The Standard Model of Electroweak Physics

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The Standard Model of Electroweak Physics
Christopher T. Hill Head of Theoretical
Physics Fermilab
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Lecture II Structure of the Electroweak Theory
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Summary of Five Easy Pieces
I. Local Gauge Symmetry
II. Can a gauge field have a mass? Yes!
Landau-Ginzburg Superconductor
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Summary of Five Easy Pieces
III. Chiral Symmetry of massless fermions
IV. Spontaneous Symmetry Breaking
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Summary of Five Easy Pieces
III. Chiral Symmetry of massless fermions
IV. Spontaneous Symmetry Breaking
of chiral symmetry
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Higgs Boson
Nambu-Goldstone Boson
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Summary of Five Easy Pieces
IV. Gauged Spontaneously Broken Chiral Symmetry
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Yang-Mills Local Gauge Invariance on a Wallet Card
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Standard Electroweak Model
SU(2) x U(1)

• Weak Force

Based upon a nonabelian gauge symmetry
Yang-Mills Field Theory
d
nu
W
SU(2)xU(1) is Spontaneously broken Symmetry
e
u
Higgs Field?
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Symmetry Groups

• A group G is a collection of elements rj
• G has a multiplication operation rj x rk rk
  where rk is in G
• There is a unique identity in G, 1, such that 1
  x rk rk x 1 rk
• Each element rk has a unique inverse rk-1 such
  that rk-1 x rk rk x rk-1 1
• Group multiplication is associative

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Continuous Symmetry GroupsCartan Classification

• Spheres in N dimensions O(2),
  O(3), ..., SO(N)
• Complex Spheres in N dimensions U(1), SU(2),
  ..., SU(N)
• N dimensional phase space Sp(2N)
• Exceptional Groups
  G2, F4, E6, E7, E8

Continuous rotations are exponentiated angles x
generators. Generators form a Lie Algebra, e.g.
SU(N) has N2-1 generators.
Generators are in 11 correspondence with the
gauge fields in a Yang-Mills threory.
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Electroweak TheorySU(2) X U(1) Yang-Mills Gauge
Theory
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Electroweak TheorySU(2) X U(1) Yang-Mills Gauge
Theory
SU(2) Lie Algebra
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Choose representations of the charges
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Spontaneous Symmetry Breaking
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Standard Model Symmetry Breaking
alignment of Higgs VEV simply specifies the
charge basis (coordinate system)
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Standard Model Symmetry Breaking
annihilates ltHgt corresponds to unbroken
electric charge operator
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Higgs Kinetic term determines Gauge Mass
Eigenstates
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Gauge Boson Mass Eigenstates
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Introduce the Fermions
e.g., Top and Bottom
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Apply to muon decay

W
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Neutrino masses
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Lightning Review ofRadiative Corrections to
Standard Model
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W,Z
W,Z
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Searching for the Higgs (Vacuum Electroweak
Superconductivity)
114 GeV lt mH lt 260 GeV
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What is the Higgs Boson?
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(BCS Theory of a Higgs)
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introduce auxiliary field
factorized interaction
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Renormalize
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Low Energy Effective Lagrangian
renormalization group
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renormalization group
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Can be applied to Higgs top anti-top boundstate
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Application Top Seesaw Model
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The mysterious role of Scale Symmetry

• We live in 13 dimensions
• The big cosmological constant conundrum
• The Higgs Boson mass scale
• QCD solves its own problem of hierarchy
• New Strong Dynamics?

Origin of Mass in QCD
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Gell-Mann and Low
Gross, Politzer and Wilczek
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A Puzzle Murray Gell-Mann lecture ca 1975
!???
QCD is scale invariant!!!???
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Resolution The Scale Anomaly
Origin of Mass in QCD Quantum Mechanics
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A heretical Conjecture
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Predictions of the Conjecture
We live in D4!
Cosmological constant is zero in classical limit
QCD scale is generated in this way Hierarchy is
naturally generated
Testable in the Weak Interactions?
Weyl Gravity in D4 is QCD-like
Is the Higgs technically natural?
On naturalness in the standard model.William A.
Bardeen (Fermilab) . FERMILAB-CONF-95-391-T, Aug
1995. 5pp.
Conjecture on the physical implications of the
scale anomaly.Christopher T. Hill (Fermilab) .
hep-th/0510177
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Symmetry Principles Define Modern Physics
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Symmetry
Beauty
Physics