Chapter 1 - Kinematics and invariants

Abstract

The chapter analyzes different aspects of kinematics and invariants in heavy-ion collisions. Some kinematic variables that are useful to describe a particle's position and momentum are introduced in the chapter. The collision of two particles at ultrarelativistic energies is also analyzed. The chapter describes vertical axis as the time direction where the lower half plane is before the collision while the upper half plane is after the collision. The particle production in a real collision occurs in the upper half plane within the light cone. The invariants, based on four-momenta, are used to describe interactions among particles and appear in calculations of the scattering cross sections. The invariants are the squares of sums or differences of four-momenta. One way to characterize the missing energy was to observe a high energy electron or a muon track with no opposing track to balance it and conserve energy and momentum in decays. In deep inelastic scattering of an electron off a proton, the interaction is characterized by the change in the energy of the electron after it scatters and the angle through which it scatters.