Inelastic neutron and x-ray scattering as probes of the sign structure of the Fe-pnictide superconducting gap

Neutron spin-flip scattering observations of a resonance in the superconducting state is often taken as evidence of an unconventional superconducting state in which the gap changes sign $\Delta(k+Q)=-\Delta(k)$ for momentum transfers $Q$ which play an important role in the pairing. Recently questions regarding this identification for the Fe-pnictide superconductors have been raised and it has been suggested that $\Delta(k+Q)=\Delta(k)$. Here we propose that inelastic neutron or x-ray scattering measurements of the spectral weight of a phonon of momentum $Q$ can distinguish between these two pairing scenarios.