  GRB 221009A has posed a significant challenge to our current understanding of
the mechanisms that produce TeV photons in gamma-ray bursts (GRB). On one hand,
the Klein-Nishina (KN) effect of the inverse Compton scattering leads to less
efficient energy losses of high-energy electrons. In the other hand, at a
redshift of 0.151, the TeV spectrum of GRB 221009A undergoes significant
absorption by the Extragalactic Background Light (EBL). Therefore, the
observation of 18-TeV and 250-TeV photons in this event implies the presence of
enormous photon fluxes at the source, which cannot be easily generated by the
Synchrotron Self-Compton mechanism in external shocks. As an alternative, some
authors have suggested the possibility of converting the TeV-photons into
Axion-like particles (ALPs) at the host galaxy, in order to avoid the effects
of EBL absorption, and then reconverting them into photons within the Milky
Way. While this solution relaxes the requirement of very-high photon fluxes,
the KN effect still poses a challenge. Previously, we have showed that the
injections of ALPs could explain the observation of 18-TeV photons. Here, we
include the energy dependence of the survival probability to determine the
spectral conditions that would be required for the injection of such ALPs,
limit the ALP's candidate region, and discuss the implications in the maximum
particle rate for different light-curve assumptions.
