Z Branching Ratios

In the ghostly quantum world that particles inhabit any individual Z particle is bound to decay but it is impossible to know in advance what kind of particles it will decay into. All that can be said is that it has a certain probability of decaying into certain kinds of particles.

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.

  1. Launch WIRED by clicking on the file of 100 events below that you are assigned by your teacher.

  2. Use the Zoom button and the mouse to zoom in on details and the Rotate button and the mouse to rotate the event on the screen.

  3. By using what you have just learned about particle detectors, decide whether the Z has decayed into electrons, muons, taus, or quarks. Keep a tally of the number of times the Z particle decays into each.

  4. When you have decided what kind of particles the Z in the event you are looking at has decayed into, go to the next event by clicking on the ">".

  5. When you have looked at all the events, or as many as your teacher tells you to look at, work out the percentages of the Z particle decays into electrons, muons, taus and quarks.

  6. These are your measurements of the branching ratios of the Z particle, but your work isn't over yet.

  7. Write your answer on the blackboard next to everyone else's.

  8. Are they all the same? If not, why not?

Here are the event samples:

  1. - 91 GeV collisions, Z decays during 1998 (1-100)
  2. - 91 GeV collisions, Z decays during 1998 (101-200)
  3. - 91 GeV collisions, Z decays during 1998 (201-300)
  4. - 91 GeV collisions, Z decays during 1998 (301-400)
  5. - 91 GeV collisions, Z decays during 1998 (401-500)
  6. - 91 GeV collisions, Z decays during 1998 (501-600)
  7. - 91 GeV collisions, Z decays during 1998 (601-700)
  8. - 91 GeV collisions, Z decays during 1998 (701-800)
  9. - 91 GeV collisions, Z decays during 1998 (801-900)
  10. - 91 GeV collisions, Z decays during 1998 (901-1000)

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:

So, for example if you looked at 100 events and found 30 events where the Z decayed into muons, your branching ratio would be 30 +/- 6 %.

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.