"Z branching ratios" project
One of the things physicists want to know about Z particles is how they decay
into other particles. 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.
- Launch WIRED by clicking on the file of 100 events below that
you are assigned by your teacher.
- 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.
- 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.
- 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 ">".
- 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.
- These are your measurements of the branching ratios of the Z particle, but
your work isn't over yet.
- Write your answer on the blackboard next to everyone else's.
- Are they all the same? If not, why not?
- 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:
- take the reciprocal of the total number events you looked at,
- take the reciprocal of the number of decays producing muons that you identified,
- add these two numbers,
- and take the square root of the result to get the percentage error on your result.
- 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.
Measuring branching ratios is a way of finding out about how forces work in
Here are the event samples:
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.
- - 91 GeV collisions, Z decays during 1998 (1-100)
- - 91 GeV collisions, Z decays during 1998 (101-200)
- - 91 GeV collisions, Z decays during 1998 (201-300)
- - 91 GeV collisions, Z decays during 1998 (301-400)
- - 91 GeV collisions, Z decays during 1998 (401-500)
- - 91 GeV collisions, Z decays during 1998 (501-600)
- - 91 GeV collisions, Z decays during 1998 (601-700)
- - 91 GeV collisions, Z decays during 1998 (701-800)
- - 91 GeV collisions, Z decays during 1998 (801-900)
- - 91 GeV collisions, Z decays during 1998 (901-1000)
| Particle Physics Education CD-ROM ©1999 CERN