Colangelo, Gilberto; Hoferichter, Martin; Procura, Massimiliano; Stoffer, Peter (2017). Dispersion relation for hadronic lightbylight scattering: twopion contributions. Journal of High Energy Physics, 2017(4), p. 161. Springer 10.1007/JHEP04(2017)161

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In this third paper of a series dedicated to a dispersive treatment of the hadronic lightbylight (HLbL) tensor, we derive a partialwave formulation for twopion 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 byproduct, 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 pionbox contribution, defined by twopion intermediate states with a pionpole lefthand cut, and demonstrate how the full known result is reproduced when resumming the partial waves. Using dispersive fits to highstatistics data for the pion vector form factor, we provide an evaluation of the full pion box, aπbox = −15.9(2)×10−11. As an μ application of the partialwave formalism, we present a first calculation of ππrescattering effects in HLbL scattering, with γ∗γ∗ → ππ helicity partial waves constructed dispersively using ππ phase shifts derived from the inverseamplitude 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 chargedpion rescattering implements corrections related to the corresponding pion polarizability and show that these are moderate. Our final result for the sum of pionbox contribution and its Swave rescattering corrections reads aπbox + aππ,πpole LHC = −24(1) × 10−11.
Item Type: 
Journal Article (Original Article) 

Division/Institute: 
10 Strategic Research Centers > Albert Einstein Center for Fundamental Physics (AEC) 08 Faculty of Science > Institute of Theoretical Physics 
UniBE Contributor: 
Colangelo, Gilberto; Hoferichter, Martin; Procura, Massimiliano and Stoffer, Peter 
Subjects: 
500 Science > 530 Physics 
ISSN: 
10298479 
Publisher: 
Springer 
Language: 
English 
Submitter: 
Esther Fiechter 
Date Deposited: 
27 Oct 2017 15:42 
Last Modified: 
27 Oct 2017 15:42 
Publisher DOI: 
10.1007/JHEP04(2017)161 
ArXiv ID: 
1702.07347 
BORIS DOI: 
10.7892/boris.102040 
URI: 
https://boris.unibe.ch/id/eprint/102040 