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

Lecture II: Structure of the Electroweak Theory

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

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

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

Nambu-Goldstone Boson “Higgs” Boson

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

Yang-Mills Local Gauge Invariance on a Wallet Card

Standard Electroweak Model Weak Force: u d e nu W Based upon a nonabelian gauge symmetry: Yang-Mills Field Theory Higgs Field? SU(2)xU(1) is “Spontaneously broken Symmetry” SU(2) x U(1)

Symmetry Groups A group G is a collection of elements { r j } G has a “multiplication” operation: r j x r k = r k where r k is in G There is a unique identity in G, 1, such that 1 x r k = r k x 1 = r k Each element r k has a unique inverse r k -1 such that r k -1 x r k = r k x r k -1 = 1 Group multiplication is associative

Continuous Symmetry Groups Cartan 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: G 2, F 4, E 6, E 7, E 8 Continuous rotations are exponentiated angles x generators. Generators form a Lie Algebra, e.g. SU(N) has N 2 -1 generators. Generators are in 1:1 correspondence with the gauge fields in a Yang-Mills threory.

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

SU(2) Lie Algebra

Choose representations of the charges:

Spontaneous Symmetry Breaking

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

Standard Model Symmetry Breaking annihilates corresponds to unbroken electric charge operator

Higgs Kinetic term determines Gauge Mass Eigenstates

Gauge Boson Mass Eigenstates

Introduce the Fermions e.g., Top and Bottom

W Apply to muon decay

Neutrino masses

Lightning Review of Radiative Corrections to Standard Model

W,Z

114 GeV < m H < 260 GeV Searching for the Higgs (Vacuum Electroweak Superconductivity)

What is the Higgs Boson?

(BCS Theory of a Higgs)

introduce auxiliary field: “factorized interaction”

Renormalize

Low Energy Effective Lagrangian: renormalization group:

Can be applied to Higgs = top anti-top boundstate

Application: Top Seesaw Model

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

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

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

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

A heretical Conjecture :

On naturalness in the standard model. William A. Bardeen (Fermilab). FERMILAB-CONF T, Aug pp. William A. BardeenFermilab Conjecture on the physical implications of the scale anomaly. Christopher T. Hill (Fermilab). hep-th/ Christopher T. HillFermilab 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? “Predictions” of the Conjecture:

Symmetry Principles Define Modern Physics

Symmetry BeautyPhysics