12 LGRBs best fitted by a 2SBPL (Table 1) shown with orange symbols. Their value of R_E = E_break/E_peak is shown vs. the value of the index α_Band that is obtained by fitting their spectrum with a Band function. SGRBs (whose spectrum is always best fitted by the Band function) are represented here assuming that, if the underlying spectrum were 2SBPL, it would be expected to have E_break ∼ E_peak (green symbols). The orange dashed lines show the results of simulations (see Sect. 4.2); blue arrows represent the upper and lower limits on R_E for the 15 LGRBs whose spectra are best fitted by Band (see Sect. 4.3).