Abstract
We suggest a few particle physics processes in which excited 2p pionium $\mathrm{A}^\prime_{2\pi}$ may be observed. They include the $e^+e^-\to\pi^+\pi^-$ annihilation, the $V^0\to\pi^0\ell^+\ell^-$ and $K^\pm\to\pi^\pm\ell^+\ell^-$ ($\ell=e,\mu$) decays, and the photoproduction of two neutral pions from nucleons. We analyze available experimental data and find that they, in some cases, indicate the presence of 2p pionium, but do not provide definite proof.
Highlights
The first thoughts about an atom composed of a positive pion and a negative pion appeared almost sixty years ago
Applying formula (11) to the decay widths on the righthand side of Eq (7), we find that the jFV0π0ðM2Þj2 acquires, in comparison with the standard vectormeson dominance (VMD), an extra factor of
We will only use the results of the latter experiment, presented as the mean values of the ωπ0 transition form factor squared in 20 M2 (GeV) Γ2 (MeV)-wide dimuon mass bins
Summary
The first thoughts about an atom composed of a positive pion and a negative pion (pionium, or A2π in the presentday notation) appeared almost sixty years ago. The mean lifetime of 2p pionium τ2p 1⁄4 0.45þ−01..3008 × 10−11 s: ð1Þ is close to the value which comes for the πþπ− atom assuming a pure Coulomb interaction [8]. Assuming pure Coulombic interaction, the binding energy of pionium can be calculated from the hydrogen-atom formula bn 1⁄4. Our experience with 2p kaonium shows that the crucial role in discovering the bound-state pole, which lies below the reaction threshold, is played by the cross section data at low energies, as close to the threshold as possible [12]. It cannot be considered proof of 2p pionium existence because a perfect fit exists without it The rise is cut off by the pÃπ3 factor in Eq (3) and a vanishing cross section is reached at the reaction threshold
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