Electroweak Theory

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Electroweak Theory

• Mr. Gabriel Pendas
• Dr. Susan Blessing

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The Standard Model

• The Standard Model describes our current view of
  particle physics incorporating the leptons,
  hadrons, and bosons (the force carriers)
• The four forces in the standard model are
• Strong force between quarks in nuclei
• Electromagnetic
• Weak
• Gravity weakest force between very large
  objects

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Electromagnetic Force

• It has an infinite range!
• Its has a relative strength to the strong force
  of 10-2 if the strong force is give a strength
  of one
• Its mediator particle is the photon
• It is whats responsible for making sure you
  dont fall through the ground

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Weak Force

• Extremely short range 10 -17 m
• Strength of about 10-5
• Its mediator particles are not known to us right
  now for the purposes of this presentation
• It is what is responsible for beta decay and
  violation of strangeness

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Quantum Electrodynamics

• Quantum theory of the interaction of charged
  particles with the electromagnetic field
• Rests on the idea that the charged particles
  interact by emitting and absorbing photons, the
  particles of light that transmit the
  electromagnetic force
• QED is both renormalizable and gauge invariant

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Renormalization

• In QED when you have a virtual photon
  electron-positron pairs may be created with as
  high energy or momentum as can be allowed
• These are quantum fluctuations because energy and
  momentum are not conserved locally
• This creates infinities when doing any type of
  physical calculation, the most well known being
  cross-sections
• You use the technique of renormalization which
  sort of sweeps these inifinities under the rug
  and is explained further in Quantum Field Theory
  A
• Seriously, its a very advanced mathematical
  technique that is beyond the scope of this talk

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Gauge Invariance

• Physics has many globally invariant quantities
  like space, time, voltage, etc
• Can quantities be locally invariant as well?
• Yes, begin with the Schrodinger equation of a
  particle moving in empty space, and introduce a
  complex phase
• You will find that the probability of finding a
  particle in a state does not change even if we
  introduce a different complex phase at different
  points in space as long as we introduce a
  modification to our vector potential known as a
  gauge transformation
• The gauge transformation requires the
  introduction of additional fields known as gauge
  fields.
• The quantization of these fields produces the
  gauge boson

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Gauge Invariance (cont.)

• In the electromagnetic case our vector potential
  can be interpreted as the electromagnetic vector
  potential which leads to the introduction of the
  magnetic and electric field
• Electromagnetic gauge invariance is a local
  symmetry called a U(1) gauge symmetry
• The gauge boson for the electromagnetic force is
  the photon

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Search for a Weak Theory

• So a quantum theory of the weak theory must be
  two things, it must be gauge invariant and its
  must be renormalizable
• Gauge invariance requires that the boson which
  carries the force be massless, which is okay in
  EM but the weak force is short range which would
  imply that its boson would have mass

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Symmetries

• Physicists were trying to come up with numerous
  models that were symmetric to explain the weak
  force, this is the method Weinberg used when he
  introduced the symmetry for his and Salaams
  electroweak theory
• If we look at leptons, there are two left-handed
  electron type leptons and one right handed
  electron type so we can start with the group U(2)
  x U(1)
• Breaking up U(2) into unimodular transformations
  and phase transformations, one could say the
  group was SU(2)x U(1)x U(1)
• But, since one of the U(1)s can be identified
  with lepton number and lepton number is conserved
  our new symmetry is SU(2) x U(1)

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Symmetry Breaking

• If this new symmetry is to uphold then all four
  particles must be massless, but the weak force is
  a short range force not an infinite one so its
  boson must have mass
• The symmetry must be broken so the Higgs
  mechanism was introduced.
• When a particle interacts with a Higgs potential
  they might begin at the origin at the maximum
  which will still conserve symmetry however the
  Higgs field pushes the particle to the minimum
  and symmetry is broken!

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Symmetry Breaking (cont.)

• In our case the SU(2)xU(1)is broken to the U(1)
  symmetry of ordinary electromagnetic gauge
  invariance.
• Since we have four parameters or rather four
  particles this symmetry breaking would allow
  three of our four particles to have mass.
• These four particles were found found to be our
  three weak bosons the, W, W- and Z, and the
  massless particle that was left over is the
  photon of the electromagnetic force
• Therefore, we had a unified theory of electroweak
  interactions

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Weak Theory (cont.)

• So we have shown how we can have massive bosons
  with gauge invariance, what about
  renormalization?
• This wasnt done till later by t Hooft and
  Veltman who in 1971 introduced dimensional
  regularization which put the second to final nail
  in the coffin for electroweak theory and won them
  the Nobel prize in 1999.
• The final nail in the coffin was made by the
  discovery of the W and Z bosons in 1983 by Carlo
  Rubbia and Simon Van der Meer which won them the
  Nobel prize in 1984.
• For their contributions in the construction of
  the electroweak theory Weinberg, Salaam, and
  Glashow won the Nobel Prize in 1979.

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