  We compute the massive-sector worldsheet S-matrix for superstring theories in
AdS(n) x S(n) x T(10-2n) (with n=2,3,5) in the near BMN expansion up to
one-loop order in inverse string tension. We show that, after taking into
account the wave function renormalization, the one-loop S-matrix is UV finite.
In an appropriate regularization scheme the S-matrix is consistent with the
underlying symmetries of the superstring theory, i.e. for the n=3,5 cases it
coincides with the one implied by the light-cone gauge symmetries with the
dressing phases determined from the crossing equations. For the n=2,3 cases we
observe that the massless modes decouple from the one-loop calculation of
massive mode scattering, i.e. the 2n-dimensional supercoset sigma model and the
full 10-dimensional superstring happen to have the same massive one-loop
S-matrix.
