New light on electromagnetic corrections to the scattering parameters obtained from experiments on pionium Original Research Article

We calculate the electromagnetic corrections needed to obtain isospin invariant hadronic pion–pion s-wave scattering lengths a0, a2 from the elements acc,a0c of the s-wave scattering matrix for the (π+π−,π0π0) system at the π+π− threshold. The latter can be extracted from experiments on the π+π− atom (pionium). Our calculation uses energy-independent hadronic pion–pion potentials V0 and V2 that satisfactorily reproduce the low-energy phase shifts given by two-loop chiral perturbation theory, with the hadronic mass of the pion taken first as the charged-pion mass and then as the neutral-pion mass. We also take into account an important relativistic effect whose inclusion influences the corrections considerably.