Abstract
It is important to correct for finite-volume (FV) effects in the presence of QED, since these effects are typically large due to the long range of the electromagnetic interaction. We recently made the first lattice calculation of electromagnetic corrections to the hadronic vacuum polarisation (HVP). For the HVP, an analytical derivation of FV corrections involves a two-loop calculation which has not yet been carried out. We instead calculate the universal FV corrections numerically, using lattice scalar QED as an effective theory. We show that this method gives agreement with known analytical results for scalar mass FV effects, before applying it to calculate FV corrections for the HVP. This method for numerical calculation of FV effects is also widely applicable to quantities beyond the HVP.
Highlights
There is a discrepancy greater than 3σ between Standard Model predictions and experimental measurements of the muon g − 2 [1]
In an effort to reduce the theoretical uncertainty in the hadronic vacuum polarisation (HVP), lattice calculations of QED corrections to the HVP are in progress
We introduce a method for the efficient numerical calculation of universal QED finite volume corrections to hadronic observables, using lattice simulations of scalar QED as an effective field theory
Summary
There is a discrepancy greater than 3σ between Standard Model predictions and experimental measurements of the muon g − 2 [1] This is a tantalising hint of possible new physics, and new experiments at Fermilab and J-PARC are set to reduce the experimental error in the measurement [2, 3]. We have made an exploratory lattice calculation of QED corrections to the HVP [4,5,6], and there is an ongoing effort to calculate these corrections at the physical point [7]. Finite volume (FV) effects for QED are much larger than those for QCD, typically scaling with inverse powers of L rather than exponentially [10], and they must be taken into account in any physical calculation of QED effects on the lattice.
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