Determination of pi-N scattering lengths from pionic hydrogen and pionic deuterium data

Abstract

The pi-N s-wave scattering lengths have been inferred from a joint analysis of the pionic hydrogen and the pionic deuterium x-ray data using a non-relativistic approach in which the pi-N interaction is simulated by a short-ranged potential. The pi-d scattering length has been calculated exactly by solving the Faddeev equations and also by using a static approximation. It has been shown that the same very accurate static formula for pi-d scattering length can be derived (i) from a set of boundary conditions; (ii) by a reduction of Faddeev equations; and (iii) through a summation of Feynman diagrams. By imposing the requirement that the pi-d scattering length, resulting from Faddeev-type calculation, be in agreement with pionic deuterium data, we obtain bounds on the pi-N scattering lengths. The dominant source of uncertainty on the deduced values of the pi-N scattering lengths are the experimental errors in the pionic hydrogen data.

RevTeX, 20 pages,4 PostScript figures

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• Hadronic Atoms
• Chiral restoration from pionic atoms?
• On rescattering effects in the reaction ${\pi }^{-}d\to {\pi }^{-}d$
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