Lifetime Measurements of $ \pi ^+ \pi ^- $ and $\pi^{+-} K^{-+}$ Atoms to Test Low-Energy QCD Predictions

%PS212 \\ \\ The proposed experiment aims to measure the lifetime of $ \pi ^+ \pi ^- $ atoms in the ground state with 10\% precision, using the 24~GeV/c proton beam of the CERN Proton Synchrotron. As the value of the above lifetime of order 10$ ^- ^{1} ^{5} $s is dictated by a strong interaction at low energy, the precise measurement of this quantity enables to determine a combination of S-wave pion scattering lengths to 5\%. Pion scattering lengths have been calculated in the framework of chiral perturbation theory and values predicted at the same level of accuracy have, up to now, never been confronted with accurate experimental data. Such a measurement would submit the understanding of chiral symmetry breaking of QCD to a crucial test.