Dispersion relation for hadronic light-by-light scattering

Procura, Massimiliano; Colangelo, Gilberto; Hoferichter, Martin; Stoffer, Peter; D’Ambrosio, G.; Iacovacci, M.; Passera, Massimo; Venanzoni, G.; Massarotti, P.; Mastroianni, S. (2016). Dispersion relation for hadronic light-by-light scattering. EPJ web of conferences, 118, 01030. EDP Sciences 10.1051/epjconf/201611801030

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The largest uncertainties in the Standard Model calculation of the anomalous magnetic moment of the muon (g − 2)μ come from hadronic contributions. In particular, in a few years the subleading hadronic light-by-light (HLbL) contribution might dominate the theory uncertainty. We present a dispersive description of the HLbL tensor, which is based on unitarity, analyticity, crossing symmetry, and gauge invariance. This opens up the possibility of a data-driven determination of the HLbL contribution to (g − 2)μ with the aim of reducing model dependence and achieving a reliable error estimate.
Our dispersive approach defines unambiguously the pion-pole and the pion-box contribution to the HLbL tensor. Using Mandelstam’s double-spectral representation, we have proven that the pion-box contribution coincides exactly with the one-loop scalar QED amplitude, multiplied by the appropriate pion vector form factors.

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