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A Dalitz decay replaces a radiated real photon with a virtual photon converting to a charged-lepton pair. The neutral-pion example is ${\pi }^0\to \gamma e^{+}{e}^{-}$. Double Dalitz decay converts both virtual photons in the two-photon mode.

Double Dalitz decay converts both virtual photons from a two-photon hadronic transition into charged-lepton pairs. The neutral-pion four-electron final state avoids the specific two-lepton helicity suppression of ${\pi }^0\to e^{+}{e}^{-}$, despite its more restricted phase space.

The original table gives the dimensionless branching fractionsThus the four-lepton channel is about $517$ times as frequent, despite its smaller available phase space.

The dominant neutral-pion interaction is with two photons. In double Dalitz decay, both are virtual and convert to separate Electron-Positron pairs:This requires two electromagnetic conversions but does not force the whole final state into a helicity-suppressed two-fermion configuration. The two virtual photons and four final leptons allow the necessary angular momentum correlations.

For the two-lepton mode, a single virtual photon cannot mediate a $0^{-+}$ pion into $e^{+}{e}^{-}$: the electromagnetic vector current has the wrong quantum numbers. The leading electromagnetic mechanism involves two virtual photons attached to the same lepton line, with a loop integration. The resulting pseudoscalar two-lepton amplitude vanishes as $m_e\to 0$, so its decay width has an additional helicity suppression factor proportional to $m_e^2/m_{\pi }^2$.

Both channels involve extra electromagnetic couplings relative to ${\pi }^0\to \gamma \gamma$. The crucial distinction is the extra leptonic loop and helicity suppression of the two-lepton channel; counting final particles or couplings alone misses it. The pion-two-photon interaction itself already contains strong-interaction structure, so “extra loop” here compares the diagrams after representing that common interaction by an effective ${\pi }^0\gamma \gamma$ vertex.