%0 Generic %1 Colangelo2017Dispersion %A Colangelo, Gilberto %A Hoferichter, Martin %A Procura, Massimiliano %A Stoffer, Peter %D 2017 %K g-2, lbl %T Dispersion relation for hadronic light-by-light scattering: two-pion contributions %U http://arxiv.org/abs/1702.07347 %X 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)\_\mu\$, 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 \$\gamma^*\gamma^*\to\pi\pi\$. 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\_\mu^\pi-box=-15.9(2)10^-11\$. As an application of the partial-wave formalism, we present a first calculation of \$\pi\pi\$-rescattering effects in HLbL scattering, with \$\gamma^*\gamma^*\to\pi\pi\$ helicity partial waves constructed dispersively using \$\pi\pi\$ 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 \$f\_0(500)\$ to HLbL scattering in \$(g-2)\_\mu\$. 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 \$a\_\mu^\pi-box + a\_\mu,J=0^\pi\pi,\pi-pole LHC=-24(1)\times 10^-11\$.

@misc{Colangelo2017Dispersion, abstract = {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)\_\mu\$, 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 \$\gamma^*\gamma^*\to\pi\pi\$. 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\_\mu^{\pi\text{-box}}=-15.9(2)\times 10^{-11}\$. As an application of the partial-wave formalism, we present a first calculation of \$\pi\pi\$-rescattering effects in HLbL scattering, with \$\gamma^*\gamma^*\to\pi\pi\$ helicity partial waves constructed dispersively using \$\pi\pi\$ 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 \$f\_0(500)\$ to HLbL scattering in \$(g-2)\_\mu\$. 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 \$a\_\mu^{\pi\text{-box}} + a\_{\mu,J=0}^{\pi\pi,\pi\text{-pole LHC}}=-24(1)\times 10^{-11}\$.}, added-at = {2019-02-23T22:09:48.000+0100}, archiveprefix = {arXiv}, author = {Colangelo, Gilberto and Hoferichter, Martin and Procura, Massimiliano and Stoffer, Peter}, biburl = {https://www.bibsonomy.org/bibtex/2c3dc01b1fa1a98b37e9fed69a3c56439/cmcneile}, citeulike-article-id = {14288452}, citeulike-linkout-0 = {http://arxiv.org/abs/1702.07347}, citeulike-linkout-1 = {http://arxiv.org/pdf/1702.07347}, day = 23, eprint = {1702.07347}, interhash = {e896695403bbfffbdc5ecbfa1a42cdef}, intrahash = {c3dc01b1fa1a98b37e9fed69a3c56439}, keywords = {g-2, lbl}, month = feb, posted-at = {2017-02-27 11:43:40}, priority = {2}, timestamp = {2019-02-23T22:15:27.000+0100}, title = {{Dispersion relation for hadronic light-by-light scattering: two-pion contributions}}, url = {http://arxiv.org/abs/1702.07347}, year = 2017 }