Isospin breaking corrections to hadronic observables from the lattice

 Lattice QCD calculation of some hadronic observables have reached the percent level of precision. Lattice simulations are mostly performed in the isospin-symmetric limit, i.e. in a fictitious universe in which the up and down quarks have the same mass and zero electric charge. However at the percent level of precision, isospin-breaking corrections cannot be neglected, and must be fully taken into account in the calculation of hadronic observables.

The inclusion of QED corrections is a game-changer in lattice QCD simulations in many respects, and can be implemented in different ways. After reviewing different possible approaches, I will focus on the ongoing effort of the RC* collaboration to calculate isospin breaking corrections to hadronic observables from lattice QCD+QED simulations. The signature of this long-term project is the use of C-periodic boundary conditions, which allow us to describe electrically-charged states in a finite volume in a rigorous way. After discussing the importance of C-periodic boundary conditions, I will review the status of our simulations, while highlighting the challenges that we need to face.