2017/02/28 by Gilberto Colangelo, Martin Hoferichter, Massimiliano Procura +1 · 1 citation
Physics and Astronomy · #hep-ph #hep-ex #hep-lat #nucl-th
paper · pdf · doi:10.1007/jhep04(2017)161
70 pages, 14 figures, Mathematica notebook with full expressions for the basis change included as supplementary material. Version accepted for publication in JHEP
arxiv created 2017/05/01 · arxiv updated 2017/05/02
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.