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Standard Model Assembly and Consistency

This chapter assembles the Standard Model as one quantum field theory with explicitly checkable consistency conditions. It connects the field and parameter map to the faithful gauge-group quotient, perturbative and global anomaly tests, accidental selection rules, coupled running, vacuum criteria, and controlled SMEFT or HEFT deformations. The central discipline is to keep those checks distinct: passing one never substitutes for the others.

Enter this chapter

Section titled “Enter this chapter”

Begin with The Standard Model Lagrangian and Parameter Map to assemble the fields, interactions, and independent parameters of the model.

Topics

Section titled “Topics”
  1. The Standard Model Lagrangian and Parameter Map — Collects the minimal Lagrangian and its parameter definitions.
  2. The Global Form of the Standard Model Gauge Group — Distinguishes the gauge Lie algebra from allowed global groups.
  3. Gauge-Anomaly Cancellation and Quantum Consistency — Checks perturbative and global gauge anomalies.
  4. Accidental Symmetries and Their Violations — Identifies selection rules that fail beyond the renormalizable action.
  5. Standard Model Running, Effective Potential, and Vacuum-Stability Criteria — Connects running and matching to conditional vacuum statements.
  6. SMEFT and HEFT in Standard Model Observables — Maps linear and nonlinear electroweak EFTs into observables.

How the ideas fit together

Section titled “How the ideas fit together”

A local Lagrangian fixes the Lie algebra and matter couplings but does not always fix the global gauge group. Allowed line operators and bundles can distinguish theories with the same perturbative vertices. Similarly, cancellation of local anomaly sums does not replace a global consistency check. These distinctions matter before interpreting effective operators or running couplings: two descriptions must agree on the physical theory being compared. Neither anomaly cancellation nor perturbative running alone determines vacuum stability or a complete ultraviolet theory. Aharony, Seiberg, and Tachikawa 2013, §§ 1–2.

Where to go next

Section titled “Where to go next”

Continue to Precision Standard Model: Observables and Inference to separate physical amplitude singularities from conventions used to report resonance measurements.

References

Section titled “References”
  • Aharony, Ofer, Nathan Seiberg, and Yuji Tachikawa. “Reading between the Lines of Four-Dimensional Gauge Theories.” Journal of High Energy Physics 2013, no. 8 (2013): 115, §§1–2. DOI.