Tripla: Anomaly That Counts Colours
Nuclear & Particle Physics arc, page 183 of 193. Back to The Pixelated Physics Universe
Who they are
Tripla, a pion-sprite with three coloured crown gems, bursts into two photon wings.
Tripla is a character of the Nuclear & Particle Physics arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
For massless fermions the axial current is conserved classically, but quantum effects break it: a triangle loop with one axial and two vector vertices spoils the conservation. This is the ABJ (chiral) anomaly, and it gives the neutral pion its fast decay into two photons. At leading order, with three quark colours and the up and down quark charges built in, the predicted width is about 7.8 eV.
$$ \begin{gathered} \pi^{0}\rightarrow\gamma\gamma: \quad \Gamma = \frac{\alpha^{2} m_\pi^{3}}{64\pi^{3} f_\pi^{2}} \approx 7.8\ \mathrm{eV} \quad (f_\pi \approx 92\ \mathrm{MeV},\ 3 \text{ colours}) \\ \text{Measured: } \Gamma = 7.80 \pm 0.12\ \mathrm{eV} \quad (\text{PrimEx-II, 2020}) \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $\pi^{0}$ | neutral pion | 1 |
| $\gamma$ | photon | 1 |
| $\Gamma$ | decay width of the neutral pion to two photons | eV |
| $\alpha$ | fine-structure constant ≈ 1/137.036 | 1 |
| $m_\pi$ | neutral-pion mass, ≈ 135 MeV/c² | eV |
| $f_\pi$ | pion decay constant (≈ 92 MeV convention) | eV |
Honest caveat: The match with three colours is strong evidence for three quark colours, not a proof. Small corrections beyond the anomaly are still studied, and f_π ≈ 92 MeV here is the convention that goes with this formula (others quote about 130 MeV).
Sources
- Adler (1969) Axial-Vector Vertex in Spinor Electrodynamics, Phys. Rev. 177, 2426
- Bell & Jackiw (1969) A PCAC puzzle: π0→γγ in the σ-model, Nuovo Cim. A 60, 47
- Larin et al. (PrimEx-II) (2020) Precision measurement of the neutral pion lifetime, Science 368, 506
Crossovers
Tripla meets Quarkbinders (Quantum Chromodynamics / Strong Nuclear Force). Tripla's pion decay to two photons counts the quark colours. The rate matches experiment for three colours, which backs Quarkbinders' charge.
Tripla meets Counterterra (Renormalization). Counterterra can remove infinities, but Tripla's anomaly survives every renormalisation scheme. It is a real quantum effect, not an artefact.
Wear the lore
Concept keywords: Anomaly That Counts Colours, Tripla, Nuclear & Particle Physics, physics lore, Pixelated Physics