Teaching Modern Physics - QuarkNet - Fermilab

And finally, we need to remember spherical coordinates. Given a specific momentum, polar and
azimuthal angle (p, θ, φ ) (and assuming the particle is massless), we can write:
So let’s do an example.
p
p
p
E
x
y
z
= p sinθ
cosφ
= p cosθ
=
= p sinθ
sinφ
Event #1 µ1 µ2 Sum Sum 2
ϕ 108° 336°
θ 54° 107°
P Gev/c 42.3 56.0
Px Gev/c -10.575 48.923 38.348 1470.581 (GeV/c) 2
Py Gev/c 32.547 -21.782 10.765 115.875 (GeV/c) 2
Pz Gev/c 24.86 -16.373 8.491 72.089 (GeV/c) 2
E Gev 42.3 56.0 98.3 9662.89 (GeV) 2
And doing:
1
c
1
= 2
c
=
2
pc
2 2 2 2 2 2 2
m = E − c p − c p − c p
2
x y z
9662.
89
89.
5 GeV/c
−1470.
58 −115.
88 −
140
72.
09
One can do a 2D example, which basically is equivalent to setting θ = 90°.