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_μis dominantly given by two-pion states satisfying Lüscher'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 ππphase shift and time-like pion form factor, we obtain an estimate for the finite-volume effects on a_μ, which is consistent with previous works. Numerical results are given for the ``window'' observables of a_μ.

a few errors corrected; precision issues fixed