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

Abstract

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.