Aims: We investigate the behavior of the frequency-centered light curves expected within the standard model of Gamma Ray Bursts allowing the maximum electron energy to be a free parameter permitted to take low values. Methods: We solve the spatially averaged kinetic equations which describe the simultaneous evolution of particles and photons, obtaining the multi-wavelength spectra as a function of time. From these we construct the frequency-centered light curves giving emphasis in the X-ray and optical bands. Results: We show that in cases where the maximum electron energy takes low values, the produced X-ray light curves show a plateau as the synchrotron component gives its place to the Synhro Self-Compton one in the X-ray band.
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