Isospin breaking effects from lattice QCD and QED
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 hadronic and nuclear physics. For example, the neutron-proton mass difference is responsible for the stability of the hydrogen atom and it is an important initial condition of Big-Bang nucleosynthesis. Even if these effects are well known experimentally, a theoretical determination from first principles is still an open problem because of the non-perturbative nature of low-energy QCD.
In this talk I will present a way to include isospin breaking effects in lattice QCD simulation in order to perform ab-initio computations of isospin mass splittings. The main challenge is to formulate the electromagnetic interaction on a finite and periodic lattice and to couple it to lattice QCD. Finally, I will present the results of the Budapest-Marseille-Wuppertal collaboration for the octet baryon mass splittings and the individual up and down quark masses.