π+π− Atom in Chiral Perturbation Theory

The pion-pion scattering lengths from DIRAC

The scattering lengths of a two pion system are the golden magnitudes to test the QCD predictions in the low energy sector. The DIRAC (PS-212) experiment at CERN will obtain a particular combination of the S-wave isospin 0 and 2 scattering lengths by measuring the lifetime of pionium, the hydrogen-like π+π− atom. This measurement tests the accurate predictions of the Chiral Perturbation Theory....

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

We calculate the electromagnetic corrections needed to obtain isospin invariant hadronic pion-pion s-wave scattering lengths a, a from the elements acc, a0c of the s-wave scattering matrix for the (π+π−, ππ) 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 V , V 2 that sat...

η → π + π − π 0 γ in Chiral Perturbation Theory

The influence of the hadronic interaction on the pionium wave functions

The influence of the hadronic ππ interaction on the wave functions of pionium (the Coulomb bound π+π− system) at distances ≤ 10 fm is calculated for s-states with principal quantum numbers n ≤ 4. Hadronic ππ potentials are used that reproduce the scattering phase shifts of two-loop chiral perturbation theory. The pionium wave functions ψn(r) are obtained by integrating the coupled Schrödinger e...

Effective theories and hadronic bound states ∗

Recent progress in the description of the properties of hadronic atoms on the basis of non-relativistic effective Lagrangian approach and Chiral Perturbation Theory (ChPT) is reported. For the case of the π + π − atom decay, the problem is completely solved, both conceptually and numerically. For the π − p atom, a general expression for the ground-state energy is obtained in the first non-leadi...