Homework # 3

Due April 14th, 1999

Compute and plot the districbutions for the following kinematic properties of the Z and W events recorderd by the D0 detector at Fermilab :

Invariant Mass "M" of the two electrons in Z events

where M = sqrt(2*E1*E2* (1-Cos(alpha)) ) and

cos(alpha) = cos(theta1)*cos(theta2) +sin(theta1)*sin(theta2)*cos(phi1-phi2)

Transverse Mass "MT" for the electron and neutrino in W events

MT = sqrt(2*pT(e)*mpT* (1-cos(phi(e)-phi(v)) )

where pT(e) = E*sin(theta) = transverse momentum of electrons in W events (assuming m<<E)
mpT = transverse momentum of neutrino in W events = missing transverse momentum in W events
phi(e)= phi of the electrons in W events
phi(v)= phi of the missing momentum in W events

Energy of electrons in Z events (two entries for each event)
Energy of electrons in W events
Transverse momentum of electrons in Z events (two entries fo each event)
Transverse momentum of electrons in W events
Transverse component of missing momentum in Z events
Transverse component of missing momentum in W events
phi of the electrons in Z events
phi of the electrons in W events
eta of electrons in Z events
eta of electrons in W events

where eta = -log(tan(theta/2))

For each of the above distribution, compare the shapes for W and Z events. Note the differences and explain the reason for the differences if any.

Note :

Assume h=c=1, while computing the variables

Clearly specify the units for all the plots

There are two files with datasets.

A) Z -> two electrons (click here to access the datafile)
There are 2215 events in this dataset.
This file contains 8 columns of data for each event, which are

Energy of electron 1
Energy of electron 2
Polar angle (theta) of electron 1
Polar angle (theta) of electron 2
Azimuthal angle (phi) of electron 1
Azimuthal angle (phi) of electron 2
Transverse component of missing momentum
Phi angle of missing momentum

AND

B) W -> electron+neutrino (click here to access the datafile)
There are 2373 events in this dataset.
This file contains 5 columns of data for each event, which are

Energy of electron
Polar angle (theta) of electron
Azimuthal angle (phi) of electron
Transverse component of missing momentum
Phi angle of missing momentum

Note : In the above files, Energy, momentum are in GeV, angles are in radians.

Meenakshi Narain <narain@buphy.bu.edu>

Last modified: Fri Apr 2 14:00:20 EST 1999