DIRAC

Theory, using Low Energy QCD, predicts with high precision the pion-pion and pion-kaon scattering lengths. There is accurate relation between $\pi^+\pi^-$ atom lifetime and a difference of S-wave pion-pion scattering lengths with isospin 0 ($a_0$) and 2 ($a_2$). Similar relation exists for $K^+\pi^-$ and $\pi^+K^-$ atoms lifetime and pion-kaon scattering lengths with isospin 1/2 ($a_{1/2}$) and 3/2 ($a_{3/2}$). 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.

The experimental observation of the long-lived $\pi^+\pi^-$ atoms is shown. The scheme to use the obtained data for the long-lived atom lifetime measurement will be described. Possibility of the long-lived $\pi^+\pi^-$ atom Lamb shift measurement and evaluation of pion-pion scattering length new combination ($|2 \cdot a_0 + a_2|$) is discussed.