We use the framework of effective field theories to discuss the determination
of the S-wave \pi N 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 a_{\pi d} is extracted from the data. Next, a_{\pi d} is related to the
S-wave \pi N 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.Comment: The replacement includes an erratum, which is published in Eur. Phys.
J.
