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Tools of Particle Physics

Explore the fundamental principles of particle physics, focusing on the equations of motion, energy conservation, and the symmetry underlying natural phenomena. Discover the impact of Newton's laws and the principle of least action on the behavior of particles, as well as the significance of SU(2) symmetry in particle interactions and mass generation via Higgs mechanisms. This comprehensive overview also discusses the application of Lagrangian and Hamiltonian formulations, showcasing the connections between classical mechanics and modern physics.

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Tools of Particle Physics

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  1. Tools of Particle Physics • Kevin Giovanetti • James Madison University

  2. Equations of Motion Newton Abstract idea of Natural Motion Introduce interaction F=ma Action = Reaction {essentially energy transfer}

  3. Energy energy conservation

  4. ??? Energy energy conservation ???

  5. SYMMETRY

  6. a The Lagrangian L can be calculated at several instants of time t, and a graph of L against t can be drawn. The area under the curve is the action. Any different path between the initial and final positions leads to a larger action than that chosen by nature. Nature chooses the smallest action - this is the Principle of Least Action.

  7. Require Nature to be Rotationally symmetric

  8. Require Nature to be Rotationally symmetric Equation of motion must be invariant under rotation Energy Conservation Time translation

  9. Add a new symmetry SU(2) Proton same as Neutron Interchange proton with a neutron and nothing changes Throw away the charge

  10. Strange IDEA Rotate by different amounts at different locations Add a force to compensate

  11. Strange IDEA Take my internal SU(2) symmetry and require it to be valid even if I vary the amount as a function of x Add a force to compensate Get WEAK & E&M UNIFIED

  12. Take my internal SU(2) symmetry and require it to be valid even if I vary the amount as a function of x Strange IDEA Add a force to compensate Get WEAK & E&M UNIFIED Interacting fields must have 0 mass

  13. Symmetry Breaking HIGGS

  14. Symmetry Breaking HIGGS Most mass E=mc2 quark masses are few MeV Proton mass is 938 MeV Neglect Dark Matter & Dark Energy

  15. Higgs Mass Point particle mass, charge Space-time ==> separate ingredient but transformations via Lorentz transformations. Standard notions [infinite, continuous] Basic mathematics for some underlying rules [vectors, derivatives…] Basic mechanics Relativezed Newton’s Laws ==>energy, momentum cons… Lagrangian, Hamilton formulations are equivalent Interactions Maxwell’s equations ==> E, B fields Newtonian Gravity

  16. Scintillator Photomultiplier SiPM

  17. TOF E&M showers (high speed ==> Bremstrahlung) Hadronic Showers (neutron Nucleus collision) Ionization track through a low mass ==> gas + wires Pb/scintillator Sample a shower Chernkov radiation

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