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.