The pion-nucleon scattering lengths from pionic deuterium
Ulf-G. Meißner, Udit Raha, Akaki Rusetsky
Abstract
We use the framework of effective field theories to discuss the determination of the S-wave πN scattering lengths from the recent high-precision measurements of pionic deuterium observables. The theoretical analysis proceeds in several steps. Initially, the precise value of the pion-deuteron scattering length aπd is extracted from the data. Next, aπd is related to the S-wave πN scattering lengths a+ and a-. We discuss the use of this information for constraining the values of these scattering lengths in the full analysis, which also includes the input from the pionic hydrogen energy shift and width measurements, and throughly investigate the accuracy limits for this procedure. In this paper, we also give a detailed comparison to other effective field theory approaches, as well as with the earlier work on the subject, carried out within the potential model and multiple scattering framework.
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