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

Colangelo, Gilberto; Hoferichter, Martin; Procura, Massimiliano; Stoffer, Peter (2017). Rescattering Effects in the Hadronic-Light-by-Light Contribution to the Anomalous Magnetic Moment of the Muon. Physical review letters, 118(23), p. 232001. American Physical Society 10.1103/PhysRevLett.118.232001

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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 aπ box = −15.9(2) × 10−11. We then construct a suitable input for the μγ0γ0 → 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 aπ box þ aππ;π-pole LHC = −24(1) × 10−11.

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