Question 1 :
Make invariant mass plot (100 bins between 0 and 200 GeV)
for every step of cuts.
You should get 6 plots in total including one before
any cuts applied.
cos_theta*
As stated in the paper, cos_theta* is determined
in the Collis-Soper frame (Phys. Rev. D 16, 2219
(1977)).
please read this paper.
Divide the samle using invariant mass.
sample #1 (Z region) : 75 < M(e,e) < 105 GeV
sample #2 (High mass region) : M(e,e) > 105 GeV
Question 2 :
Fill the following table
Z pole region
High mass region
# of total events
# of forward events
# of backward events
Question 3 :
Make Figure 1(CDF paper)
Question 4 :
Make Figure 2(CDF paper)
Question 5 :
Fit the previous two plots (Figure 2) with
A (1 + cos^2_theta*) + B cos_theta*, and
get the value A.
cos_theta* definition
cos_theta* = 2 (
l1+ l2-
-
l1- l2+)
/ ( M x sqrt(M*M + Pt*Pt) )
where
M = the mass of electron-position pair
Pt = transverse momentum of electron-positron pair
l1 = the four-momentum of the electron
l2 = the four-momentum of the positron
l+ = (l^0 + l^3) / sqrt(2)
l- = (l^0 - l^3) / sqrt(2)
Thus,
l1+ = l+ for electron
l1- = l- for electron
l2+ = l+ for positron
l2- = l- for positron
INCLUDE FORWARD ELECTRONS (if you have time)
Because high |cos_theta*| values mainly come from
electrons in the forward region, and our selection above
is only in the central region, cos_theta* plot from above
dominates around 0.
Selection
one of the two electrons should be in the central
(use cuts above) to remove background.
the other is in the forward region
(no tracking detector is covered, thus
no Pt cut nor E/p cut can be applied)