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The current precision reached by lattice QCD calculations of low-energyhadronic observables, requires not only the introduction of electromagneticcorrections, but also control over all the potential systematic uncertaintiesintroduced by the lattice version of QED. Introducing a massive photon as aninfrared regulator in lattice QED, provides a well defined theory, dubbed QEDM,amenable to numerical evaluation [arXiv:1507.08916]. The photon mass is removedthrough extrapolation. In this contribution we scrutinise aspects of QEDM suchas the presence and fate of the zero modes contributions and we describe thedetermination of the photon mass corrections in finite and infinite volume. Wedemonstrate that the required extrapolations are well controlled usingnumerical data obtained on two ensembles which only differ in volume.

QED with massive photons for precision physics: zero modes and first result for the hadron spectrum