as well as the missing transverse energy due to the escaping neutrino.
The statistics is tremendous, and so is the level of agreement with the data. The statistical error on the W mass which can be fit with these events amounts to 15 MeV – which explains the amount of care which is needed to study all systematics. Incidentally, the final state provides a similar statistical accuracy, and once the two measurements are combined, the total uncertainty in the W mass measurement will be in the 20 MeV ballpark.