To elucidate the pairing states in Fe-based superconductors, we perform a 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 is 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 a self-energy driven resonancelike peak in the s₊₊-wave state proposed in our previous semimicroscopic study: The enhancement in χ^S(q,ω) due to the self-energy effect exceeds the suppression due to the coherence factor effect near the magnetic QCP. We stress that the hump structure in the s₊₊-wave state given by the FLEX method smoothly changes to a resonancelike sharp peak structure as the system approaches the magnetic QCP, which was not reported in our previous studies. The obtained ω and T dependence of χ^S(q,ω) in the s₊₊-wave states resembles the resonancelike feature in inelastic neutron scattering spectra recently observed in Na(Fe,Co)As and FeSe.

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