A Monte Carlo calculation of the pionium break-up probability with different sets of pionium target cross sections

Chiral perturbation theory predicts the lifetime of pionium, a hydrogen-like π+π- atom, to better than 3% precision. The goal of the DIRAC experiment at CERN is to obtain and check this value experimentally by measuring the break-up probability of pionium in a target. In order to accurately measure the lifetime one needs to know the relationship between the break-up probability and the lifetime to 1% accuracy. We have obtained this dependence by modelling the evolution of pionic atoms in the target using Monte Carlo methods. The model relies on the computation of the pionium-target-atom interaction cross sections. Three different sets of pionium-target cross sections with varying degrees of complexity were used: from the simplest first-order Born approximation involving only the electrostatic interaction to a more advanced approach, taking into account multiphoton exchanges and relativistic effects. We conclude that, in order to obtain the pionium lifetime to 1% accuracy from the break-up probability, the pionium-target cross sections must be known with the same accuracy for the low excited bound states of the pionic atom. This result has been achieved, for low Z targets, with the two most precise cross section sets. For large Z targets only the set accounting for multiphoton exchange satisfies the condition