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0 mA. Each beam consisted of four equally spaced bunches of electrons/positrons. 8 × 104 μm2 . Calculate the instantaneous luminosity on the assumption that the beams collided head-on. 2 Underlying concepts Much of particle physics is concerned with the high-energy interactions of relativistic particles. Therefore the calculation of interaction and decay rates requires a relativistic formulation of quantum mechanics. Relativistic quantum mechanics (RQM) is founded on the two pillars of “modern” physics, Einstein’s theory of special relativity and the wave mechanics developed in the early part of the twentieth century.
Electrons are identified as charged-particle tracks that are associated with an electromagnetic shower in the ECAL. Neutral hadrons will usually interact in the HCAL and charged hadrons are identified as charged-particle tracks associated with a small energy deposit in the ECAL (from ionisation energy loss) and a large energy deposition in the HCAL. Finally, muons can be identified as charged-particle tracks associated with small energy depositions in both the ECAL and HCAL and signals in the muon detectors on the outside of the detector system.
2 Probability density and probability current The physical interpretation of the wavefunction ψ(x, t) is that ψ∗ ψ d3 x is the probability of finding the particle represented by the wavefunction in the volume element d3 x. This is equivalent to identifying the probability density ρ(x, t) as ρ(x, t) = ψ∗ (x, t) ψ(x, t). Assuming the particle does not decay or interact, its associated total probability will be constant. This conservation of probability can be expressed in terms of a continuity equation by defining the probability current density (sometimes referred to as the probability flux density), denoted j(x, t), such that the flux of probability across an elemental surface dS is given by j · dS.