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.
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