The isoscalar S-wave pi-N scattering length a+ from pi-deuteron scattering

We consider constraints on the isoscalar S-wave pi-N scattering length a+ from pi-deuteron scattering, to third order in small momenta and pion masses in chiral perturbation theory. To this order, the pi-deuteron scattering length is determined by a+ together with three-body corrections that involve no undetermined parameters. We extract a novel value for a combination of dimension two low-energy constants which is in agreement with previous determinations.