Tripla

Tripla, a pion-sprite with three coloured crown gems, bursts into two photon wings.

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.

π⁰ → γγ: Γ = α² m_π³ / (64 π³ f_π²) ≈ 7.8 eV (f_π ≈ 92 MeV, 3 colours)

• Γ: decay width of π⁰ → γγ (eV)
• α: fine-structure constant ≈ 1/137.036 (dimensionless)
• m_π: neutral pion mass, 134.977 MeV
• f_π: pion decay constant in the ~92 MeV convention (MeV)

PrimEx-II measured Γ = 7.80 ± 0.12 eV in 2020, confirming the anomaly prediction at the percent level. The anomaly was found by Adler (Phys. Rev. 177, 2426, 1969) and by Bell and Jackiw (Nuovo Cimento A 60, 47, 1969).

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).

On the shirt

Front: Tripla, the pixel-art character, with the title. Back: the anomaly formula, the PrimEx-II measurement and the 1969 papers. Printed on a unisex tee.