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

Abstract

We calculate the electromagnetic corrections needed to obtain isospin invariant hadronic pion-pion s-wave scattering lengths a^0, a^2 from the elements a_cc, a_0c of the s-wave scattering matrix for the (π^+ π^-, π^0 π^0) system at the π^+ π^- threshold. These elements can be extracted from experiments on pionium. Our calculation uses energy independent hadronic pion-pion potentials that satisfactorily reproduce the low-energy phase shifts given by two-loop chiral pertur- bation theory. We also take into account an important relativistic effect whose inclusion influences the corrections considerably.

14 pages including 3 figures. Uses elsart.cls. Some numbers have been updated and a few typos have been corrected

References in corpus (1)

• Decays of the pi+ pi- atom

Cited by in corpus (5)

• First measurement of the ${\pi }^{+}{\pi }^{-}$ atom lifetime
• Detection of ${\pi }^{+}{\pi }^{-}$atoms with the DIRAC spectrometer at CERN
• Hadronic potentials from effective field theories
• The isospin symmetry breaking effects in $K_{e4}$ decays
• Energy and decay width of the pi-K atom