Search for the Production of Pionium Atoms near Threshold

We propose a model-independent method to extract a linear combination of the $s$-wave $\pi -\pi$ scattering lengths by measuring the $\gamma \gamma$ decay branching ratio for a tagged sample of ${\pi }^{+}{\pi }^{-}$ atoms (pionium). In the first experimental search for an appropriate tagging reaction, we observed ${\sigma }_{\mathrm{tot}}=76\mathrm{}\pm 21\pm 11\mathrm{pb}$ for free pion pair production in $\mathrm{pd}{\to }^3\mathrm{He}{\pi }^{+}{\pi }^{-}$ 1.0 MeV above threshold. This result suggests a pionium production cross section $\lesssim 1\mathrm{pb}$.