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We argue that a multiband superconductor with sign-changing gaps may havemultiple spin resonances. We calculate the RPA-based spin resonance spectra ofa pnictide superconductor by using the five band tight-binding model orangle-resolved photoemission spectroscopy (ARPES) Fermi surface (FS) andexperimental values of superconducting (SC) gaps. The resonance spectra splitin both energy and momenta due to the effects of multiband and multiple gaps in$s^{\pm}-$pairing; the higher energy peak appears around the commensuratemomenta due to scattering between $\alpha-$FS to $\gamma/\delta-$FS pockets.The second resonance is incommensurate coming from $\beta-$FS to$\gamma/\delta-$FS scatterings and its $q-$vector is doping-dependent and henceon the FS topology. Energies of both resonances $\omega^{1,2}_{res}$ arestrongly doping dependent and are proportional to the gap amplitudes at thecontributing FSs. We also discuss the evolution of the spin excitation spectrawith various other possible gap symmetries, which may be relevant when eitherboth the electron pockets or both the hole pockets completely disappear.

Two energy scales in the magnetic resonance spectrum of electron and hole doped pnictide superconductors