Hadronic vacuum polarization contribution to the anomalous magnetic moments of leptons from first principles

TL;DR

This paper presents a first-principles lattice QCD calculation of the leading hadronic vacuum polarization contributions to the anomalous magnetic moments of the electron, muon, and tau, achieving high precision with physical quark masses and large volumes.

Contribution

It provides the first comprehensive lattice QCD determination of these contributions at physical parameters, including all contractions and continuum extrapolation.

Findings

Precise values for electron, muon, and tau anomalous magnetic moments.

Inclusion of all quark flavors and contractions.

Systematic and statistical uncertainties quantified.

Abstract

We compute the leading, strong-interaction contribution to the anomalous magnetic moment of the electron, muon and tau using lattice quantum chromodynamics (QCD) simulations. Calculations include the effects of $u$, $d$, $s$ and $c$ quarks and are performed directly at the physical values of the quark masses and in volumes of linear extent larger than $6\,\mathrm{fm}$. All connected and disconnected Wick contractions are calculated. Continuum limits are carried out using six lattice spacings. We obtain $a_e^\mathrm{LO-HVP}=189.3(2.6)(5.6)\times 10^{-14}$, $a_\mu^\mathrm{LO-HVP}=711.1(7.5)(17.4)\times 10^{-10}$ and $a_\tau^\mathrm{LO-HVP}=341.0(0.8)(3.2)\times 10^{-8}$, where the first error is statistical and the second is systematic.