  Quantum field theories with purely virtual particles, or fakeons, require
suitable modifications in one-loop integrals. We provide the expressions for
the modified scalar integrals in the case of the bubble, triangle and box
diagrams. The new functions are defined by means of their difference with the
`t Hooft-Veltman scalar integrals. The modifications do not affect the
derivation of the Passarino-Veltman reduction and one-loop integrals with
nontrivial numerators can be decomposed in the same fashion. Therefore, the new
functions can be directly used to study the phenomenology of any models with
standard particles and fakeons. We compare our results with standard amplitudes
and show that the largest differences are often localized in relatively small
energy ranges and are characterized by additional nonanalyticities. Finally, we
give explicit examples in the context of a toy model, where cross sections and
decay widths of standard particles are modified by the presence of fakeons.
