Description
TreeLevel is a workbench for tree-level particle physics: enter a theory, draw diagrams, and the app computes — Feynman rules, amplitude, |M|², cross sections, decay widths and lifetimes, energy scans.
THE THEORY FIRST
• The full Standard Model (Feynman gauge, complex CKM matrix), QED, φ⁴, minimal SU(5), and an effective hadron model of 32 particles (nucleons, hyperons, π, K, η, D, B, ρ, ω, φ, J/ψ, Υ…).
• Write your own in a readable language, in a few lines: fields, parameters, interaction Lagrangian. Feynman rules are derived, not copied.
• Import a UFO folder (FeynRules/MadGraph): the MSSM imports completely, 822 vertices, in a second.
DRAW, CHECK
• Three tools: vertex, line, select. The canvas reads the diagram along the time axis — a line running backwards in time is an antiparticle.
• The inspector tells you at once whether the diagram is consistent, and if not why, suggesting the neighbouring vertices that exist.
• Generate enumerates every tree diagram of a process; tick the ones you want to sum.
COMPUTE
• Helicity amplitudes on all cores: a σ(√s) scan over hundreds of energies takes a second.
• 2 → 2 by quadrature, exact 1 → 2 and 1 → 3, RAMBO Monte Carlo with cuts beyond.
• Partial widths, lifetimes, branching ratios; cross sections in pb; charts exported as PNG, PDF, SVG and CSV.
AND SEE THE FORMULA
• The symbolic engine computes |M|² in s, t, u: Dirac traces, polarisation and colour sums.
• Rules and amplitude are displayed in LaTeX.
• Majorana fermions and baryon-number-violating couplings handled with fermion-flow rules.
VALIDATED
The 129 Standard Model vertices agree one by one with MadGraph; muon lifetime 2.19 µs, Z, W and Higgs widths, e⁺e⁻ → W⁺W⁻ with its gauge cancellation, π⁰ → γγ, hyperon decays, σ(e⁺e⁻ → neutralinos) in the MSSM. Symbolic and numerical results agree to 10⁻⁸.
WHO IT IS FOR
The student learning Feynman rules who wants to see them act on their own diagram; the teacher preparing an exercise and its solution; the physicist who needs a tree-level order of magnitude, or wants to check the rules of a model just written.
TreeLevel computes at tree level: no loops, no parton distribution functions. Documentation, guide and tutorials on the website.
