Spin susceptibility of underdoped cuprates: the case of Ortho-II YBa$_2$Cu$_3$O$_{6.5}$

Recent inelastic neutron scattering measurements found that the spin susceptibility of detwinned and highly ordered ortho-II YBa$_2$Cu$_3$O$_{6.5}$ exhibits, in both the normal and superconducting states, one-dimensional incommensurate modulations at low energies which were interpreted as a signature of dynamic stripes. We propose an alternative model based on quasiparticle transitions between the arcs of a truncated Fermi surface. Such transitions are resonantly enhanced by scattering to the triplet spin resonance. We show that the anisotropy in the experimental spin response is consistent with this model if the gap at the saddle points is anisotropic.