Sea quark QED effects and twisted mass fermions

We show that maximally twisted mass fermions can be employed to regularize on the lattice the fully unquenched QCD+QED theory with vanishing $\theta$-term. We discuss how the critical mass of the up and down quarks can be conveniently determined beyond the electroquenched approximation by imposing that certain symmetries of continuum QCD+QED, which are broken by Wilson terms, get restored in the continuum limit. A mixed action setup is outlined that allows to extend beyond the electroquenched approximation the computation (with only O($a^2$) artifacts) of the leading isospin breaking corrections to physical observables using the RM123 method and (pure QCD) ETMC gauge ensembles with $N_f=2+1+1$ dynamical quark flavours.