A Quantum Diaries Survivor

Ok… I think I have an obligation to explain here what is the jet energy scale and the jet energy resolution, why a working group in CDF (and another one in D0) has been using lots of human resources to determine them, and what good their knowledge does to the physics measurements at the Tevatron. Three things, three posts. Here comes the first.This post is quite long, and it is conceived for non-experts. I hope it is both readable and informative. If you are a physicist, and you want to know more about the issue, I suggest you rather read my proceedings of the Corfu 2005 conference at http://www.pd.infn.it/~dorigo/dorigo.ps

When observing the products of a hard collision between subatomic particles such as protons or electrons, one sometimes finds out that the originated particles come out in collimated streams - we call them "jets".

A jet is a stream of particles emitted when a quark (or a gluon, but let us take a quark here - things are the same) materializes into "stable" particles (not really stable, but so for detection purposes). We measure the total energy of the particles to try and determine the energy of the original quark, because a knowledge of the latter allows us to make important measurements and new discoveries.

For example, we can find the signal of the Higgs boson, a particle which may decay to a pair of jets: we have a chance to see a signal if we reconstruct the Higgs mass from the energy of the emitted quarks.

The jet energy is determined with a device called calorimeter, typically (but not always) composed by a sandwich of lead and plastic scintillator sheets. Particles interact with lead nuclei, create a cascade of secondary interactions, the resulting particles generate light as they traverse the scintillator sheets, and by measuring the amount of light produced by the process we can tell how much of a mess the originating particles created - that is, how much energy they originally had.

Of course, we need to know how much energy corresponds to a certain amount of light - we get information on that by shooting into the calorimeter particles of known energy, and measuring the light output. We do this before assembling our detectors, in what we call a test beam. In a test beam we can shoot particles whose identity is certain and whose energy is predetermined through the calorimeter, while after assembly, the experimental setup does not allow that kind of test any longer.

This is all good and well: we observe a collision, measure light from a small region of the calorimeter (the part hit by the stream of particles), and we convert that into energy. Are we done yet ? Unfortunately, no.

There are a number of effects that spoil the accuracy of the conversion of light into a jet energy - and the subsequent measurement of the originating quark energy. For instance, particles punch through the calorimeter without leaving all their energy inside, or they hit parts of the device which are uninstrumented or malfunctioning. The part of the calorimeter measuring the jet may be hit by additional particles not belonging to the jet originated from the quark, affecting our measurement. And so on. So what do we do ?

We model all these effects with a detailed simulation program. The program knows in detail how the detector is made, knows the physics of the interaction of energetic particles with matter, and knows how a jet is produced from a quark. We can thus study how the energy measurement is degraded by all the known effects.

From a rather complicated method using both real and simulated events we are able to determine a correction to the energy measured in the calorimeter. The correction is able to rescale the measured jet energy to match the one the originating quark had. We have a similar correction for the simulated jets, such that we can compare data and simulation after the jet energy correction.

Unfortunately, this whole process is very nice, but we need to check that what we did - correct the energy of real jets according to their characteristics, and correct that of simulated jets likewise - did not cause a bias: maybe we corrected simulated jets too much, or too little, with respect to jets in real data. If we did, all our subsequent measurements of physical quantities based on comparisons between data and simulation would result in a systematic error.

To check whether we have introduced a bias in our energy measurement, we really need a calibration point: a jet signal with known energy, which allows us to determine whether our measurement procedure returns -on average- the correct value of a jet's energy.                                          * * *

Let us now make a different example, that allows us to play with a quantity we are all more familiar with: temperature, rather than particles kinetic energy.

Imagine you have a thermometer, and you have the suspicion that it gives a biased measurement of temperature. You insert its probe in melting ice -which, having been awake on day three of Physics 101, you know has a temperature of 32°F. You note the reading. You do it a hundred times, with different containers, at different hours of the day, different weather conditions. At the end of this rather tedious process, you get a graph similar to the one shown here.

… What the graph shows is that the distribution does not peak at 32°F as it should. The deviation of the peak of the distribution from the true value (2°F in our case) is called a scale error. The shift indicates that the thermometer is indeed biased. Of course! Every instrument has a scale error of some magnitude. Ours will measure 2°F more, on average.

You also see what the typical error of any individual measurement of water+ice is: it is the width of the distribution of measured temperatures (0.2°F in our case). The width tells you how much you are going to err, on average, on any single measurement - if the distribution was centered on the true value. The width is the resolution of your instrument, folded with the variation expected from the measuring conditions - but let's leave these concepts alone now, and return to the scale error.

A calibration point is a great thing! It allows you to tune your measurement: from now on, when you read 64°F with your device, you know the true measurement is roughly 62+-0.2°F.

Now what would you have done if you had a big computer in your kitchen instead of a fridge ? The computer does not provide you with real melting ice, so in that case you would have no calibration point. But you would not despair. You are a good programmer, and you know the basic physics of melting ice and of mercury expansion inside a glass tube. So you would do a simulation of the measuring device, a simulation of the measuring process, and of the melting ice system, and you would end up with a set of simulated measurements, quite like the graph above. From it, you would get a measurement of the expected scale and resolution of your temperature measurement.

                                                   * * *

The above example shows that you use a calibration point - the melting ice - if you have one, and resort to a simulation of the physical process otherwise.

Alas, for jets we do have calibration points, but they are quite tough to measure! One of them is the decay of the Z boson to a pair of b-quark jets. The Z has a perfectly well known mass, but is hard to extract from the proton-antiproton collisions provided by the Tevatron collider. The other one is the decay of the W boson to a pair of light quark jets. This is even harder to see by itself, but W bosons decaying to jet pairs are extractable in events featuring top quark pair production…

Ok ok I went too far… But have a look at this graph. It shows the Z–>bb decay signal obtained by CDF in data collected before August 2004. The Z decay is the green stuff, but it is buried in a large background of jet pairs that have a non-determined total mass - the gray stuff. Notwithstanding the very small signal fraction, we can extract the measured mass value of those events, and compare to the true Z mass (91.19 GeV): we thus get a measurement of the bias - the Jet Energy Scale, that in the case at hand only refers to b-quark jets, the ones emitted by the Z in their decay: b-jets are different from original jets, but we do need to know their JES as well as we could. Why ?

That is the subject of a post to follow soon.