Towards a precise lattice determination of the leading hadronic contribution to (g − 2) μ

Michele Della Morte,Benjamin Jäger,Hartmut Wittig,Andreas Jüttner

doi:10.1007/jhep03(2012)055

Abstract

Abstract We report on our computation of the leading hadronic contribution to the anomalous magnetic moment of the muon using two dynamical flavours of non-perturbatively O(a) improved Wilson fermions. The strange quark is introduced in the quenched approximation. Partially twisted boundary conditions are applied to improve the momentum resolution in the relevant integral. Our results, obtained at three different values of the lattice spacing, allow for a preliminary study of discretization effects. We explore a wide range of lattice volumes, namely 2 fm ≤ L ≤ 3 fm, with pion masses from 600 to 280 MeV and discuss different chiral extrapolations to the physical point. We observe a non-trivial dependence of $a_\mu^{HLO}$ on m π especially for small pion masses. The final result, $a_\mu^{HLO} = 618\left( {64} \right) \times {10^{ - 10}}$ , is obtained by considering only the quark connected contribution to the vacuum polarization. We present a detailed analysis of systematic errors and discuss how they can be reduced in future simulations.

Highlights

JHEP03(2012)055 be determined experimentally, either from the cross section e+e− → hadrons or from the rate of hadronic τ -decays
We report on our computation of the leading hadronic contribution to the anomalous magnetic moment of the muon using two dynamical flavours of nonperturbatively O(a) improved Wilson fermions
The relevant lattice quantity receives contributions from quark disconnected diagrams, which are intrinsically noisy and difficult to estimate with good statistical accuracy at a reasonable numerical cost

Summary

Introduction

JHEP03(2012) be determined experimentally, either from the cross section e+e− → hadrons or from the rate of hadronic τ -decays. The relevant lattice quantity (the hadronic vacuum polarization discussed ) receives contributions from quark disconnected diagrams, which are intrinsically noisy and difficult to estimate with good statistical accuracy at a reasonable numerical cost. The dependence of the hadronic vacuum polarization on the momentum transfer must be accurately traced down to momenta of order m2μ and beyond This value is well below the lowest Fourier momentum (2π/L) which can be reached in current lattice QCD simulations. In [15, 16] we have shown how (partially) twisted boundary conditions [17,18,19] can be used to improve the momentum resolution in the connected part of the hadronic vacuum polarization, and we have obtained an estimate of the disconnected contribution in Chiral Perturbation Theory, addressing the first two systematic effects discussed above. The simulation parameters are collected in table 1, including the values of the twist angle θ, whose role will be explained below

Objectives

Results

Conclusion