  We discuss the new surprising observational results that indicate quite
convincingly that the prompt emission of Gamma-Ray Bursts (GRBs) is due to
synchrotron radiation produced by a particle distribution that has a low energy
cut-off. The evidence of this is provided by the low energy part of the
spectrum of the prompt emission, that shows the characteristic F(nu) \propto
nu^(1/3) shape followed by F(nu) \propto nu^(-1/2) up to the peak frequency.
This implies that although the emitting particles are in fast cooling, they do
not cool completely. This poses a severe challenge to the basic ideas about how
and where the emission is produced, because the incomplete cooling requires a
small value of the magnetic field, to limit synchrotron cooling, and a large
emitting region, to limit the self-Compton cooling, even considering
Klein-Nishina scattering effects. Some new and fundamental ingredient is
required for understanding the GRBs prompt emission. We propose
proton-synchrotron as a promising mechanism to solve the incomplete cooling
puzzle.
