Lattice QCD and the anomalous magnetic moment of the muon

TL;DR

This paper reviews the progress of lattice QCD calculations in determining the hadronic contributions to the muon's anomalous magnetic moment, aiming to resolve the discrepancy with experimental measurements and test the Standard Model.

Contribution

It provides a comprehensive overview of current lattice QCD methods and results for calculating the hadronic vacuum polarization and light-by-light scattering contributions to a_mu.

Findings

Lattice QCD estimates of a_mu^hvp have reached a few percent accuracy.

Progress has been made in reducing the uncertainty of a_mu^hlbl to 10-15%.

Systematic effects in lattice calculations are identified and discussed.

Abstract

The anomalous magnetic moment of the muon, a_mu, has been measured with an overall precision of 540 ppb by the E821 experiment at BNL. Since the publication of this result in 2004 there has been a persistent tension of 3.5 standard deviations with the theoretical prediction of a_mu based on the Standard Model. The uncertainty of the latter is dominated by the effects of the strong interaction, notably the hadronic vacuum polarisation (HVP) and the hadronic light-by-light (HLbL) scattering contributions, which are commonly evaluated using a data-driven approach and hadronic models, respectively. Given that the discrepancy between theory and experiment is currently one of the most intriguing hints for a possible failure of the Standard Model, it is of paramount importance to determine both the HVP and HLbL contributions from first principles. In this review we present the status of lattice QCD calculations of the leading-order HVP and the HLbL scattering contributions, a_mu^hvp and a_mu^hlbl. After describing the formalism to express a_mu^hvp and a_mu^hlbl in terms of Euclidean correlation functions that can be computed on the lattice, we focus on the systematic effects that must be controlled to achieve a first-principles determination of the dominant strong interaction contributions to a_mu with the desired level of precision. We also present an overview of current lattice QCD results for a_mu^hvp and a_mu^hlbl, as well as related quantities such as the transition form factor for pi0 -> gamma*gamma*. While the total error of current lattice QCD estimates of a_mu^hvp has reached the few-percent level, it must be further reduced by a factor 5 to be competitive with the data-driven dispersive approach. At the same time, there has been good progress towards the determination of a_mu^hlbl with an uncertainty at the 10-15%-level.