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S-wave pion nucleon scattering lengths from $πN$, pionic hydrogen and deuteron data

The isoscalar and isovector scattering lengths (b_0,b_1) are determined using a unitarized coupled channel approach based on chiral Lagrangians. Using experimental values of pionic hydrogen and deuterium as well as low energy pi N scattering data, the free parameters of the model are calculated. Isospin violation is incorporated to a certain extent by working with physical particle masses. For the deuterium scattering length a_{pi-d} new significant corrections concerning real and imaginary parts are evaluated, putting new constraints from pi-d scattering on the values of (b_0,b_1). In particular, dispersion corrections, the influence of the Delta(1232) resonance, crossed terms and multiple scattering in a Faddeev approach are considered.