Dispersion relation for hadronic lightbylight scattering: twopion contributions
In our 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, a$$πbox\atop{μ}$$ =15.9(2) × 10 ^{11}. As an 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 isospin0 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 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 a$$πbox\atop{μ}$$ + a$$ππ, πpole LHC\atop{μ, J=0}$$ = 24(1) × 10 ^{11}.
 Authors:

^{[1]};
^{[2]};
^{[3]};
^{[4]}
 Univ. of Bern (Switzerland). Inst. for Theoretical Physics
 Univ. of Washington, Seattle, WA (United States). Inst. for Nuclear Theory; Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics
 European Organization for Nuclear Research (CERN), Geneva (Switzerland). Theoretical Physics Dept.
 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:
 SC0009919
 Type:
 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 10298479
 Publisher:
 Springer Berlin
 Research Org:
 Univ. of California, San Diego, CA (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Chiral Lagrangians; Effective Field Theories; Nonperturbative Effects; Precision QED
 OSTI Identifier:
 1393483
Colangelo, Gilberto, Hoferichter, Martin, Procura, Massimiliano, and Stoffer, Peter. Dispersion relation for hadronic lightbylight scattering: twopion contributions. United States: N. p.,
Web. doi:10.1007/JHEP04(2017)161.
Colangelo, Gilberto, Hoferichter, Martin, Procura, Massimiliano, & Stoffer, Peter. Dispersion relation for hadronic lightbylight scattering: twopion contributions. United States. doi:10.1007/JHEP04(2017)161.
Colangelo, Gilberto, Hoferichter, Martin, Procura, Massimiliano, and Stoffer, Peter. 2017.
"Dispersion relation for hadronic lightbylight scattering: twopion contributions". United States.
doi:10.1007/JHEP04(2017)161. https://www.osti.gov/servlets/purl/1393483.
@article{osti_1393483,
title = {Dispersion relation for hadronic lightbylight scattering: twopion contributions},
author = {Colangelo, Gilberto and Hoferichter, Martin and Procura, Massimiliano and Stoffer, Peter},
abstractNote = {In our 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, a$πbox\atop{μ}$ =15.9(2) × 1011. As an 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 isospin0 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 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 a$πbox\atop{μ}$ + a$ππ, πpole LHC\atop{μ, J=0}$ = 24(1) × 1011.},
doi = {10.1007/JHEP04(2017)161},
journal = {Journal of High Energy Physics (Online)},
number = 4,
volume = 2017,
place = {United States},
year = {2017},
month = {4}
}