  Most of the hadronic jet models for quasars (QSOs) and microquasars (MQs)
found in literature represent beams of particles (e.g. protons). These
particles interact with the matter in the stellar wind of the companion star in
the system or with crossing clouds, generating gamma-rays via proton-proton
processes. Our aim is to derive the particle distribution in the jet as seen by
the observer, so that proper computation of the $\gamma$-ray and neutrino
yields can be done. We use relativistic invariants to obtain the transformed
expressions in the case of a power-law and power-law with a cutoff particle
distribution in the beam. We compare with previous expressions used earlier in
the literature. We show that formerly used expressions for the particle
distributions in the beam as seen by the observer are in error, differences
being strongly dependent on the viewing angle. For example, for $\Gamma =10$
($\Gamma$ is the Lorentz factor of the blob) and angles larger than $\sim
20^o$, the earlier-used calculation entails an over-prediction (order of
magnitude or more) of the proton spectra for $E>\Gamma mc^2$, whereas it always
over-predicts (two orders of magnitude) the proton spectrum at lower energies,
disregarding the viewing angle. All the results for photon and neutrino fluxes
in hadronic models in beams that have made use of the earlier calculation are
affected. Given that correct gamma-ray fluxes will be in almost any case
significantly diminished in comparison with published results, and that the
time of observations in Cherenkov facilities grows with the square of the
flux-reduction factor in a statistically limited result, the possibility of
observing hadronic beams is undermined.
