Search for Long-Lived States of $\pi^+\pi^-$ Atoms: Addendum to the DIRAC Proposal

The proposed experiment is a further development of the DIRAC experiment already running at CERN PS. Up to now more than 21000 $\pi^+\pi^-$ pairs originated from the $\pi^+\pi^-$ atom ($A_{2\pi}$) breakup were identified and the overall accuracy of the $A_{2\pi}$ lifetime is about 9% in accordance with the DIRAC proposal. This measurement allowed to extract the difference $|a_0-a_2|$ of $s$-wave $\pi\pi$-scattering length with accuracy of 4.3%. The observation of long-lived (metastable) $A_{2\pi}$ states will be performed with the same setup. This observation opens a possibility to measure the energy difference between $ns$ and $np$ states and to determine the value of another combination $2a_0+a_2$ of $\pi\pi$ scattering length in a model-independent way. In combination with the first measurement it allows to get $a_0$ and $a_2$ separately. An additional measurement of the multiple scattering angles in different materials with accuracy better than 1% will be performed in parallel with the observation. This measurement is needed to improve the systematic accuracy in the $A_{2\pi}$ lifetime for the data already collected in 2008--2010.