Rescattering Effects in the Hadronic-Light-by-Light Contribution to the Anomalous Magnetic Moment of the Muon

We present a first model-independent calculation of ππ intermediate states in the hadronic-light-by-light (HLBL) contribution to the anomalous magnetic moment of the muon (g - 2) _μ that goes beyond the scalar QED pion loop. To this end, we combine a recently developed dispersive description of the HLBL tensor with a partial-wave expansion and demonstrate that the known scalar-QED result is recovered after partial-wave resummation. Using dispersive fits to high-statistics data for the pion vector form factor, we provide an evaluation of the full pion box a ^π _μ ^box = –15.9(2) x 10 ^-11. We then construct a suitable input for the γ*γ* → ππ helicity partial waves, based on a pion-pole left-hand cut and show that for the dominant charged-pion contribution, this representation is consistent with the two-loop chiral prediction and the COMPASS measurement for the pion polarizability. This allows us to reliably estimate S-wave rescattering effects to the full pion box and leads to our final estimate for the sum of these two contributions a ^π _μ ^box + a ^ππ,π-pole _μ,J=0 ^LHC = –24(1) x 10 ^-11.