Application of effective field theory to finite-volume effects in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>a</mml:mi><mml:mi>μ</mml:mi><mml:mrow><mml:mi>HVP</mml:mi></mml:mrow></mml:msubsup></mml:math>
Christopher Aubin, Thomas Blum, Maarten Golterman, Santiago Peris
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, ${a}_{\ensuremath{\mu}}^{\mathrm{HVP}}$, is the distortion due to a finite spatial volume. In order to reach subpercent 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 ${a}_{\ensuremath{\mu}}^{\mathrm{HVP}}$ 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 ${a}_{\ensuremath{\mu}}^{\mathrm{HVP}}$ in infinite volume are known to a given order, also the finite-volume corrections can be predicted to that order in the chiral expansion.