S-wave pion nucleon scattering lengths fromπN, pionic hydrogen, and deuteron data

Abstract

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 $\ensuremath{\pi}N$ 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 ${a}_{{\ensuremath{\pi}}^{\ensuremath{-}}d}$ new significant corrections concerning real and imaginary parts are evaluated, putting new constraints from ${\ensuremath{\pi}}^{\ensuremath{-}}d$ scattering on the values of $({b}_{0},{b}_{1})$. In particular, dispersion corrections, the influence of the $\ensuremath{\Delta}(1232)$ resonance, crossed terms and multiple scattering in a Faddeev approach are considered.