A differential cross section is a measure of the probability of a particle being scattered in a certain direction after interacting with another particle or system. It is typically denoted by the symbol σd and is dependent on the scattering angle and the energy of the incoming particle.
The differential cross section is calculated using the formula σd = |M|2 / (16π2 s), where |M|2 is the squared amplitude of the scattering process and s is the center-of-mass energy of the particles involved. The amplitude can be obtained from the Lagrangian of the system using Feynman diagrams.
An amplitude in particle physics is a complex number that represents the probability amplitude for a particular scattering process to occur. It is related to the probability of the process by taking the absolute value squared of the amplitude. The amplitude is obtained from the Lagrangian of the system and is used to calculate the differential cross section.
The Lagrangian is a mathematical function that describes the dynamics of a system in terms of its physical properties. In particle physics, it is used to derive the equations of motion and interactions between particles. The amplitude of a scattering process can be obtained from the Lagrangian and is then used to calculate the differential cross section.
The differential cross section is an important quantity that is used to compare theoretical predictions with experimental results in particle physics. By measuring the differential cross section, researchers can determine the likelihood of a certain scattering process occurring and compare it with the predictions of various theoretical models. This helps to validate or refine our understanding of the fundamental particles and their interactions.