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The examples

File › Open an exampleLoad an example gives eighteentwenty-sixtwenty-seven documents ready to compute. They are not screenshots: each one opens, recomputes and can be edited. The values below are those the engine returns on the document as it ships. On the iPad the list shows only twenty of them: examples 21 and 26, the Pythia ones, join once its module is installed; those of Herwig, Sherpa, WHIZARD and CalcHEP (22 to 25) stay on the Mac and the PC. On the iPad the list shows only twenty of them: examples 21, 26 and 27, the Pythia ones, join once its module is installed; those of Herwig, Sherpa, WHIZARD and CalcHEP (22 to 25) stay on the Mac and the PC.

They are read-only: at the first edit, macOS offers to save a copy: save a copy with File › Save as… before touching one; on the iPad, they load from the Load an example button in the toolbar, which copies their content into the open document. For a guided walk rather than a catalogue, see the tutorials.

The Standard Model

Example	What it shows	What it gives
01 — $e^+e^-\to\mu^+\mu^-$ , the Z peak	Four diagrams summed, $\gamma$ and $Z$ together, at $\sqrt s = M_Z$ . The energy plot draws the resonance, and the Analysis tab shows the interference.	$\sigma = 1.98\ \mathrm{nb}$ at 91.19 GeV
02 — Muon decay	A three-body decay, integrated by Monte Carlo over phase space. It is the measurement that fixes $G_F$ , and the tree-level computation recovers it: the gap to the measured 2.197 µs is the radiative corrections, which are not there.	$\tau = 2.19\ \mu\mathrm s$
03 — $e^+e^-\to W^+W^-$	Gauge cancellation: taken alone, the $\gamma$ , $Z$ and $\nu$ diagrams grow with energy; their sum does not. Untick one in the Diagrams box to watch the sum diverge.	$\sigma = 19.2\ \mathrm{pb}$ at 200 GeV
06 — $Z\to b\bar b$	A partial width and its branching ratio, from the model's total width.	$\Gamma = 363\ \mathrm{MeV}$ , BR $14.5\ \%$
07 — $h\to\tau^+\tau^-$	The Higgs coupling is proportional to the mass: the same document with a muon gives a number three hundred times smaller.	$\Gamma = 0.259\ \mathrm{MeV}$ , BR $6.4\ \%$
08 — $u\bar u\to t\bar t$	QCD: five diagrams, with the colour sum and the average over the initial state done by the engine.	$\sigma = 5.09\ \mathrm{pb}$ at 1 TeV

QED alone

Two textbook processes, in the QED model — four fields, one vertex. This is where what the engine does is easiest to read, because there is nothing else to read.

Example	What it shows
04 — Bhabha	$e^+e^-\to e^+e^-$ : $s$ channel and $t$ channel, and their interference. Its total cross section does not exist — the photon pole in the forward direction makes it diverge —, which is exactly the lesson: one looks at dσ/dΩ, or at $\sigma$ under an angular cut.
05 — Compton	$e^-\gamma\to e^-\gamma$ : a photon in the initial state, a sum over its polarisations, and the Klein–Nishina formula recovered.

Hadrons

The Hadrons model treats hadrons as point-like: no form factors, hence nothing above momentum transfers of the order of half a GeV. Its couplings are fitted to the PDG partial widths, and that is what makes these examples comparable to measurement.

Example	What it shows	What it gives
09 — $\pi^0\to\gamma\gamma$	The axial anomaly, written as an effective vertex.	$\Gamma = 7.79\ \mathrm{eV}$
10 — Neutron decay	A three-body decay, integrated over the Dalitz phase space. The gap to the measurement (879 s) is the one expected of a tree-level computation without radiative corrections.	$\tau = 946\ \mathrm s$
11 — $\Lambda\to p\pi^-$	A non-leptonic hyperon decay, S and P amplitudes.	$\Gamma = 1.61\times10^{-15}\ \mathrm{GeV}$ , BR $63.9\ \%$
12 — $\tau\to\pi\nu$	A decay constant, $f_{\pi}$ , measurable in this branching ratio.	BR $10.6\ \%$
13 — $J/\psi\to\mu^+\mu^-$	A vector meson coupling to the photon; the constant is fixed by $\Gamma_{ee}$ .	$\Gamma = 5.55\ \mathrm{keV}$ , BR $6.0\ \%$
14 — $e^+e^-\to\pi^+\pi^-$	The $\rho$ resonance seen from the leptonic initial state. The energy plot from 0.5 to 1 GeV gives its shape.	$\sigma = 1.15\ \mu\mathrm b$ at the peak
19 — $\pi^+p\to\pi^+p$	The $\Delta(1232)$ resonance, carried by a spin-3/2 field. It is the only example where one sees a hadronic cross section of full size.	$0.18\ \mathrm b$ at the peak
20 — $\Omega^-\to\Lambda K^-$	The heaviest member of the decuplet, spin 3/2 as well.	$\Gamma = 5.44\times10^{-15}\ \mathrm{GeV}$ , BR $67.8\ \%$

Beyond the Standard Model

Example	What it shows	What it gives
15 — $e^-e^-\to W^-W^-$	Lepton number violation by a Majorana neutrino: a process impossible without one. Denner's fermion-flow rules are at work.	$\sigma = 7.6\times10^{-3}\ \mathrm{pb}$ at 500 GeV
16 — $X\to uu$	The X boson of Georgi–Glashow, which violates baryon number. Its width depends on nothing but $g_5$ and its mass.	$\Gamma = g_5^2M/24\pi$
17 — $uu\to e^+\bar d$	Proton decay seen as a scattering, at the unification scale. The cross section says why it has never been seen.	$\sigma \approx 7\times10^{-26}\ \mathrm{pb}$ at $2\times10^{15}\ \mathrm{GeV}$
18 — $e^+e^-\to\tilde\chi^0_1\tilde\chi^0_1$	A model imported from a UFO — MSSM_SLHA2, 822 vertices — at the SPS1a point. The Theory tab shows its import notes.	$\sigma = 269\ \mathrm{fb}$ at 500 GeV (literature: 250–300 fb)

The generators at work

Six documents that are only of interest with TreeLevel Tools installed: the same process, $e^+e^-$ at 200 GeV, handed in turn to each generator. Open them in the Generation workspace; without the tools, they remain ordinary computation documents.

On the iPad, only the two Pythia documents, 21 and 26, are offered, and only once the Pythia 8 module is installed. The other four — Herwig, Sherpa, WHIZARD, CalcHEP — stay on the Mac and the PC.

On the iPad, only the three Pythia documents, 21, 26 and 27, are offered, and only once the Pythia 8 module is installed. The other four — Herwig, Sherpa, WHIZARD, CalcHEP — stay on the Mac and the PC.

Example	What it shows
21 — Pythia 8	$e^+e^-\to b\bar b$ ( $\sigma = 3.07\ \mathrm{pb}$ ) picked up by Pythia: parton shower, hadronisation, decays. One starts from four partons and arrives at a few hundred particles.
22 — Herwig 7	The same work on $e^+e^-\to W^+W^-$ ( $\sigma = 19.2\ \mathrm{pb}$ ), with an angular-ordered shower and a cluster model. Two showers are better than one: comparing them is the point.
23 — Sherpa 3	Sherpa does not read the events back: it receives the process — beams, final state — and computes it itself. Its cross section is therefore its own, to be set against the 3.07 pb of the tree.
24 — WHIZARD 3	Same principle, another engine: WHIZARD rewrites the process in Fortran and compiles it at run time. It goes through the container.
25 — CalcHEP 3	Matrix element alone, without a shower, on $e^+e^-\to\mu^+\mu^-$ ( $\sigma = 2.99\ \mathrm{pb}$ ): a second opinion on the number, and nothing else.
26 — Collider modeThe Machine source	The only one that does not start from the diagram: you fix the beams and the energy, Pythia produces what it produces, and the cross section of the drawn process is measured by counting. See Generating events.
27 — The interaction zone	The process of example 21, with the positions Pythia gives its partons and hadrons. Once the events are generated, enlarge a Detector cut and choose the atom button: the shower, the strings and the hadrons born from them, at the femtometre — the generator's model, nothing measured. See The interaction zone.

Opening them, changing them

An example is a document like any other: the theory is embedded in it, so it computes as it is on any machine. What makes it an example is that it is already set up — the legs named, the energy chosen, the diagrams generated. The shortest way to learn is to open one, save a copy, and change one thing: a mass, an energy, a leg. The result redoes itself.