Measurement of $\pi^{+}\pi^{-}$ Bound State Lifetime with the DIRAC Spectrometer at CERN

The goal of the DIRAC experiment at CERN is to measure the lifetime of the pionium atom, a bound state of a pi+ and pi- meson, through the determination of its breakup probability. The experimental data collection has taken place during several runs between 1999 and 2003. The accumulated results will allow us to determine this lifetime with precision of 0.3 fs. Once this value is known, |a_0- a_2|, the isospin 0 and 2 scattering lengths difference, will be determined unambiguously. On the theoretical side, the value of pionium lifetime has been obtained with high precision by the Chiral Perturbation Theory (ChPT), yielding 2.9 +/- 0.1 fs and |a_0- a_2| difference yielding 0.265 +/- 0.004 [1/M_pi]. Our experimental approach is model-independent and, as such, will provide a crucial cross-check of these results. In this thesis we will analyze the data taken during 2002 and 2003 runs. For these run periods the dual target method will be used for the first time to determine the value of pionium lifetime taking into account statistical and systematic uncertainties.