Anatomy of finite-volume effect on hadronic vacuum polarization contribution to muon g-2

Abstract

Low-energy spectrum relevant to the lattice calculation of hadronic vacuum polarization contribution to muon anomalous magnetic moment a_\mu is dominantly given by two-pion states satisfying L\"uscher's finite-volume quantization condition. Finite-volume effects from those states may exhibit power-law dependence on the volume, contrary to an exponential suppression as suggested by chiral effective theory. Employing the finite-volume state decomposition of Euclidean correlators, we systematically investigate the volume dependence and identify the different volume scalings depending on the region. Using phenomenological inputs for \pi \pi phase shift and time-like pion form factor, we obtain an estimate for the finite-volume effects on a_\mu, which is consistent with previous works. Numerical results are given for the ``window'' observables of a_\mu.