  Recent multi-wavelength observations of gamma-ray burst afterglows observed
in the TeV energy range challenge the simplest Synchrotron Self-Compton (SSC)
interpretation of this emission, and are consistent with a single power-law
component spanning over eight orders of magnitude in energy. To interpret this
generic behaviour in the single-zone approximation without adding further free
parameters, we perform an exhaustive parameter space study using the public,
time-dependent, multi-messenger transport software AM3. This description
accounts for the radiation from non-thermal protons and the lepto-hadronic
cascade induced by pp- and p{\gamma}-interactions. We summarise the main
scenarios which we have found (SSC, Extended-syn, Proton-syn, pp-cascade, and
p{\gamma}-cascade), and discuss their advantages and limitations. We find that
possible high-density environments, as may be typical for surrounding molecular
cloud material, offer an alternative explanation for producing flat hard
(source) spectra up to and beyond energies of 10 TeV.
