The S-Wave Pion-Nucleon Scattering Lengths from Pionic Atoms using Effective Field Theory

Abstract

The pion-deuteron scattering length is computed to next-to-next-to-leading order in baryon chiral perturbation theory. A modified power-counting is then formulated which properly accounts for infrared enhancements engendered by the large size of the deuteron, as compared to the pion Compton wavelength. We use the precise experimental value of the real part of the pion-deuteron scattering length determined from the decay of pionic deuterium, together with constraints on pion-nucleon scattering lengths from the decay of pionic hydrogen, to extract the isovector and isoscalar S-wave pion-nucleon scattering lengths, a^- and a^+, respectively. We find a^-=(0.0918 \pm 0.0013) M_π^{-1} and a^+=(-0.0034 \pm 0.0007) M_π^{-1}.

19 pages LaTeX, 7 eps figs

References in corpus (7)

• Effective Field Theory for Few-Nucleon Systems
• Nuclear forces in the chiral limit
• Ground-state energy of pionic hydrogen to one loop
• Variation of Fundamental Couplings and Nuclear Forces
• Building light nuclei from neutrons, protons, and pions
• Pions in the Pionless Effective Field Theory
• Chiral corrections to the isovector double scattering term for the pion-deuteron scattering length

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