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. To be published in The Physical Review C (2002), Brief Reports The tool to systematically investigate the consequences of spontaneous and explicit chiral symmetry breaking in QCD is chiral perturbation theory. Recently, methodology has been developed [1] which allows one to relate scattering processes involving a single nucleon to nuclear scattering processes. For instance, one can relate pion-nucleon scattering to piondeuteron scattering. The non-perturbative effects responsible for deuteron binding are accounted for by (phenomenological) deuteron wavefunctions. Although this introduces some model dependence one can evaluate matrix elements of chiral operators in a variety of wavefunctions in order to estimate the theoretical error induced by the off-shell behavior of different NN-potentials. In a recent precision experiment the PSI-group has extracted the isoscalar and isovector pion-nucleon scattering lengths a±πN from the shift and the width of the 1s-level in pionic hydrogen, with the result [2]: T πN = 4π (