Time-kernel for lattice determinations of NLO hadronic vacuum polarization contributions to the muon $g$-$2$

TL;DR

This paper develops a new time-kernel method for lattice QCD calculations of the NLO hadronic vacuum polarization contributions to the muon g-2, improving accuracy for large time values.

Contribution

It introduces analytical and numerical series expansions for the time-kernel, enhancing lattice QCD computations of muon g-2 at NLO.

Findings

Series expansions improve large-time accuracy

Method overcomes limitations of naive asymptotic expansions

Applicable to lattice QCD determinations of muon g-2

Abstract

We study the time-momentum representation of the kernel needed to compute hadronic vacuum polarization contributions to the muon $g$-$2$ in the space-like region at next-to-leading order. For small values of the time, we present analytical series expansions; for large values of the time, we present numerical series expansions which overcome the problems showed by na\"ive asymptotic expansions. These results are to be employed in lattice QCD determinations of hadronic vacuum polarization contributions to the muon $g$-$2$ at next-to-leading order.