Basics

Simple kinematics

1. Relativistic kinematics and four-momentum conservation
   
2. Orientation with respect to an axis (the beam axis)
   
3. Mandelstam variables
   
4. Hadronic collisions
   
5. Problems
   
   1. Convince yourself that the equation correctly describes boosts along the z-axis. Hint: The energy and momentum along this axis, seen from an observer with velocity v are given by with
   2. Prove that is correct.
   3. What would an u-channel process look like in a scetch?
   4. Consider 2→2 processes on the parton level with incoming hadrons.
      • Express the partonic scattering angle (the angle between an incoming and an outgoing particle) θ in the c.m. (laboratory) frame through the rapidites of the two outgoing particles.
      • Calculate do the Mandelstam variables t and u for this process in terms of rapidities and transverse momenta of the outgoing particles.