On the Time Momentum Representation of Hadronic Vacuum Polarization and $\boldsymbol{g_{\mu}-2}$

TL;DR

This paper introduces a new set of model-independent approximants for the time momentum representation of hadronic vacuum polarization, aiding lattice QCD calculations and comparison with experimental data for the muon g-2.

Contribution

The paper develops novel approximants tailored for TMR of HVP, enabling better extrapolation of lattice QCD results and comparison with data-driven estimates.

Findings

New approximants facilitate extrapolation of lattice QCD results.

They enable confrontation of LQCD results with full data-driven contributions.

The method improves the precision of HVP contribution estimates to g-2.

Abstract

We propose a new set of model independent approximants adapted to the time momentum representation (TMR) of hadronic vacuum polarization (HVP) and its contribution to $g_{\mu}-2$. They provide a way to extrapolate lattice QCD (LQCD) results obtained in an optimal time-region, to the full range required for an evaluation of the HVP contribution to $g_{\mu}-2$. They offer as well a new way to confront LQCD results in restricted TMR regions, with the full contribution obtained from data driven determinations.