Leading-order hadronic contributions to the lepton anomalous magnetic moments from the lattice

Florian Burger,Xu Feng,Marcus Petschlies,Dru B Renner,Karl Jansen,Grit Pientka,G D’Ambrosio,S Mastroianni,G Venanzoni,P Massarotti,M Iacovacci,M Passera

doi:10.1051/epjconf/201611801029

Abstract

The hadronic leading-order (hlo) contribution to the lepton anomalous magnetic moments $a_l^\mathrm{hlo}$ of the Standard Model leptons still accounts for the dominant source of the uncertainty of the Standard Model estimates. We present the results of an investigation of the hadronic leading order anomalous magnetic moments of the electron, muon and tau lepton from first principles in twisted mass lattice QCD. With lattice data for multiple pion masses in the range $230 \mathrm{~MeV} \lesssim m_{PS} \lesssim 490 \mathrm{~MeV}$, multiple lattice volumes and three lattice spacings we perform the extrapolation to the continuum and to the physical pion mass and check for all systematic uncertainties in the lattice calculation. As a result we calculate $a_{l}^\mathrm{hlo}$ for the three Standard Model leptons with controlled statistical and systematic error in agreement with phenomenological determinations using dispersion relations and experimental data. In addition, we also give a first estimate of the hadronic leading order anomalous magnetic moments from simulations directly at the physical value of the pion mass.

Highlights

Lattice QCD offers the opportunity to study hadronic contributions to electroweak observables from first principles
The calculation shown here can be adapted to a broad range of applications for a variety of quantities such as the next-to-leading order vacuum-polarization type contributions to the lepton anomalous magnetic moments, the hadronic running of the electroweak couplings αQED and sin2 (θ), the Adler function or ΛQCD amongst others [25]
With this contribution we report on the determination of the hadronic leading order anomalous magnetic moments of all three Standard Model leptons by the ETM Collaboration with N f = 2 + 1 + 1 dynamical quarks

Summary

Introduction

Lattice QCD offers the opportunity to study hadronic contributions to electroweak observables from first principles. The lattice calculation generically provides us with data points for the vacuum polarization function for a finite set of discrete, nonzero momenta.

Results

Conclusion