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Electroweak Theory and the Higgs

The electroweak theory relates chiral charges, particle masses, and weak currents through one gauge–Higgs Lagrangian. This chapter follows those relations from the Higgs vacuum orbit to low-energy weak interactions, high-energy longitudinal scattering, and renormalized Higgs predictions.

Enter this chapter

Section titled “Enter this chapter”

Begin with Electroweak Gauge and Matter Structure to specify the representations and hypercharges before deriving masses.

Topics

Section titled “Topics”
  1. Electroweak Gauge and Matter Structure — Sets the chiral representations and charge assignments.
  2. The Higgs Doublet and Electroweak Symmetry Breaking — Finds the Higgs vacuum orbit and physical fluctuations.
  3. Gauge-Boson Masses and Electroweak Mixing — Derives charged and neutral mass eigenstates.
  4. Charged and Neutral Weak Currents — Constructs electromagnetic, charged, and neutral currents.
  5. Yukawa Couplings and Fermion Masses — Relates Yukawa matrices to masses and mixing.
  6. Higgs Self-Interactions and the Scalar Potential — Determines scalar self-couplings from the potential.
  7. The Fermi Limit of Weak Interactions — Matches heavy-vector exchange onto four-fermion interactions.
  8. Longitudinal Vector Bosons and the Equivalence Theorem — Explains cancellations in longitudinal-vector scattering.
  9. Electroweak Renormalization and Input Schemes — Translates measured inputs into renormalized parameters.
  10. Higgs Interactions, Production, Decay, and Pole Observables — Connects Higgs amplitudes to pole and fiducial observables.

How the ideas fit together

Section titled “How the ideas fit together”

The neutral mass matrix leaves a massless photon because the chosen vacuum preserves electric charge. The same covariant Higgs kinetic term fixes vector masses and Higgs couplings, which participate in the high-energy cancellations of longitudinal scattering. These are linked consequences of the Lagrangian, not independent adjustable relations. Beyond tree level, the parameters must be defined through a consistent input and renormalization scheme before confronting measurements; tree identities cannot indiscriminately combine differently defined experimental inputs. Schwartz 2014, §§ 29.1–29.4.

Where to go next

Section titled “Where to go next”

Continue to Quark Flavor and CP to identify flavor breaking through the Yukawa matrices.

References

Section titled “References”
  • Schwartz, Matthew D. Quantum Field Theory and the Standard Model. Cambridge University Press, 2014, §§29.1–29.4, pp. 584–604. DOI.