Dispersion relations for hadronic light-by-light and the muon g - 2

Massimiliano Procura, Gilberto Colangelo, Martin Hoferichter, Peter Stoffer

The largest uncertainties in the Standard Model calculation of the anomalous magnetic moment of the muon ( g 2) come from hadronic e ffects, namely hadronic vacuum polarization (HVP) and hadronic lightby-light (HLbL) contributions. Especially the latter is emerging as a potential roadblock for a more accurate determination of (g 2) . The main focus here is on a novel 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) 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 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. Using dispersive fits to high-statistics data for the pion vector form factor, we obtain a-box = 15:9(2) 10 11. A first model-independent calculation of e ffects of intermediate states that go beyond the scalar-QED pion loop is also presented. We combine our 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. After constructing suitable input for the helicity partial waves based on a pion-pole left-hand cut (LHC), we find 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 e ffects to the full pion box and leads to a-box =0 = 24(1) x 10 11.

Particle Physics
External organisation(s)
Universität Bern, University of Washington, University of California, San Diego
EPJ Web of Conferences
No. of pages
Publication date
Peer reviewed
Austrian Fields of Science 2012
103034 Particle physics
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