🧬Particle Physics & Standard Model - particle chart, hadron builder, conservation laws, decay kinematics

How to use Particle physics & the Standard Model

1. 1On the Standard Model tab, click a particle for details; tick Show antiparticles to see the charges flip
2. 2On the Hadron builder tab, combine quarks into qqq or qq̄ and see whether it is colour neutral and which hadron it is
3. 3On the Conservation laws tab, type a reaction such as n -> p + e- + anti-nu_e or pick a preset, and read the conservation table and verdict
4. 4On the Decay kinematics tab, pick a parent and two daughters, read the rest-frame momentum, then drag the parent momentum to see lab energies and angles
5. 5Enter four-momenta in the invariant-mass calculator to reconstruct the parent mass

FAQ

How do I tell whether a reaction is strong, electromagnetic or weak?

First check the absolute laws: charge, baryon number and the electron, muon and tau lepton numbers must hold in every interaction, otherwise the process is forbidden. If they hold, any neutrino, W or Z, or any change in strangeness, charm or bottomness means only the weak force can do it (e.g. Λ → pπ⁻ with ΔS = 1). If flavour is unchanged and only hadrons take part, the strong force can do it (Δ⁺⁺ → pπ⁺ lives about 10⁻²³ s); photons or charged leptons make it electromagnetic (π⁰ → γγ). A weak vertex changes strangeness by at most one unit, so Ξ⁻ → nπ⁻ (ΔS = 2) is not seen.

Why is n → p + e⁻ + νₑ forbidden?

The neutron has electron lepton number Lₑ = 0. The final electron has Lₑ = +1, and a neutrino νₑ adds another +1, giving +2. The correct partner is the electron antineutrino ν̄ₑ with Lₑ = −1, which makes the final total 0. Change anti-nu_e to nu_e in the tool and the lepton-number row turns red.

Where does the 29.79 MeV/c for π⁺ → μ⁺ν_μ come from?

In the parent rest frame the two daughters of a two-body decay have equal and opposite momenta, p* = √λ(M², m₁², m₂²) / 2M with λ the Källén function. With the π⁺ at 139.570 MeV, the μ⁺ at 105.658 MeV and a massless neutrino this becomes p* = (M² − m_μ²)/2M ≈ 29.79 MeV/c, and the muon gets about 4.12 MeV of kinetic energy. Because two-body decays give a single daughter energy, the continuous beta-decay spectrum led Pauli to propose the neutrino.

Why must hadrons be qqq or qq̄?

Quarks carry one of three colour charges, and because gluons interact with each other the colour field energy grows with distance; only colour-singlet ("white") combinations can exist on their own. This is confinement. Three quarks of different colours (a baryon) or a colour plus its anticolour (a meson) are singlets; mathematically n_q − n_q̄ must be divisible by 3. So qq or qqq̄ cannot exist, while qqq̄q̄ tetraquarks and qqqqq̄ pentaquarks are allowed, and LHCb has found several.

Why are the quark masses quoted so differently?

Quarks are never free, so their mass depends on the scheme. PDG gives u, d and s as MS-bar current masses at a 2 GeV scale (a few MeV up to about 94 MeV), c and b as m(m), and the top quark, which decays before forming hadrons, as a mass reconstructed directly from its decay products (172.57 GeV). Most of the proton's 938 MeV comes from gluon fields and quark kinetic energy, not from the roughly 9 MeV of its three quarks' current masses.