Beginner's Guide

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The Crystal Calorimeter (CC)
You already heard about the crystals in CLEO. You know thay are used to find uncharged particles, how can we use them for charged particles?

Well, the previous pictures showed that also charged particles create light flashes in those crystals. (Go back to check that this is really true...)
But in that case they are used to measure the energy loss of particles going through them.

This picture shows the ratios for a large number of tracks. As you can see most of the particles leave a small amount of their energy, but there is also a clear ``peak'' at 1. These tracks are identified electrons!

The Electron ID Package
Besides the E/p ratio, there are other information to cross check that a track is a good ``electron candidate'' (see also the following pages). The way a physicist uses those information is by combining all data into a single number (via a well-defined mathematical algorithm) that reflects the overall ``probability'' of a track to be an electron. This means, the larger this ``figure of merit'' is the more unlikely it becomes that you misidentify the track.
But since a real electron can have badly measured values, a cut that is too tight will diminish your sample. In the extreme you could end up with no electron at all...

In CLEO jargon, this number is called R2ELEC. It can vary from large negative numbers to large positive numbers. Reasonable values are between 0 and 10, but you normaly cut only at the lower value...
If you want to be sure you only have electron tracks in your data sample (with a small contamination), you accept only candidates that have an R2ELEC value larger than a certain ``cut value''.
The choice of this cut value is a trade off between many events in your data sample and large contamination of your data.

How to visualize data?
The above picture is a typical example, how you analyze your event data set. If you suspect a interesting physical effect shows up in a certain variable, you calculate the value of it for each track or combinations of tracks in all events you found in your detector.
Then you create a ``histogram'' of this variable. A histogram shows, how often you found this variable to be in a certain range of values (the upper and lower limit of the histogram). The picture above has 0 and 1.5 as limits. In order to see the distribution of this variable, you do this for each ``bin'' in this histogram, a number you can choose to get a good resolution but not to few entries per bin. The example above has 150 bins, so each bin has a ``width'' of 0.01 in the value of E/p. So if you found E/p to be 0.955, you increase the number in bin 96 by one, since it contains all ``entries'' where E/p was between 0.95 and 0.96. (The first bin has everything between 0.00 and 0.01)

Now try it yourself!
Now you are equipped with all what you need to actually do some parts of the work of a physicist in HEP!
We prepared an interactive Form in which you look for muons and electrons in an event data set. The results will be presented as a histogram, and each bin entry will have an ``error'' (shown as a bar). This error shows you, how far you can trust the measured numbers in each bin. In these pages this is explained a little bit more...

In this form you should try to find optimal cuts and then look into the invariant mass of the two oppositely charged muons or electrons. There is a well-known particle, that decays into muon and electron pairs. A small list of steps you should follow is written in the next section. You will find the answer, how heavy this resonance acutally is, in the next page. Try to get it right, before you read the next page

Steps to find a resonance in the next form:

1. Plot the muon pen. length for all tracks.
   Remember there are lots of tracks with the value 0. Try the default plot format, first. You will see a huge number in the first bin. To suppress this bin, just change the lower limit, to exclude 0.
2. Now you should see peaks for various penetration lengths. You can place a cut on this variable just below the first non-zero entries.
3. Check out the effect on the momentum of these tracks. You should see a difference of the momentum plot with and without that cut
4. Combine muon tracks only, now.
5. Look at the invariant mass of the muons... Can you see a``bump''?
   If not, try to setup the plot in a way that you have good resolution and you look at positive values, only...
6. Increase the resolution around the ``bump'', by adjusting the upper and lower end of your histogram... but don't go too far! What is the mass of the mother particle?
7. Now, try to find a bump at the same mass for electrons.
   Just select combinations with electrons.
8. The electron probability is better with larger numbers, the minimum requirement is normally that it is larger than 0. Add an electron ID cut.Try it with 0, first.
9. After this you can try to optimize the cut by raising it until you remove most of the background...
10. Do you see a bump? It should be at the same place, as the muon bump...
    What is it's mass?

Beginner's Guide

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