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

Abstract

Chiral perturbation theory predicts the lifetime of pionium, a hydrogen-likeπ+π− atom, to better than 3% precision. The goal of the DIRAC experiment at CERN is toobtain and check this value experimentally by measuring the break-up probability ofpionium in a target. In order to accurately measure the lifetime one needs to know therelationship between the break-up probability and the lifetime to 1% accuracy. We haveobtained this dependence by modelling the evolution of pionic atoms in the target usingMonte Carlo methods. The model relies on the computation of the pionium–target-atominteraction cross sections. Three different sets of pionium–target cross sections with varyingdegrees of complexity were used: from the simplest first-order Born approximationinvolving only the electrostatic interaction to a more advanced approach, taking intoaccount multiphoton exchanges and relativistic effects. We conclude that, in order toobtain the pionium lifetime to 1% accuracy from the break-up probability, thepionium–target cross sections must be known with the same accuracy for the lowexcited bound states of the pionic atom. This result has been achieved, for lowZ targets, with the two most precise cross section sets. For largeZ targets only the set accounting for multiphoton exchange satisfies the condition.