QED on the lattice and numerical perturbative computation of $g-2$

TL;DR

This paper calculates the electron g factor to five-loop order in quenched QED on the lattice, analyzing finite volume effects and proposing an efficient simulation strategy for high-precision results.

Contribution

It introduces a novel lattice computation approach for the five-loop electron g factor in quenched QED, including finite volume correction analysis and regularization strategies.

Findings

Finite volume corrections depend on IR regularization method.

Finite photon mass regularization suppresses finite volume effects exponentially.

Feasibility of high-order lattice calculations demonstrated with small lattices.

Abstract

We compute the electron $g$ factor to the $\mathcal{O}(\alpha^5)$ order on the lattice in quenched QED. We first study finite volume corrections in various IR regularization methods to discuss which regularization is optimal for our purpose. We find that in QED$_L$ the finite volume correction to the effective mass can have different parametric dependences depending on the size of Euclidean time $t$ and match the `naive on-shell result' only at very large $t$ region, $t \gg L$. We adopt finite photon mass regularization to suppress finite volume effects exponentially and also discuss our strategy for selecting simulation parameters and the order of extrapolations to efficiently obtain the $g$ factor. We perform lattice simulation using small lattices to test feasibility of our calculation strategy. This study can be regarded as an intermediate step toward giving the five-loop coefficient independently of the preceding studies.