The extraction of hadronic parameters from experiments on pionium

✍ Scribed by A. Gashi; G.C. Oades; G. Rasche; W.S. Woolcock

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 530 KB
• Volume: 628
• Category: Article
• ISSN: 0375-9474
• DOI: 10.1016/s0375-9474(97)00645-3

✦ Synopsis

We show how experimental values of the lifetime of the l s level of pionium and of the difference between the energies of the 2s and 2p levels yield values of the elements ao,. and a,. respectively of the s-wave scattering matrix for the two-channel (Tr+Tr -, 7r°Tr °) system at the 7r+Tr -threshold. We then develop a method, using energy independent hadronic potentials which reproduce the best available pion-pion phase shifts up to 500 MeV total energy in the c.m. frame, 0 and 2a ° + a~ from aoc and a,,. for obtaining the values of the isospin invariant quantities a~ -a 0 respectively. We emphasize that the isospin invariant scattering lengths a ° and a~ universally used in the literature cannot be considered to be purely hadronic quantities. (~) 1998 Elsevier Science B.V.