Abstract
Radiative corrections for several heavy fermions bound together via the Higgs boson exchange are studied. The fermion bags considered include 12, or fewer, fermions occupying the lowest S_{1/2} shell. It is shown that for `moderately heavy' fermions with masses 0.4< m c^2< 1 TeV the radiative corrections are small, 10^{-2}, and have an attractive nature. Therefore they do not put existence of the fermion bag in doubt. This proves that these fermion bags can exist in nature.
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