Examples Gallery

examples/ contains full worked models, used as both documentation and manual smoke tests. Each file is runnable end to end (python examples/<name>.py) and doubles as the “how do I actually write this in feynlag” reference for the corresponding physics.

sm_scalar_gauge.py — the complete Standard Model

Higgs sector + electroweak gauge (SU(2)_L × U(1)_Y) + one lepton generation

• a full 3-generation quark/QCD sector (SU(2) doublet QL, SU(3)_c-triplet singlets uR/dR, flavor-generic Yukawas — no CKM diagonalization, since CKM mixing is orthogonal to SU(3) vertex dynamics). Exercises every stage of the pipeline: gauge invariance, EWSB, tadpoles, the Higgs/Goldstone/gauge mass matrices, the Weinberg rotation, fermion gauge currents and Yukawa mass matrices via the bilinear track, and both LaTeX and UFO export (including real SU(3) color-tensor strings for qqg/ggg/gggg).

sm_vll.py — vector-like lepton doublet

Adds a vector-like SU(2) doublet Ψ = (N, E) with a bare Dirac mass to the lepton sector. Demonstrates biunitary 2×2 diagonalization (diagonalize_svd_2x2) of the resulting charged-lepton mass matrix, fermion mass-basis rotations through Indexed fields, and the physics signature of doublet VLL mixing: a right-handed-only Z FCNC, an h-coupling sum rule, and the correct SM-decoupling limit as M → ∞. See Tutorials for the step-by-step notebook.

sm_u1x.py — SM × U(1)_X with a Z′

Extends the SM by a second abelian factor with symbolic charge assignment X = a·Y + b·(B−L). An X-charged Higgs singlet VEV drives tree-level Z–Z′ mixing through two chained 2×2 rotations (Weinberg, then Z–Z′). Also adds 3 right-handed neutrinos with a Dirac Yukawa via H̃. Demonstrates keeping physics symbolic in an extra charge parameter, Goldstone counting across two broken U(1)s, and multi-stage rotation chaining (Model.physical_lagrangian applies registered rotations in registration order). No UFO export — UFO’s particle table calls float() on charges, incompatible with the symbolic a/b.

thdm.py — softly-broken Z₂ 2HDM

The scalar sector of a two-Higgs-doublet model with a softly-broken Z₂ symmetry. Demonstrates the analytic 2×2 orthogonal diagonalization (diagonalize_orthogonal_2x2) and the α mixing angle, cross-checked against the standard Gunion–Haber/Branco expressions.

thdm_s3.py — 3HDM with an S₃ flavor symmetry

Three Higgs doublets, (H1, H2) forming an S₃ doublet and HS a singlet. The potential is built entirely from the library’s own S₃ Clebsch–Gordan products (S3.doublet_product) rather than hand-written invariants — a stress test of the discrete-symmetry machinery. The tadpole system is deliberately over-constrained and forces a specific vacuum alignment (v₁ = √3 v₂ in the literature basis).

Each model is described algorithmically, stage by stage, in the 1. The Pipeline; the manual cites which pinned test in tests/ fixes each physical result these examples produce.