TreeLevel: Feynman Diagrams
From Lagrangian to events
Free · In‑App Purchases
Free to try for 14 days. Draw a Feynman diagram: TreeLevel checks it, derives the rules, computes the amplitude, the cross section or the lifetime. Native and instant.
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.
Ratings & Reviews
- This app hasn’t received enough ratings or reviews to display an overview.
• After a purchase — the trial or the unlock — TreeLevel opens at once, without having to leave the app and come back.
The developer, Guglielmo Pasa, indicated that the app’s privacy practices may include handling of data as described below. For more information, see the developer’s privacy policy .
Data Not Collected
The developer does not collect any data from this app.
Accessibility
The developer has not yet indicated which accessibility features this app supports. Learn More
Information
- Seller
- Guglielmo Pasa
- Size
- 9 MB
- Category
- Education
- Compatibility
Requires iPadOS 17.0 or later.
- iPad
Requires iPadOS 17.0 or later. - Mac
Requires macOS 14.0 or later. - Apple Vision
Requires visionOS 1.0 or later.
- iPad
- Languages
English and 10 more
- English, French, German, Hindi, Italian, Japanese, Korean, Portuguese, Russian, Simplified Chinese, Spanish
- Age Rating
4+
- 4+
- In-App Purchases
Yes
- Unlock TreeLevel $49.99
- 14-day Trial $0.00
- Copyright
- © 2026 Guglielmo Pasa

