To elucidate the pairing states in Fe-based superconductors, we perform careful calculation of the dynamical spin susceptibility χ S (q, ω) at very low temperatures (T > ∼ 1meV). The feedback effect on both the self-energy and χ S (q, ω) from the superconducting gap are self-consistently analyzed based on the fluctuation-exchange (FLEX) approximation. In the s±-wave state, which has sign-reversal in the gap function, χ S (q, ω) at the nesting momentum q = Q shows a resonance peak even when the system is away from the magnetic quantum-critical-point (QCP). In the s++-wave state that has no sign-reversal, χ S (q, ω) shows a large hump structure when the system is close to the magnetic QCP. This result confirms the validity of self-energy driven resonance-like peak in s++-wave state proposed in our previous semi-microscopic study: The enhancement in χ S (q, ω) due to self-energy effect exceeds the suppression due to coherence factor effect near magnetic QCP. We stress that the hump structure in the s++-wave state given by the FLEX method smoothly changes to resonancelike sharp peak structure as the system approaches magnetic QCP, which was not reported in our previous studies. The obtained ω-and T -dependences of χ S (q, ω) in the s++-wave state resemble to the resonance-like feature in inelastic neutron scattering spectra recently observed in Na(Fe,Co)As and FeSe.

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