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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 $gamma^* gamma^* to$ 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.
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The quark-connected part of the hadronic light-by-light scattering contribution to the muons anomalous magnetic moment is computed using lattice QCD with chiral fermions. We report several significant algorithmic improvements and demonstrate their effectiveness through specific calculations which show a reduction in statistical errors by more than an order of magnitude. The most realistic of these calculations is performed with a near-physical, $171$ MeV pion mass on a $(4.6;mathrm{fm})^3$ spatial volume using the $32^3times 64$ Iwasaki+DSDR gauge ensemble of the RBC/UKQCD Collaboration.
For reliable comparison of the standard model prediction to the muon g-2 with its experimental value, the hadronic light-by-light scattering (HLbL) contribution must be calculated by lattice QCD simulation. HLbL contribution has many types of disconnected-type diagrams. Here, we start with recalling the point that must be taken care of in every method to calculate them by lattice QCD, and present one concrete method called nonperturbative QED method.
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_{pi^0 gamma^* gamma^*}(q_1^2, 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 gamma^* gamma^* -> hadrons fusion cross sections and then compared with phenomenological models.
The form factor that yields the light-by-light scattering contribution to the muon anomalous magnetic moment is computed in lattice QCD+QED and QED. A non-perturbative treatment of QED is used and is checked against perturbation theory. The hadronic contribution is calculated for unphysical quark and muon masses, and only the diagram with a single quark loop is computed. Statistically significant signals are obtained. Initial results appear promising, and the prospect for a complete calculation with physical masses and controlled errors is discussed.
The hadronic light-by-light scattering contribution to the muon g-2 is the most troublesome component of its theoretical prediction; (1) it cannot be determined from the other measurable quantities, (2) the dimensional argument and the estimation based on hadronic models imply that the magnitude of this contribution may be comparable to the discrepancy between the standard model prediction and the experimental value. The direct approach to evaluate the hadronic light-by-light scattering contribution requires the evaluation of the correlation function of {it four} hadronic electromagnetic currents, and the summation of it over two independent four-momenta of off-shell photons, which is far from the reach of direct lattice simulation. Here we propose an alternative method using combined (QCD + QED) lattice simulations to evaluate the hadronic light-by-light scattering contribution.
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