A Monte Carlo Calculation of the Pionium Break-up Probability with Different Sets of Pionium Target Cross Sections

Abstract

Chiral Perturbation Theory predicts the lifetime of pionium, a hydrogen-like ${\pi }^{+}{\pi }^{-}$ 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 lifetime to a 1% accuracy. We have obtained this dependence by modeling 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 multi-photon 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.

arXiv commentJournal of Physics B: Atomic, Molecular and Optical Physics; (submited; 17 pages, 6 figures, 18 references)

References in corpus (5)

• The pi pi S-wave scattering lengths
• Numerical analysis of the pi+pi- atom lifetime in ChPT
• Coherent and incoherent atomic scattering: Formalism and application to pionium interacting with matter
• The Influence of Strong Interaction on the Pionium Wave Functions at Small Distances
• QED Radiative Corrections to the Pionium Life Time

Cited by in corpus (9)

• First measurement of the ${\pi }^{+}{\pi }^{-}$ atom lifetime
• Determination of $\pi \pi$ scattering lengths from measurement of ${\pi }^{+}{\pi }^{-}$ atom lifetime
• First $\pi K$ atom lifetime and $\pi K$ scattering length measurements
• Detection of ${\pi }^{+}{\pi }^{-}$atoms with the DIRAC spectrometer at CERN
• Relativistic time dilatation and the spectrum of electrons emitted by 33 TeV lead ions penetrating thin foils
• Direct calculation of the probability of pionium ionization in the target
• Dynamics of the Pionium with the Density Matrix Formalism
• Dimesoatom breakup in the Coulomb field
• Transition of dimuonium through foil