spectrum with spectral indexes $\Gamma_{\rm{e,1}}$/$\Gamma_{\rm{e,2}}$ with an exponential cut-off. The break at energy $E_{\rm{b}}$ is assumed to be due to cooling so we set $\Gamma_{\rm{e,2}}$ = $\Gamma_{\rm{e,1}}$ + 1 while the cut-off defines the maximum attainable energy of the particles $E_{\rm{max,e}}$. The proton spectrum is described as a power law with spectral index $\Gamma_{\rm{p}}$ with an exponential cut-off $E_{\rm{max,p}}$. In our models we consider by default the CMB as the only photon seed for IC scattering.\

### Leptonic scenario

We first investigate the leptonic scenario for which we vary the values of the magnetic field $B$, the total energy budget in electrons $W_{\rm{e}}$ and protons $W_{\rm{p}}$, and the break and maximum energy of the particles. Figure \[fig:Fit\_naima\_SNR\_Lepto\] (left) shows one of the combinations that simultaneously fits the radio and the $\gamma$-ray data. Since this solution is not unique, we report in Table \[tab:Phys\_param\] the range of permitted values of these parameters. For clarity, we fix the total energy in protons to W$_{\rm{p}}$ = 5 $\times$ 10$^{49}$ erg (corresponding to 10% of $E_{\rm{SN}}$) and we report the range of permitted values of the electron-proton ratio $K_{\rm{e-p}}$. Since the maximum energy of protons is always higher than that of electrons, which suffer 