Abstract
An analytic expression is derived for the leading-order finite-volume effects arising in lattice QCD calculations of the hadronic-vacuum-polarization contribution to the muon’s magnetic moment . For calculations in a finite spatial volume with periodicity , admits a transseries expansion with exponentially suppressed scaling. Using a Hamiltonian approach, we show that the leading finite-volume correction scales as with a prefactor given by the (infinite-volume) Compton amplitude of the pion, integrated with the muon-mass-dependent kernel. To give a complete quantitative expression, we decompose the Compton amplitude into the spacelike pion form factor and a multiparticle piece. We determine the latter through next-to leading order in chiral perturbation theory and find that it contributes negligibly and through a universal term that depends only on the pion decay constant, with all additional low-energy constants dropping out of the integral.
- Received 3 May 2019
DOI:https://doi.org/10.1103/PhysRevLett.123.172001
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Published by the American Physical Society