Pionium

Abstract: We obtain reliable ππ scattering amplitudes consistent with experimental data, both at low and high energies, and fulfilling appropriate analyticity properties. We do this by first fitting experimental low energy [s^(1/2) ≤ (1.42 GeV] phase shifts and inelasticities with expressions that incorporate analyticity and unitarity. In particular, for the S wave with isospin 0, we discuss in detail several sets of experimental data. This provides low energy partial wave amplitudes that summarize the known experimental information. Then, we impose Regge behavior as follows from factorization and experimental data for the imaginary parts of the scattering amplitudes at higher energy, and check fulfillment of dispersion relations up to 0.925 GeV. This allows us to improve our fits. The ensuing ππ scattering amplitudes are then shown to verify dispersion relations up to 1.42 GeV, as well as s t u crossing sum rules and other consistency conditions. The improved parametrizations therefore provide a reliable representation of pion-pion amplitudes with which one can test chiral perturbation theory calculations, pionium decays, or use as input for CP-violating K decays. In this respect, we find [a^(0)_0 a^(2)_0]^2 = (0.077 ± 0.008) M^(-2)_π and δ^(0)_(0) (m^(2)_K δ^(2)_(0) (m^(2)_(K) = 5209 ±1.6o.

Abstract: The formalism allowing one to account for the effect of a finite space-time extent of particle production region is given. Its applications to the lifetime measurement of hadronic atoms produced by a high-energy beam in a thin target, as well as to the femtoscopy techniques widely used to measure space-time characteristics of the production processes, are discussed. Particularly, it is found that the neglect of the finite-size effect on the pionium lifetime measurement in the experiment DIRAC at CERN could lead to the lifetime overestimation comparable with the 10% statistical error. The theoretical systematic errors arising in the calculation of the finite-size effect due to the neglect of non-equal emission times in the pair center-of-mass system, the space-time coherence and the residual charge are shown to be negligible.

Abstract: The DIRAC spectrometer has been commissioned at CERN with the aim of detecting π+π− atoms produced by a 24 GeV /c high intensity proton beam in thin foil targets. A challenging apparatus is required to cope with the high interaction rates involved, the triggering of pion pairs with very low relative momentum and the measurement of the latter with resolution around 0.6 MeV /c . The general characteristics of the apparatus are explained and each part is described in some detail. The main features of the trigger system, data-acquisition, monitoring and set-up performances are also given.