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Title: Dispersion relation for hadronic light-by-light scattering: two-pion contributions

In our 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, a$$π-box\atop{μ}$$ =-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 also 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 a$$π-box\atop{μ}$$ + a$$ππ, π-pole LHC\atop{μ, J=0}$$ = -24(1) × 10 -11.
 [1] ;  [2] ;  [3] ;  [4]
  1. Univ. of Bern (Switzerland). Inst. for Theoretical Physics
  2. Univ. of Washington, Seattle, WA (United States). Inst. for Nuclear Theory; Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics
  3. European Organization for Nuclear Research (CERN), Geneva (Switzerland). Theoretical Physics Dept.
  4. Univ. of Bonn (Germany). Helmholtz Inst. for Radiation and Nuclear Physics, Bethe Center for Theoretical Physics; Univ. of California, San Diego, CA (United States). Dept. of Physics
Publication Date:
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 4; Journal ID: ISSN 1029-8479
Springer Berlin
Research Org:
Univ. of California, San Diego, CA (United States)
Sponsoring Org:
Country of Publication:
United States
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Chiral Lagrangians; Effective Field Theories; Nonperturbative Effects; Precision QED
OSTI Identifier: