Download 03 Homework File

Elementary Particle Physics
SPA6306
Exercise Sheet 3
To be handed in: Tuesday 31st January
Answer scripts should be returned in the box provided on the first floor in the Physics Building (G.O.
Jones) by 4pm on the day quoted above.
Course title, week number and student’s name should appear on every sheet of the worked exercises,
which should be securely bound together.
Marked exercises will be returned in the box provided on the first floor the following week. The
number of marks for each part is shown in [].
Remember to use symbolic calculations as much as possible and substitute the numerical values only
at the very last step.
Dr M.Bona
1. The PEP accelerator used to collide 9 GeV electrons with 3.1 GeV positrons head on to produce
collision in the BaBar experiment. Calculate the centre of mass energy of this system and the
Lorentz boost βγ in case a ϒ(4S) resonance with a mass of 10.578 GeV is produced in the
collision.
[ 6]
2. It is proposed to use the LHC to collide 7 TeV protons with 50 GeV electrons, in the so-called
LHeC. Calculate the centre of mass energy of this system.
[ 3]
What electron energy would be required to obtain the same centre of mass energy with electrons
on stationary protons?
[ 3]
3. Particle A (energy E) hits particle B (at rest) producing particles C1 , C2 , C3 . . . Calculate the
threshold (i.e. minimum E) for this reaction, in terms of the various particle masses mA , mB ,
mC1 , mC2 , mC3 ,. . . .
[ 9]
Apply the formula derived above to obtain the threshold energy for the process π− + p →
p + p̄ + n, where the initial state corresponds to a beam of π− hitting a target of protons. Use
mπ− = 140 MeV, m p = 938 MeV, mn = 940 MeV.
[ 3]