Precise determination of the branching ratio of the neutral-pion Dalitz decay

We provide a new value for the ratio $R={\Gamma(\pi^0\to e^+e^-\gamma(\gamma))}/{\Gamma(\pi^0\to\gamma\gamma)}=11.978(6)\times10^{-3}$, which is by two 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: $\mathcal{B}({\pi }^0\to \gamma \gamma )=98.8131(6)\mathrm{\%}$ and $$\mathcal{B}$(\pi^0\to e^+e^-\gamma(\gamma))=1.1836(6),%$.