Isospin-breaking corrections and QED finite-volume effects for meson masses and the hadronic vacuum polarisation

The search for new physics requires experimental tests of the Standard Model, with the aim of identifying the limits of its validity. In an effort to produce more precise theoretical predictions with which to confront experimental results, lattice quantum chromodynamics calculations of some hadronic quantities are now reaching a precision at which isospin-breaking corrections become significant. An example is the hadronic vacuum polarisation (HVP) contribution to the muon anomalous magnetic moment. In the first part of this work, we compare two different methods for including electro-quenched QED corrections in lattice QCD calculations; a nonperturbative, stochastic approach, and a perturbative approach. We calculate isospin-breaking corrections to meson masses and the HVP on a 243⇥64 lattice with pion mass m⇡ = 340 MeV and inverse lattice spacing a1 = 1.78 GeV. We find agreement between results obtained using the two methods, up to O ↵2 effects which are present only in the data from the stochastic method. We find that the electromagnetic correction to the HVP contribution to the muon anomalous magnetic moment is less than 1% for the up quark and 0.1% for the strange quark, and the strong isospin-breaking correction is ⇡ 0.9%. These results constituted the first calculation of isospin-breaking corrections to the HVP, although this is an exploratory calculation at largerthan-physical light quark mass. Comparing the precision achievable with the same computational cost from each method, we find that the stochastic method can produce results with smaller statistical errors. Large systematic effects typically arise as a result of restricting QED to a finite volume, and correcting for these effects in lattice calculations including QED is an important area of study. In the second part of this work, we develop a new technique for numerical calculation of QED finite volume effects using efficient lattice simulations of scalar QED. We verify the method by comparing numerical calculations of QED finite volume effects for the self energy of a scalar particle and for the HVP with analytical calculations of the same effects. We find that our numerical method can produce results with sufficiently high precision to resolve discretisation effects, and that after correcting for these effects our results agree with the analytical predictions up to exponentially-suppressed finite volume effects neglected in the analytical calculations. We find that the leading QED finite volume correction to the HVP is O 1/L3 , meaning that these effects are negligible in lattice calculations of the HVP at current achievable precision. We also implement a new technique to suppress QED finite volume effects by modifying the photon action, and demonstrate that it can be used to suppress the relative size of scalar mass finite volume effects to less than 1%. The numerical method we have developed is applicable to a wider range of processes, towards cases where analytical computations would be difficult