I will report the current status of RBC/UKQCD's calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment. I will review quark connected and disconnected contributions as well as progress on QED and strong isospin-breaking contributions at the physical pion mass. I will furthermore present a combined lattice and R-ratio analysis.

After a brief introduction on ongoing experimental and theoretical activities on $(g-2)_\mu$, I will describe recent progress in approaching the calculation of the hadronic light-by-light contribution with dispersive methods. I will discuss general properties of the four-point function of the electromagnetic current in QCD, its Lorentz decomposition and dispersive representation. Based on these I ... More