Lifetime of (π+π−) atom: analysis of the role of strong interactions

The expression for the (π+π−) atom lifetime is derived within the Bethe-Salpeter approach. First-order perturbative corrections due to the contribution of strong interactions are taken into account. It is demonstrated that the atom lifetime can be expressed in terms of the solutions of the Coulombic problem (the wave function of the 1S state at the origin Ψ1(0), the binding energy of the S-state E1), the difference of the S-wave ππ scattering lengths and the energy shift ΔE1 of the level due to the strong interactions: 1gt1 − (a00 - a02)2|Ψ1(0)|2 (1 - 9ΔE18E1).