In the challenge part 2 you learned how to distinguish events in which a Z⁰ decays to produce the different sorts of particle-antiparticle pairs. Now you might like to try your hand at one of the important measurements we make at LEP. This is to measure the fractions of Z⁰s that decay to each type of particle-antiparticle pair.

In this section you will be provided with a large number of events containing particle-antiparticle pairs from Z⁰ decays. Look at each one and keep a separate count of the number of: , , and events.

Unfortunately, when it comes to events, things become complicated. The number of such events is not the same as the number of or events. The details of this are not important in doing this challenge. Simply multiply the number of or events by a correction factor of 0.61 to get the expected number of events. If however, you wish to know more about this click here.

Once you have classified all the events there are a number of interesting questions to ask yourself:

• An important prediction of the Standard Model of particle physics is that the probability for a Z⁰ to decay to an electron-positron pair should be the same as the probability for it to decay to a muon-antimuon pair or a tau-antitau pair. Are the numbers of: , and events you have counted statistically consistent with one another?
• Another prediction of the Standard Model is that Z⁰s decay to quark-antiquark pairs much more frequently than to electron-positron, muon-antimuon or tau-antitau pairs. In fact, the number of muon-antimuon pairs should be only about 0.048 times the number of quark-antiquark pairs. Using the number of events you have observed, calculate the number of events you should have expected to see. Is the number of events you actually observed statistically consistent with the number you expected? What about the number of and events?

Note: in order to decide whether or not two numbers are "statistically consistent" you need to have some idea about "statistical errors" or "statistical uncertainties". Here is some help if this is unfamiliar to you.

Here are the events. Don't worry if you don't have time to look at them all. You can make measurements even if you look only at a subset. Of course, your measurements will be more accurate the larger the number of events you do look at. Another way might be to collaborate with a few of your friends: you could each scan a different set of events and then combine your results.

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