Chiral corrections to the isovector double scattering term for the pion-deuteron scattering length

The empirical value of the real part of the pion-deuteron scattering length can be well understood in terms of the dominant isovector πN double scattering contribution. We calculate in chiral perturbation theory all one-pion loop corrections to this double scattering term which in the case of πN scattering close the gap between the current-algebra prediction and the empirical value of the isovector threshold T-matrix T_πN^-. In addition to closing this gap, there is in the πd system a loop-induced off-shell correction for the exchanged virtual pion. Its coordinate space representation reveals that it is equivalent to 2π exchange in the deuteron. We evaluate the chirally corrected double scattering term and the off-shell contribution with various realistic deuteron wave functions. We find that the off-shell correction contributes at most -8% and that the isovector double scattering term explains at least 90% of the empirical value of the real part of the πd-scattering length.