Precise Determination of the Branching Ratio of the Neutral-Pion Dalitz Decay

We provide a new value for the ratio $R=\mathrm{\Gamma }\mathbf{(}{\pi }^0\to e^{+}{e}^{-}\gamma (\gamma )\mathbf{)}/\mathrm{\Gamma }({\pi }^0\to \gamma \gamma )=11.978(6)\times {10}^{-3}$, which is by 2 orders of magnitude more precise than the current Particle Data Group average. It is obtained using the complete set of the next-to-leading-order radiative corrections in the QED sector, and incorporates up-to-date values of the ${\pi }^0$-transition-form-factor slope. The ratio $R$ translates into the branching ratios of the two main ${\pi }^0$ decay modes: $\mathcal{B}({\pi }^0\to \gamma \gamma )=98.8131(6)\%$ and $\mathcal{B}\mathbf{(}{\pi }^0\to e^{+}{e}^{-}\gamma (\gamma )\mathbf{)}=1.1836(6)\%$.

Figure 1

NLO QED radiative corrections for ${\pi }_{\mathrm{D}}^0$: (a) vacuum-polarization insertion; (b),(c) one-loop $1\gamma \mathrm{IR}$ contribution; (d) vertex correction; (e) bremsstrahlung.