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The Standard Model of Electroweak Physics

This lecture by Christopher T. Hill, head of Theoretical Physics at Fermilab, explores the Standard Model of Electroweak Physics through five essential pieces: local gauge symmetry, mass of gauge fields, chiral symmetry of massless fermions, spontaneous symmetry breaking, and the role of the Higgs boson. It discusses critical topics such as Yang-Mills theory, gauge invariance, and symmetry groups. This presentation aims to clarify complex concepts and their relevance in particle physics and cosmology, shedding light on ongoing challenges in the field.

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The Standard Model of Electroweak Physics

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  1. The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab

  2. Lecture II: Structure of the Electroweak Theory

  3. Summary of Five Easy Pieces: I. Local Gauge Symmetry II. Can a gauge field have a mass? Yes! Landau-Ginzburg Superconductor

  4. Summary of Five Easy Pieces: III. Chiral Symmetry of massless fermions IV. Spontaneous Symmetry Breaking

  5. Summary of Five Easy Pieces: III. Chiral Symmetry of massless fermions IV. Spontaneous Symmetry Breaking of chiral symmetry:

  6. “Higgs” Boson Nambu-Goldstone Boson

  7. Summary of Five Easy Pieces: IV. Gauged Spontaneously Broken Chiral Symmetry

  8. Yang-Mills Local Gauge Invariance on a Wallet Card

  9. 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?

  10. 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 1x rk = rk x 1 = rk • Each element rk has a unique inverse rk-1 such that rk-1x rk = rk x rk-1 = 1 • Group multiplication is associative

  11. 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 1:1 correspondence with the gauge fields in a Yang-Mills threory.

  12. Electroweak Theory:SU(2) X U(1) Yang-Mills Gauge Theory

  13. Electroweak Theory:SU(2) X U(1) Yang-Mills Gauge Theory SU(2) Lie Algebra

  14. Choose representations of the charges:

  15. Spontaneous Symmetry Breaking

  16. Standard Model Symmetry Breaking alignment of Higgs VEV simply specifies the charge basis (coordinate system)

  17. Standard Model Symmetry Breaking annihilates <H> corresponds to unbroken electric charge operator

  18. Higgs Kinetic term determines Gauge Mass Eigenstates

  19. Gauge Boson Mass Eigenstates

  20. Introduce the Fermions e.g., Top and Bottom

  21. Apply to muon decay W

  22. Neutrino masses

  23. Lightning Review ofRadiative Corrections to Standard Model

  24. W,Z W,Z

  25. Searching for the Higgs (Vacuum Electroweak Superconductivity) 114 GeV < mH < 260 GeV

  26. What is the Higgs Boson?

  27. (BCS Theory of a Higgs)

  28. introduce auxiliary field: “factorized interaction”

  29. Renormalize

  30. Low Energy Effective Lagrangian: renormalization group:

  31. renormalization group:

  32. Can be applied to Higgs = top anti-top boundstate

  33. Application: Top Seesaw Model

  34. The mysterious role of Scale Symmetry • We live in 1+3 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

  35. Gell-Mann and Low: Gross, Politzer and Wilczek:

  36. A Puzzle: Murray Gell-Mann lecture ca 1975 !??? QCD is scale invariant!!!???

  37. Resolution: The Scale Anomaly Origin of Mass in QCD = Quantum Mechanics

  38. A heretical Conjecture:

  39. “Predictions” of the Conjecture: We live in D=4! 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 D=4 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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