Tools of Particle Physics Kevin Giovanetti James Madison University

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

Energy energy conservation

Energy energy conservation ???

SYMMETRY

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.action Nature chooses the smallest action - this is the Principle of Least Action.ple of Least Action. a

Require Nature to be Rotationally symmetric

Equation of motion must be invariant under rotation Time translation Energy Conservation

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

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

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

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

Symmetry Breaking HIGGS

Symmetry Breaking HIGGS Most mass E=mc 2 quark masses are few MeV Proton mass is 938 MeV Neglect Dark Matter & Dark Energy

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 Higgs Mass

Scintillator Photomultiplier SiPM

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