Lattice calculation of the pion transition form factor ${\pi }^0\to {\gamma }^{\ast }{\gamma }^{\ast }$

Abstract

We calculate the ${\pi }^0\to {\gamma }^{\ast }{\gamma }^{\ast }$ transition form factor ${\mathcal{F}}_{{\pi }^0{\gamma }^{\ast }{\gamma }^{\ast }}(q_1^2,q_2^2)$ in lattice QCD with two flavors of quarks. Our main motivation is to provide the input to calculate the ${\pi }^0$-pole contribution to hadronic light-by-light scattering in the muon $(g-2)$, $a_{\mu }^{\mathrm{HLbL};{\pi }^0}$. We therefore focus on the region where both photons are spacelike up to virtualities of about $1.5$GeV${}^2$, which has so far not been experimentally accessible. Results are obtained in the continuum at the physical pion mass by a combined extrapolation. We reproduce the prediction of the chiral anomaly for real photons with an accuracy of about $8-9\%$. We also compare to various recently proposed models and find reasonable agreement for the parameters of some of these models with their phenomenological values. Finally, we use the parametrization of our lattice data by these models to calculate $a_{\mu }^{\mathrm{HLbL};{\pi }^0}$.

31 pages - Minor text improvements. Published version

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• Anomalies in ${}^8$Be nuclear transitions and $(g-2{)}_{e,\mu }$: towards a minimal combined explanation
• Modeling interactions of photons with pseudoscalar and vector mesons
• The hadronic light-by-light contribution to the muon's anomalous magnetic moment
• Subleading power corrections to the pion-photon transition form factor in QCD
• On some properties of the fourth-rank hadronic vacuum polarization tensor and the anomalous magnetic moment of the muon
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• Next-to-Next-to-Leading-Order QCD Prediction for the Photon-Pion Form Factor
• Spacelike and timelike form factors for the $({\pi }^0,\eta ,{\eta }^{\prime })\to {\gamma }^{\ast }\gamma$ transitions in the light-front quark model
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• Power corrections to the pion transition form factor from higher-twist distribution amplitudes of photon
• Prospects for ${\gamma }^{\star }{\gamma }^{\star }\to \pi \pi$ via lattice QCD
• Recent Developments of Muon g-2 from Lattice QCD
• Photon-pion transition form factor of two photon process at BESIII from light-cone quantum field theory