No abstract

The anomalous magnetic moment of the muon currently exhibits a discrepancy of about three standard deviations between the experimental value and recent Standard Model predictions. The theoretical uncertainty is dominated by the hadronic vacuum polarization and the hadronic lightby-light (HLbL) scattering contributions, where the latter has so far only been fully evaluated using different models. To pave the way for a lattice calculation of HLbL, we present an expression for the HLbL contribution to g − 2 that involves a multidimensional integral over a position-space QED kernel function in the continuum and a lattice QCD four-point correlator. We describe our semi-analytic calculation of the kernel and test the approach by evaluating the π 0 -pole contribution in the continuum. 34th annual International Symposium on Lattice Field Theory

We report calculations of hadronic light-by-light scattering amplitudes via lattice QCD evaluation of Euclidean four-point functions of vector currents. These initial results include only the fully quark-connected contribution. Particular attention is given to the case of forward scattering, which can be related via dispersion relations to the γ * γ * → hadrons cross section, and thus allows lattice data to be compared with phenomenology. We also present a strategy for computing the hadronic light-by-light contribution to the muon anomalous magnetic moment.

We briefly review several activities at Mainz related to hadronic light-by-light scattering (HLbL) using lattice QCD. First we present a position-space approach to the HLbL contribution in the muon g−2, where we focus on exploratory studies of the pion-pole contribution in a simple model and the lepton loop in QED in the continuum and in infinite volume. The second part describes a lattice calculation of the double-virtual pion transition form factor F π 0 γ * γ * (q 2 1 , q 2 2 ) in the spacelike region with photon virtualities up to 1.5 GeV 2 which paves the way for a lattice calculation of the pion-pole contribution to HLbL. The third topic involves HLbL forward scattering amplitudes calculated in lattice QCD which can be described, using dispersion relations (HLbL sum rules), by γ * γ * → hadrons fusion cross sections and then compared with phenomenological models.

Position-space approach to the HLbL contribution to the muon g − 2 on the lattice Nils Asmussen

The well-known discrepancy in the muon g − 2 between experiment and theory demands further theory investigations in view of the upcoming new experiments. One of the leading uncertainties lies in the hadronic light-bylight scattering contribution (HLbL), that we address with our position-space approach. We focus on exploratory studies of the pion-pole contribution in a simple model and the fermion loop without gluon exchanges in the continuum and in infinite volume. These studies provide us with useful information for our planned computation of HLbL in the muon g − 2 using full QCD.

Hadronic light-by-light scattering in the anomalous magnetic moment of the muon a µ is one of two hadronic effects limiting the precision of the Standard Model prediction for this precision observable, and hence the new-physics discovery potential of direct experimental determinations of a µ . In this contribution, we report on recent progress in the calculation of this effect achieved both via dispersive and lattice QCD methods.

Hadronic light-by-light scattering is one of the virtual processes that causes the gyromagnetic factor g of the muon to deviate from the value of two predicted by Dirac’s theory. This process makes one of the largest contributions to the uncertainty of the Standard Model prediction for the muon (g − 2). Lattice QCD allows for a first-principles approach to computing this non-perturbative effect. In order to avoid power-law finite-size artifacts generated by virtual photons in lattice simulations, we follow a coordinate-space approach involving a weighted integral over the vertices of the QCD four-point function of the electromagnetic current carried by the quarks. Here we present in detail the semi-analytical calculation of the QED part of the amplitude, employing position-space perturbation theory in continuous, infinite four-dimensional Euclidean space. We also provide some useful information about a computer code for the numerical implementation of our approach that has been made public at https://github.com/RJHudspith/KQED.