In the Standard Model, the weak charged current couples up-type quarks (u, c, t) to down-type quarks (d, s, b) through the Cabibbo–Kobayashi–Maskawa matrix. Mass eigenstates and weak (flavor) eigenstates differ, so a down-type quark dj emitting a W⁻ boson converts into an up-type quark ui with amplitude Vij:
d_j → u_i + W⁻ amplitude ∝ V_ij
P(d_j → u_i) = |V_ij|² / Σ_k |V_kj|² (unitary column)
|V| ≈ 0.974 0.225 0.0037 (u row)
0.225 0.973 0.041 (c row)
0.009 0.040 0.999 (t row)
(columns: d, s, b)
Each column is (very nearly) unitary — the three branching probabilities for a given parent quark sum to 1 (verified numerically: 0.9994, 0.9990, 0.9997 for the d/s/b columns respectively — the small shortfall from 1 is the rounding of the tabulated |Vij| to 3 significant figures, not an error). This simulator samples the actual outcome from those |Vij|² weights every time you fire a decay, exactly like nature's Fermi's-Golden-Rule branching ratios (phase-space factors are ignored here for clarity).
- d / s / b buttons — choose which down-type quark decays, i.e. which CKM column is sampled.
- Emit W⁻ decay — fires one decay: the quark travels to its sampled up-type partner while a W⁻ boson is ejected, exactly conserving charge (−1/3 → +2/3 − 1).
- Auto decay rate — fires decays continuously so the measured histogram can converge on the predicted probabilities (law of large numbers).
- Flight speed — scales how fast the quark/boson animations travel across the diagram; does not affect the sampled physics, only the visualisation pace.
- Show CKM² bars — renders |Vij|² as a 3×3 bar grid beneath the diagram, with a thin tick mark showing the live measured fraction on top of each predicted bar; the bright column is the one currently selected.
- Diagram drag / scroll — the quark diagram is a real pannable, zoomable 2D view: drag to pan, scroll/pinch to zoom, "Reset view" restores the default framing.
Why it matters: this near-diagonal, Cabibbo-suppressed structure (large diagonal, small off-diagonal terms) is why strange and bottom quarks decay predominantly — but not exclusively — within their own generation, and why CP violation in the Standard Model requires all three generations to exist.