We perform a lattice QCD calculation of the hadronic light-by-light scattering amplitude in a broad kinematical range. At forward kinematics, the results are compared to a phenomenological analysis based on dispersive sum rules for light-by-light scattering. The size of the pion pole contribution is investigated for momenta of typical hadronic size. The presented numerical methods can be used to compute the hadronic light-by-light contribution to the anomalous magnetic moment of the muon. Our calculations are carried out in two-flavor QCD with the pion mass in the range of 270-450 MeV and contain so far only the diagrams with fully connected quark lines.

We provide an updated analysis of the forward J/ψ-p scattering amplitude, relating its imaginary part to γp → J/ψp and γp → ccX cross section data, and calculating its real part through a once-subtracted dispersion relation. From a global fit to both differential and total cross section data, we extract a value for the spin-averaged J/ψ-p s-wave scattering length a ψp = 0.046 ± 0.005 fm, which can be translated into a J/ψ binding energy in nuclear matter of B ψ = 2.7 ± 0.3 MeV. We estimate the forward-backward asymmetry to the γp → e − e + p process around the J/ψ resonance, which results from interchanging the leptons in the interference between the J/ψ production and the Bethe-Heitler mechanisms. We show that to good approximation this asymmetry depends linearly on a ψp , and can reach values around -25% for forthcoming J/ψ threshold production experiments at Jefferson Lab. Its measurement can thus provide a very sensitive observable for a refined extraction of a ψp .

We evaluate the forward Compton scattering off the proton, based on Kramers-Kronig kind of relations which express the Compton amplitudes in terms of integrals of total photoabsorption cross sections. We obtain two distinct fits to the world data on the unpolarized total photoabsorption cross section, and evaluate the various spin-independent sum rules using these fits. For the sum of proton electric and magnetic dipole polarizabilities, governed by the Baldin sum rule, we obtain the following average (between the two fits): αE1 + βM1 = 14.0(2) × 10 −4 fm 3 . An analogous sum rule involving the quadrupole polarizabilities of the proton is evaluated too. The spin-independent forward amplitude of proton Compton scattering is evaluated in a broad energy range. The results are compared with previous evaluations and the only experimental data point for this amplitude (at 2.2 GeV). We remark on sum rules for the elastic component of polarizabilities.

The hadronic contribution to the eight forward amplitudes of light-by-light scattering (γ * γ * → γ * γ * ) is computed in lattice QCD. Via dispersive sum rules, the amplitudes are compared to a model of the γ * γ * → hadrons cross sections in which the fusion process is described by hadronic resonances. Our results thus provide an important test for the model estimates of hadronic light-by-light scattering in the anomalous magnetic moment of the muon, a HLbL µ . Using simple parametrizations of the resonance M → γ * γ * transition form factors, we determine the corresponding monopole and dipole masses by performing a global fit to all eight amplitudes. Together with a previous dedicated calculation of the π 0 → γ * γ * transition form factor, our calculation provides valuable information for phenomenological estimates of a HLbL µ . The presented calculations are performed in two-flavor QCD with pion masses extending down to 190 MeV at two different lattice spacings. In addition to the fully connected Wick contractions, on two lattice ensembles we also compute the (2+2) disconnected class of diagrams, and find that their overall size is compatible with a parameter-free, large-N inspired prediction, where N is the number of colors. Motivated by this observation, we estimate in the same way the disconnected contribution to a HLbL µ . arXiv:1712.00421v1 [hep-lat] 1 Dec 2017 2 Contents

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.

The forward Compton scattering off the proton is determined by substituting the empirical total photoabsorption cross sections into dispersive sum rules. In addition to the spin-independent amplitude evaluated previously [Phys. Rev. D 92, 074031 (2015)], we obtain the spin-dependent amplitude over a broad energy range. The two amplitudes contain all the information about this process, and we, hence, can reconstruct the nonvanishing observables of the proton Compton scattering in the forward kinematics. The results are compared with predictions of chiral perturbation theory where available. The low-energy expansion of the spin-dependent Compton scattering amplitude yields the Gerasimov-Drell-Hearn (GDH) sum rule and relations for the forward spin polarizabilities (FSPs) of the proton. Our evaluation provides an empirical verification of the GDH sum rule for the proton, and yields empirical values of the proton FSPs. For the GDH integral, we obtain 204.5(21.4) µb, in agreement with the sum rule prediction: 204.784481(4) µb. For the FSPs, we obtain: γ0 = −92.9(10.5)×10 −6 fm 4 , andγ0 = 48.4(8.2) × 10 −6 fm 6 , improving on the accuracy of previous evaluations.

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.

We present a dispersive analysis with the aim to extract the ϒ-p scattering length from γp → ϒp experiments. In this framework, the imaginary part of the ϒ-p forward scattering amplitude is obtained from γp → ϒp cross section measurements and is constrained at high energies from existing HERA and LHC data. Its real part is calculated through a once-subtracted dispersion relation, and the subtraction constant is proportional to the ϒ-p scattering length. We perform a feasibility study for ϒ photoproduction experiments at an Electron-Ion Collider and discuss the sensitivity and precision that can be reached in the extraction of the ϒ-p scattering length.