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

Abstract

We provide a new value for the ratio $R=\Gamma ({\pi }^0\to e^{+}{e}^{-}\gamma (\gamma ))/\Gamma ({\pi }^0\to \gamma \gamma )=11.978(6)\times 10^{-3}$, 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: $\mathcal{B}({\pi }^0\to \gamma \gamma )=98.8131(6)\%$ and $\mathcal{B}({\pi }^0\to e^{+}{e}^{-}\gamma (\gamma ))=1.1836(6)\%$.

6 pages, 1 figure, 3 tables; v3: version accepted by PRL, major text improvements, figure and references added; v2: minor changes, references updated