At the Stanford Linear Accelerator, electrons and positrons collide together at very high energies to create other elementary particles. Suppose an electron and a positron, each with rest energies of 0.511 MeV, collide to create a proton (rest energy 938 MeV), an electrically neutral kaon (498 MeV), and a negatively charged sigma baryon (1197 MeV). The reaction can be written as:
e+ + e− → p+ + K0 + Σ−
(a) What is the minimum kinetic energy the electron and positron must have to make this reaction go? Assume they each have the same energy.
(b) The sigma can decay in the reaction Σ− → n + π− with rest energies of 940 MeV (neutron) and 140 MeV (pion). What is the kinetic energy of each decay particle if the sigma decays at rest?