Tools of Particle Physics

Kevin GiovanettiJames Madison University

Equations of MotionNewtonAbstract idea of Natural MotionIntroduce interaction F=maAction = Reaction {essentially energy transfer}

Energyenergy conservation

Energyenergy conservation

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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.

Nature chooses the smallest action - this is the

Principle of Least Action.

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Require Nature to be Rotationally symmetric

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 IDEAAdd a force to compensate

Get WEAK & E&M UNIFIED

Interacting fields must have 0 mass

Symmetry Breaking

HIGGS

Symmetry BreakingHIGGS

Most mass E=mc2

quark masses are few MeVProton mass is 938 MeV

Neglect Dark Matter & Dark Energy

Point particle mass, chargeSpace-time ==> separate ingredient but transformations via Lorentz transformations.Standard notions [infinite, continuous]

Basic mathematics for some underlying rules [vectors, derivatives…]Basic mechanicsRelativezed Newton’s Laws ==>energy, momentum cons…Lagrangian, Hamilton formulations are equivalent

InteractionsMaxwell’s equations ==> E, B fieldsNewtonian Gravity

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Higgs Mass

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ScintillatorPhotomultiplierSiPM

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TOFE&M showers (high speed ==> Bremstrahlung)Hadronic Showers (neutron Nucleus collision)Ionizationtrack through a low mass ==> gas + wiresPb/scintillator Sample a showerChernkov radiation

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