Dispersion relation for hadronic lightbylight scattering: twopion contributions
Abstract
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:
 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:
 Research Org.:
 Univ. of California, San Diego, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1393483
 Grant/Contract Number:
 SC0009919
 Resource Type:
 Journal Article: 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
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Chiral Lagrangians; Effective Field Theories; Nonperturbative Effects; Precision QED
Citation Formats
Colangelo, Gilberto, Hoferichter, Martin, Procura, Massimiliano, and Stoffer, Peter. Dispersion relation for hadronic lightbylight scattering: twopion contributions. United States: N. p., 2017.
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. Thu .
"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 = {Thu Apr 27 00:00:00 EDT 2017},
month = {Thu Apr 27 00:00:00 EDT 2017}
}
Web of Science

Improved Pion Pion Scattering Amplitude from Dispersion Relation Formalism
Pionpion scattering amplitude is obtained from Chiral Perturbation Theory at one and twoloop approximations. Dispersion relation formalism provides a more economic method, which was proved to reproduce the analytical structure of that amplitude at both approximation levels. This work extends the use of the formalism in order to compute further unitarity corrections to partial waves, including the Dwave amplitude. 
Hadronic lightbylight scattering in the muon g2: A new shortdistance constraint on pion exchange
Recently it was pointed out that for the evaluation of the numerically dominant pionexchange contribution to the hadronic lightbylight scattering correction in the muon g2, a fully offshell pionphotonphoton form factor should be used. Following this proposal, we first derive a new shortdistance constraint on the offshell form factor which enters at the external vertex for the muon g2 and show that it is related to the quark condensate magnetic susceptibility in QCD. We then evaluate the pionexchange contribution in the framework of largeN{sub C} QCD using an offshell form factor which fulfills all shortdistance constraints. With a value formore »