It's a bit like cars approaching a T-junction. Before they switch on their indicators, it is impossible to tell whether they are going to turn left or right. If you watched for long enough, however, you might find out that about half turned left and half turned right so you'd be able to say that each approaching car had a 50% probability of turning left.
Physicists do the same sort of thing with particles. They count up how many times a certain type of particle decays into different kinds of particles and call the result a branching ratio. For example, if they found that Z particles decay into muons 60% of the time, they would say that the branching ratio for Z particles decaying to muons is 60%. That, however, is not what they find. Measuring the Z particle branching ratios is your job.
Read all these instructions before going on, you might want to print this page and refer to it whilst you are doing your experiment.
Here are the event samples:
The answers are not all the same for a number of reasons. It is possible that you have misidentified events, for example, which would make your number come out wrong. We won't be dealing with this kind of error here and will assume that you identify the different decays with 100% accuracy!
Another source of error that we will deal with is called the statistical error. It arises from the small number of events you have looked at (CERN's physicists have powerful computer programs to do the analysis for them, they look at millions of events). Think back to the cars at the junction. If you just looked at one car and it turned left, you might say that the probability for turning left is 100%, but clearly you would be wrong. Even if the next car turned left, you might still be wrong, but you would have more confidence in your conclusion. If you watched a million cars and they all turned left, you'd be quite confident that all cars turn left, but you'd still have to assign some error to your conclusion because the million-and-first car could always turn right.
What this means is that the larger your sample, the more confidence you can have in the result. For this reason physicists calculate what they call a statistical error to go with their results. To calculate the statistical error on the muon branching ratio, for example:
When you have calculated the errors on your results, add up the results of everyone's analysis, calculate the error and plot the combined result on a graph along with the results from each group. Notice how the individual group results all scatter around the combined result, but that all results are compatible with each other within the errors you have calculated.
When you are finished, see how your results compare with the officially measured ones and learn a bit more about the consequenses of this measurement.
Particle Physics Education CD-ROM ©2001 CERN