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

TL;DR

This paper investigates how finite-volume effects influence the calculation of the hadronic vacuum polarization contribution to muon g-2, revealing power-law volume dependence and providing estimates consistent with previous studies.

Contribution

It systematically analyzes the volume dependence of two-pion states in lattice calculations of muon g-2, highlighting different scaling behaviors and offering numerical estimates.

Findings

Finite-volume effects may exhibit power-law dependence, not exponential suppression.

Different volume scalings depend on the energy region considered.

Numerical estimates align with previous research.

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.