Hadronic light-by-light scattering contribution to the muon g – 2 on the lattice

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 g̅2, 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 Fπ0γ*γ* (q21; q21) in the spacelike region with photon virtualities up to 1.5 GeV2 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.

Recent Developments in Nuclear Physics

Nuclei exhibit features that are described in superficially contradictory terms according to the different degrees of freedom that are excited by probes of different scale in space and in time. After giving some examples I concentrate on the hadron degrees of freedom such as the nucleon, the pion and the .6. isobar. These are the effective degrees of freedom on the level of intermediate resolution: about 0�5-1 fm in distance and correspondingly in time. A prime example is the deuteron :which has a nearly model-independent description in terms of pion physics to very high precision. In nuclear matter the pion propagates in close analogy to the propagation of light in a dielectric. This permits the explanation of a number of features in nuclei related to the chiral symmetry limit in which the pion mass vanishes. A consequence of this description is the analogy of the equations for the pion and its effective field with the Maxwell equations for a dielectric. A pionic collective mode should appear strongly and with characteristic properties for a well chosen probe. It is difficult to explore its properties directly and in particular physical pions are not useful for this purpose. I will discuss different alternatives involving 'virtual pion beams'. There is recent evidence for such a collective state in forward charge exchange reactions throughout the periodic system.