Dispersion relation for hadronic light-by-light scattering: two-pion contributions
By G. Colangelo, M. Hoferichter, M. Procura, P. Stoffer. Journal of High Energy Physics, 2017
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In this third paper of a series dedicated to a dispersive treatment of the hadronic light-by-light (HLbL) tensor, we derive a partial-wave formulation for two-pion intermediate states in the HLbL contribution to the anomalous magnetic moment of the muon (g − 2)μ, including a detailed discussion of the unitarity relation for arbitrary partial waves. We show that obtaining a final expression free from unphysical helicity partial waves is a subtle issue, which we thoroughly clarify. As a by-product, we obtain a set of sum rules that could be used to constrain future calculations of γ∗γ∗ → ππ. We validate the formalism extensively using the pion-box contribution, defined by two-pion intermediate states with a pion-pole left-hand cut, and demonstrate how the full known result is reproduced when resumming the partial waves. Using dispersive fits to high-statistics data for the pion vector form factor, we provide an evaluation of the full pion box, aμπ − box = − 15.9(2) × 10− 11. As an application of the partial-wave formalism, we present a first calculation of ππ-rescattering effects in HLbL scattering, with γ∗γ∗ → ππ helicity partial waves constructed dispersively using ππ phase shifts derived from the inverse-amplitude method. In this way, the isospin-0 part of our calculation can be interpreted as the contribution of the f0(500) to HLbL scattering in (g − 2)μ. We argue that the contribution due to charged-pion rescattering implements corrections related to the corresponding pion polarizability and show that these are moderate. Our final result for the sum of pion-box contribution and its S-wave rescattering corrections reads aμπ ‐ box + aμ,J = 0ππ,π ‐ pole LHC = − 24(1) × 10− 11.
Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/4e7b5608b8c834e605612fc4dd7d92654814bb76
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Citations in the corpus
- Short-distance constraints for the HLbL contribution to the muon anomalous magnetic moment (2019, methodology): “We use the notation of [10, 11] to facilitate using our results together with theirs.”
- Measurement of the anomalous precession frequency of the muon in the Fermilab Muon g−2 Experiment (2021, background): “[26] G.”