Basic Ideas for Particle Properties

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Basic Ideas for Particle Properties

• Review of Modern Physics

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Spin and Angular Momentum

• There are three angular momenta.
• Orbital (normal angular momentum)
• Spin (intrinsic angular momentum)
• Total (orbital spin)

Orbital angular momentum
(Classical)
(Quantum)
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• Quantum mechanical properties
• Eigenvalue equations
• Commutation relations

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• The eigenvalues are quantized.
• The appropriate unit for spin is ?.
• The only quantities are
• 0?, 1/2?, 1?, 3/2?, 2?, 5/2?,
• There are only 2J1 possible values.

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Fermions and Bosons
Example J Quantum statistics Many body wave function
Fermions Nucleons, electron, quarks, etc. Half-integer Only one fermion per state (Paulis exclusion principle Anti-symmetric
Bosons Photon, W?, Z, gluon, ?, etc. Integer Any number of identical particles capable of occupying the same state Symmetric
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• The wave functions for two-body system
• What are the practical wave functions?

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Magnetic Dipole Moment (Magneton)

• Particles having spin can get the magnetic
  energy.
• The constant is called magnetic dipole moment, ?.
• The magnetic moment is dependent on the spin,
  mass and charge.
• The intrinsic constant in the ? is called
  magneton, ?0e?/2mc.

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Mass Measurements 1

• Mass spectroscopy
• This utilizes the centripetal and Lorentz forces
  to find out the particle mass.
• This is useful for nuclei and atoms, but it is
  impossible for most particles.
• The initial velocity of particle produced by
  reaction cannot be known exactly.
• Neutral charges are not deflected by a magnetic
  field.

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Mass Measurements 2

• Scintillation counter
• This utilizes two scintillation counters to
  measure the velocity of a particle.
• Magnet selects particles with momentum.
• Two counters and oscilloscope measure the
  distance and time to give the velocity.
• The mass is the above momentum divided by the
  velocity.
• This method fails if the particle is neutral and
  the life time is very short.

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Mass Measurements 3

• Invariant mass plot
• This utilizes the invariant mass of particles.
• Lets suppose you measure the mass of neutral
  rho, ?0 (the life time is 6?10-24 sec). It
  decays into ? and ?-.

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Mass Measurements 3 (cont.)

• Invariant mass for the pions
• Energy momentum for rho
• Invariant mass for the rho

Namely, m? m12.
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Mass Measurement 3 (cont.)

• The invariant mass plot is capable of measuring
  mass of very-short-life-time particles.
• Not only elementary particles, but it is used for
  nuclear physics region. (e.g. 8Be)

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Particles and the Related Interactions

• Forces particle interactions
• Remember four forces.
• But those are pure form of interaction.
• In practice, the interactions between particles
  are mixed.

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Particles Type Weak Electromagnetic Hadronic
Photon Gauge boson No Yes No
W? Z0 Gauge boson Yes Yes No
Gluon Gauge boson No No Yes
Leptons
Neutrino Fermion Yes No No
Electron Fermion Yes Yes No
Muon Fermion Yes Yes No
Hadrons
Mesons Bosons Yes Yes Yes
Baryons Fermions Yes Yes Yes
Quarks Fermions Yes Yes Yes
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Decays

• Phenomenological point of view
• The number decaying in a time dt ?
• The number of particles present at time t ?

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Decays (cont.)

• Write it in terms of the time-dependent wave
  function.
• But it doesnt work!
• So introduce the imaginary part. ?
• Then, that makes sense.

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Decay (cont.)

• However, what is the ?? Is there any physical
  meaning?
• Now lets transform it into the energy space.
• The wave function will be expressed in terms of
  energy instead of time. The modulus square of
  the function will be the probability density.
• It turns out that the ? is the uncertainty of
  energy at a decaying state.
• In other words, the ? is the full width at half
  maximum.

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Decays (cont.)

• Possibility of the decay properties and its
  classification
• There is no simple connection between decay
  appears and other particle properties
• Decay energies differ with hadronic,
  electromagnetic and weak forces.
• The output from interaction and the decay time
  are not related. (It involves a deeper rule.)