Some Things to Do with Z⁰ data

I. How to distinguish Z decay into a pair of electrons from Z decay into a pair of muons.

Look at a few simulated events of each type on the event display.
(the data files are called zee.paw and zmm.paw )
How do ECAL, HCAL, and the Muon Chambers respond to electrons and to muons?

Histogram the ECAL energy and the HCAL energy for both data samples.
How does the energy response of these detectors differ for the two classes of events?

Propose a rule ( a set of cuts on energy, etc. ) to distinguish, as well as possible, between these two types of events.

Apply these cuts to your histograms and see whether the two types of events can be distinguished from one another with your cuts. Make plots with both of the files of simulated data to see the behavior of the electron sample and the muon sample.
What fraction of wanted events are accepted? (the efficiency)
What fraction of unwanted events are accepted? (quality of rejection)
( Remember that each entry in your plot is a track and that there are normally two high momentum tracks per event )

Now apply your cuts to the real data file, real.paw

The real data file has other final states in addition to the electron and muon events. Some events have a pair of tau leptons in the final state. The tau lepton decays quickly into an electron and two neutrinos, a muon and two neutrinos, a pion and a neutrino, or more complicated states involving several pions. The charged particles from tau decay will, in general, have lower momenta than for the two cases we are studying. For this reason we must also make cuts on momentum, abs(pc) , when working with the real data file.

How many e+e- events and how many mu+mu- events do you find?
What is the fraction of contamination of other event types?
Base your conclusions on histograms of variables and on displays of events.
What ratio of electron decays to muon decays did you expect? Why?
The investigation of angular distributions (next page) may suggest why the observed number of electron events is different from the observed number of muon events.

II. The Angular Distribution of the outgoing electron and muon

It is expected that the weak decay of the Z into lepton pairs gives an angular distribution proportional to 1 + cos²(theta).
Do your plots for the muon and for the electron appear consistent with this shape?
What might account for any large differences that you observe?
Your histograms can be fitted to simple functions.
Why is a second order polynomial a good choice?
How good is the agreement with expectations?

Plot the cos(theta) distribution for positive and negative outgoing particles separately. (The sign of pc is the charge.) Do this for the electron sample and also for the muon sample.
How do the cos(theta) distributions for electrons and positrons differ?
How is the muon case different?
What differences in the fundamental reactions account for this difference?
Hint: Think about how the initial electron and positron are transformed into the outgoing (final state) particles.
Is there a way that outgoing electrons can be produced which is not available for muons?