Reconciling observed gamma-ray burst prompt spectra with synchrotron radiation?

Context. Gamma-ray burst emission in the prompt phase is often interpreted as synchrotron radiation from high-energy electrons accelerated in internal shocks. Fast synchrotron cooling of a power-law distribution of electrons leads to the prediction that the slope below the spectral peak has a photon index α = −3/2 (N(E) ∝ Eα). However, this differs significantly from the observed median value α ≈ −1. This discrepancy has been used to argue against this scenario.