The ratio of pionium formation probabilities in ns-states stays at (n2/n1)^3 to O(10^-3) under first-order strong-interaction corrections, and the Deser level shift is rewritten in terms of the strong-interaction radius and the wave-function correction at the origin.
The pionium lifetime in generalized chiral perturbation theory
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abstract
Pionium lifetime corrections to the nonrelativistic formula are calculated in the framework of the quasipotential-constraint theory approach. The calculation extends an earlier evaluation, made in the scheme of standard chiral perturbation theory, to the scheme of generalized chiral perturbation theory, in which the quark condensate is left as a free parameter. The pionium lifetime is calculated as a function of the combination $(a_0^0-a_0^2)$ of the $\pi\pi$ S-wave scattering lengths with isospin I=0,2.
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Formulation of the Deser formula for the shift of energy levels of hadronic atoms in terms of the effective radius of the strong interaction with the Coulomb wave function of hadronic atoms at the origin
The ratio of pionium formation probabilities in ns-states stays at (n2/n1)^3 to O(10^-3) under first-order strong-interaction corrections, and the Deser level shift is rewritten in terms of the strong-interaction radius and the wave-function correction at the origin.