  Observations of long duration gamma-ray bursts (GRBs) with TeV emission
during their afterglow have been on the rise. Recently, GRB 221009A, the most
energetic GRB ever observed, was detected by the {LHAASO} experiment in the
energy band 0.2 - 7 TeV. Here, we interpret its afterglow in the context of a
hybrid model in which the TeV spectral component is explained by the
proton-synchrotron process while the low energy emission from optical to X-ray
is due to synchrotron radiation from electrons. We constrained the model
parameters using the observed optical, X-ray and TeV data. By comparing the
parameters of this burst and of GRB 190114C, we deduce that the VHE emission at
energies $\geq$ 1 TeV in the GRB afterglow requires large explosion kinetic
energy, $E \gtrsim 10^{54}$~erg and a reasonable circumburst density, $n\gtrsim
10$~cm$^{-3}$. This results in a small injection fractions of particles
accelerated to a power-law, $\sim 10^{-2}$. {A significant fraction of shock
energy must be allocated to a near equipartition magnetic field, $\epsilon_B
\sim 10^{-1}$, while electrons should only carry a small fraction of this
energy, $\epsilon_e \sim 10^{-3}$. Under these conditions required for a proton
synchrotron model, namely $\epsilon_B \gg \epsilon_e$, the SSC component is
substantially sub-dominant over proton-synchrotron as a source of TeV photons.}
These results lead us to suggest that proton-synchrotron process is a strong
contender for the radiative mechanisms explaining GRB afterglows in the TeV
band.
