Study of the Couplings of QED and QCD from the Adler Function

TL;DR

This paper uses lattice QCD simulations to calculate the Adler function across various momentum transfers, aiming to reduce uncertainties in the QED coupling's running and to explore the strong coupling constant at high energies.

Contribution

It provides a lattice QCD determination of the Adler function over a broad Q^2 range, including valence quark effects, and compares results with phenomenology and perturbation theory.

Findings

Lattice results agree with phenomenological data at intermediate Q^2.

The Adler function fits well with perturbation theory at high Q^2.

Potential to determine the strong coupling constant from lattice data.

Abstract

The contribution from hadronic vacuum polarisation effects is responsible for a large fraction of the theoretical uncertainty in the running of the QED coupling. The current level of uncertainty has become a limitation for electroweak precision tests. We use lattice QCD simulations with two flavours of O$(a)$ improved Wilson fermions to determine the Adler function in a broad range of the momentum transfer $Q^2$. The running of the QED coupling, including valence contributions from $u$, $d$, $s$ and $c$ quarks, is compared to phenomenological results at intermediate $Q^2$ values. In the large $Q^2$ regime, the lattice determination of the Adler function is fitted to perturbation theory in order to examine the feasibility of a determination of the strong coupling constant.