# Fundamental Particles and Interactions – Problem Sheet 1

```Fundamental Particles and Interactions – Problem Sheet 1
(due by 4pm, Saturday 29 January)
(1)
In natural units, the cross-section for the process e+e-  +- is given by:
 (e  e       ) 
4  2
3 E2
cm
where Ecm is the center-of-mass energy of the system. For two colliding electron
and positron beams of 5 GeV each, obtain the value of the cross section in nb.
(2)
A pion of rest mass 140 MeV/c decays into a muons of mass 106 MeV and a
massless neutrino:
+  +

Compute the energy of the muon in the pion rest frame
(3)
Taking into account that the mean lifetime of the K+ meson is 1,237x10-8 s, fill in
the last column of the following table and explain how your results were obtained.
(4)
In the HERA e-p collider, an 820 GeV proton beam and a 30 GeV electron beam
are circulated in two separate storage rings. Superconducting bending magnets,
providing a peak magnetic field of 4,6 T, are used to maintain the protons on their
orbits in the proton ring. Taking into account the fact that only 60% of the
circumference is occupied by bending magnets m estimate the circumference of
the proton ring.
```