What emits the TeV photons in gamma-ray burst afterglows?
In plain words
Some bursts emit photons above $1e12\,\mathrm{eV}$ for hours after the explosion, more energetic than electrons spiraling in the shock's magnetic field are thought able to make.
Precise statement
GRB 180720B, 190114C, 190829A and 221009A (photons up to $\sim 1\mathrm{e}13\,\mathrm{eV}$ with LHAASO) show TeV afterglows. Determine whether synchrotron self-Compton emission from the forward shock, synchrotron emission beyond the classical maximum ($\sim 50\,\Gamma\,\mathrm{MeV}$ for bulk Lorentz factor $\Gamma$), or hadronic processes produce them, and what the resolved TeV onset implies for the initial Lorentz factor and the surrounding density. Answer: a mechanism with physical parameters consistent across all TeV bursts.
What would settle it
Simultaneous X-ray and TeV spectra over the afterglow of several bursts that either show the separate inverse-Compton component or a single synchrotron spectrum.
Status in the literature
2021: H.E.S.S. found the X-ray and TeV spectra of GRB 190829A consistent with one synchrotron component extending past the standard maximum energy; 2023: LHAASO resolved the TeV onset of GRB 221009A.