Speaker
Description
Many low-energy precision tests of hadronic observables in the Standard Model now require the inclusion of isospin-breaking corrections due to light-quark mass differences and electromagnetism (QED). Isospin breaking typically appears for any prediction with better than percent-level precision, where examples are particle decay rates, hadron mass differences and the muon anomalous magnetic moment. Lattice quantum field theory is a first-principles approach to calculate hadronic observables in a systematically improvable fashion. In this talk I will present how normalising flows and machine learning can be used to calculate all-orders electromagnetic corrections in lattice field theory, generally bypassing the complexity in Wick-contraction diagrams needed at fixed order. The new method is applied to lattice scalar QED in two, three, and four spacetime dimensions, yielding estimates with significantly reduced variance with respect to standard methods. Flows can be trained using small lattice geometries and subsequently evaluated on much larger lattice geometries while maintaining good efficiency. A generalisation to theories with fermions is envisaged, suggesting a path to applications in challenging field theories including lattice QCD. The talk is based on [hep-lat/2605.22444].