π+π−atom in chiral perturbation theory

The hadronic ${\pi }^{+}{\pi }^{-}$ atom is studied in the relativistic perturbative approach based on the Bethe-Salpeter equation. The general expression for the atom lifetime is derived. Lowest-order corrections to the relativistic Deser-type formula for the atom lifetime are evaluated within chiral perturbation theory. The lifetime of the ${\pi }^{+}{\pi }^{-}$ atom in the two-loop order of chiral perturbation theory is predicted to be ${\tau }_1=(3.03\mathrm{}\pm 0.10)\times {10}^{-15}\hspace{0.5em}\mathrm{s}.$