The investigation of $K^+\pi^−, \pi^+K^−$ and $\pi^+\pi^−$ atoms

Theory, using Low Energy QCD, predicts with high precision the pion-pion and pion-kaon scattering lengths. There is accurate relation between $K^+\pi^−$ and $\pi^+K^-$ atoms lifetime and pion-kaon S-wave scattering lengths with isospin 1/2 and 3/2. Experiment DIRAC at CERN PS detects $345 \pm 61$ pairs from $K^+\pi^-$ and $\pi^+K^-$ atoms breakup. It allows to achieve the first observation of exotic atoms consisted of pion and kaon. Measured values of $\pi K$ atom lifetime and corresponding pion-kaon scattering length difference are presented. It is shown, that experimental accuracy for pion-kaon scattering length difference could be significantly improved with an experiment at SPS energy.