Abstract
One of the more important systematic effects affecting lattice computations of the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon, $a_\mu^{\rm HVP}$, is the distortion due to a finite spatial volume. In order to reach sub-percent precision, these effects need to be reliably estimated and corrected for, and one of the methods that has been employed for doing this is finite-volume chiral perturbation theory. In this paper, we argue that finite-volume corrections to $a_\mu^{\rm HVP}$ can, in principle, be calculated at any given order in chiral perturbation theory. More precisely, once all low-energy constants needed to define the Effective Field Theory representation of $a_\mu^{\rm HVP}$ in infinite volume are known to a given order, also the finite-volume corrections can be predicted to that order in the chiral expansion.
Highlights
Recent years have seen renewed efforts to obtain a more reliable and more precise Standard-Model estimate of the muon anomalous magnetic moment
We considered the effective field theory approach to the hadronic vacuum polarization contribution to the muon anomalous magnetic moment, aHμ VP
Our primary aim was a better understanding of how the evaluation of finite-volume effects works in an effective field theory (EFT) framework, but this led us to a discussion of the counterterm structure needed for a complete EFT representation of aHμ VP in infinite volume
Summary
Recent years have seen renewed efforts to obtain a more reliable and more precise Standard-Model estimate of the muon anomalous magnetic moment. In a finite volume Πðq2Þ takes the form of an expansion in powers of q2 in ChPT, and one might fear that the FV part of aHμ VP, defined as in Eq (1.1) with Πðq2Þ replaced by its FV part, diverges beyond NNLO in ChPT.3 This concern, that the computation of higher-order FV corrections to aHμ VP in ChPT might break down, was raised in Ref. This is the situation encountered in lattice QCD computations of aHμ VP, in which only Πðq2Þ is calculated on the lattice and in a finite volume It is beyond the scope of this paper to give an all-order proof, or even to carry out explicit ChPT calculations beyond NNLO.
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