TreeLevel: Feynman Diagrams

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. GENERATE EVENTS • Thousands of unweighted events of the process, drawn in phase space: one event at a time with its projections and particle table, histograms with error bars, a selection with its efficiency and the cross section it leaves. • With the Pythia 8 module: showered and hadronised events, and the Machine source — two beams, an energy, what the experiment records, and the cross section measured by counting. • A filter steps only through the events that meet your criteria — hard process, leptons, photons, jets, missing energy, pair mass — and the histograms follow it. • Export and import in Les Houches and HepMC3. SIMULATE A DETECTOR • Coaxial cylinders, calorimeters, muon chambers, solenoidal field; efficiencies, thresholds, anti-kT jets, missing transverse energy. • The x–y and z–ρ cross-sections of the event, the reconstructed objects, and the detector's performance over the whole sample. • The enlarged detector view: zoom up to ten quadrillion times, down to the interaction zone, scale bar, trajectories starting from their real vertices. PYTHIA 8 ON IPAD A 14 MB module downloaded from within the app (55 MB more for hadrons): Pythia 8.318 in WebAssembly, free software (GPL) separate from TreeLevel, running on the iPad without sending anything. Without it, events stay at parton level, and a HepMC3 file showered elsewhere can be imported. 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. Documentation, guide and tutorials on the website. FREE TRIAL TreeLevel is free to download and to try for 14 days, everything included. Then a single purchase unlocks it with no time limit, on Mac and iPad, shared with your family. Those who bought it before version 1.5 keep everything.