  We present a lattice calculation of the mass difference between neutron and
proton, for which we find $ M_n - M_p = 1.73(69) \, \text{MeV}$. This is
obtained at 1st order in the $QED$ coupling $\alpha_{EM}$ and in the mass
difference between $u$ and $d$ quarks $\frac{m_d-m_u}{\Lambda_{QCD}}$. We adopt
a purely hadronic scheme to renormalize the theory and provide a prescription
to separate the $QED$ and strong $IB$ contributions. The simulation is carried
out using the ETMC gauge configurations with $N_f=2+1+1$ dynamical quarks. We
extrapolate among $3$ values of the lattice spacing and pion masses in the
range $M_\pi \simeq 200 - 450 $ MeV.
