  We investigate single-particle excitation properties in the normal state of a
two-band superconductor or superfluid throughout the Bardeen-Cooper-Schrieffer
(BCS) to Bose-Einstein-condensation (BEC) crossover, within the many-body
T-matrix approximation for multi-channel pairing fluctuations. We address the
single-particle density of states and the spectral functions consisting of two
contributions associated with a waekly interacting deep band and a strongly
interacting shallow band, relevant for iron-based multiband superconductors and
multicomponent fermionic superfluids. We show how the pseudogap state in the
shallow band is hidden by the deep band contribution throughout the two-band
BCS-BEC crossover. Our results could explain the missing pseudogap in recent
scanning tunneling microscopy experiments in FeSe superconductors.
