Speaker: Antonin Portelli

Lattice QCD calculations began recently to produce theoretical predictions with sub-percent precision of non-perturbative hadronic observables. It means that these simulations technics may have reached the necessary accuracy to predict the small corrections coming from the breaking of isospin symmetry. Isospin symmetry is explicitly broken in the Standard Model by the non-zero differences of mass and electric charge between the up and down quarks. Both of these corrections are expected to have a comparable size of the order of one percent relatively to hadronic energies. Although these contributions are small, they play a crucial role in the structure of nuclear matter. Indeed, the positive mass difference between the neutron and the proton is responsible for the stability of the hydrogen atom and it allows the beta decay of the neutron which is a vital process in nuclear transmutation. As we will see, one of the main challenge in including isospin breaking effect in lattice simulations is to take into account the electromagnetic interaction in the calculation.

In this talk I will explain how to define properly QCD and QED on a finite and discrete space-time. I will then consider the different approaches to compute on the lattice correlation functions of QCD+QED observables. I will then review the recent lattice results concerning the isospin corrections to the light hadron spectrum.