Finite-size correction to the pionium lifetime due to ω and η' contributions

It is shown that for pNi interactions at 24 GeV/c, the fractions of the $π^±$$_ωπ^{\mp}$ and $\pi^{\pm}_{\eta}, \pi^{\pm}$ pairs with one pion from the ω and η' decays, respectively, at small values of the relative momentum Q ≤ 4 MeV/c of pions in the c.m. system of the $π^+π^−$ pair are $f_ω = 0.150 ± 0.019$ and $f_{η'} = 0.0102 \mp 0.0034$ . With these values of $f_ω$ and $f_{η'}$, the uncertainty in the pionium breakup probability and the corresponding overestimation of the pionium lifetime in the DIRAC experiment at CERN are $ΔP_{br}/P_{br} = (3.0 ± 1.0)%$ and $Δτ/τ = (7.8 ± 2.6)%$.