Quark Flavor Mixing: CKM Matrix & Weak Decay

Parent Down-Type Quark

Auto decay rate 0 / s

Predicted vs. Measured

Decays fired

Selected column

How it works

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 d_j emitting a W⁻ boson converts into an up-type quark u_i with amplitude V_ij:

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. This simulator samples the actual outcome from those |V_ij|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).
Show CKM² bars — renders |V_ij|² as a 3×3 bar grid; the bright column is the one currently selected.

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.

Generation 1 (u, d) Generation 2 (c, s) Generation 3 (t, b) W⁻ boson

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