Determination of the s-wave pion-nucleon threshold scattering parameters from the results of experiments on pionic hydrogen

Abstract

We give the conversion equations which lead from experimental values of the $3p\to 1s$ transition energy in pionic hydrogen and the total width of the $1s$ level to values of the s-wave threshold scattering parameters for the processes ${\pi }^{-}p\to {\pi }^{-}p$ and ${\pi }^{-}p\to {\pi }^{0}n$ respectively. Using a three-channel potential model, we then calculate the electromagnetic corrections to these quantities, which remove the effects of the Coulomb interaction, the external mass differences and the presence of the $\gamma n$ channel. We give the s-wave scattering parameters obtained from the present experimental data and these electromagnetic corrections. Finally we discuss the implications for isospin invariance.

20 pages

References in corpus (10)

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• Ground-state energy of pionic hydrogen to one loop
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• Isospin-breaking corrections in the pion-deuteron scattering length
• Phase-shift analysis of low-energy ${\pi }^{\pm }p$ elastic-scattering data
• A phenomenological negatively charged pion-proton scattering length from pionic hydrogen
• Electromagnetic corrections for the analysis of low energy pi-p scattering data
• Electromagnetic corrections to the hadronic phase shifts in low energy pi+p elastic scattering

Cited by in corpus (8)

• Improved description of the $\pi N$-scattering phenomenology in covariant baryon chiral perturbation theory
• Pionic deuterium
• Aspects of the ETH model of the pion-nucleon interaction
• A brief history of the pion-nucleon coupling constant
• Analysis of the low-energy ${\pi }^{\pm }p$ elastic-scattering data
• Analysis of the low-energy ${\pi }^{-}p$ charge-exchange data
• Analysis of the low-energy ${\pi }^{\pm }p$ differential cross sections of the CHAOS Collaboration
• A new two-body relativistic potential model for pionic hydrogen