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Lattice calculation of the $\pi^0$, $\eta$ and $\eta^{\prime}$ transition form factors and the hadronic light-by-light contribution to the muon $g-2$
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abstract
In this paper we present a first ab-initio calculation of the $\pi^0$, $\eta$ and $\eta^{\prime}$ transition form factors performed with physical light-quark masses. We provide a complete parametrization of the form factors that includes both single and double-virtual kinematics. Our results are compared with experimental measurements of the form factors in the space-like region and with the measured two-photon decay widths. In a second step, our parametrizations of the transition form factors are used to compute the dominant pseudoscalar-pole contributions to the hadronic light-by-light scattering in the muon $g-2$. Our final result reads $a_{\mu}^{\rm hlbl, ps-pole} = (85.1 \pm 5.2) \times 10^{-11}$. Although the pion-pole is dominant, we confirm that, together, the $\eta$ and $\eta^{\prime}$ provide roughly half of its contribution.
Forward citations
Cited by 4 Pith papers
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Hadronic vacuum polarization for the muon $g-2$ from lattice QCD: Long-distance and full light-quark connected contribution
The light-quark connected hadronic vacuum polarization contribution to muon g-2 is determined to 0.69% precision, 655.2(4.5) x 10^-10, from lattice QCD.
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Dispersion relation for hadronic light-by-light scattering: $\eta$ and $\eta'$ poles
A dispersive analysis of the eta and eta' transition form factors yields data-driven pole contributions to the muon g-2 of 14.7(9) x 10^-11 and 13.5(7) x 10^-11.
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Pion Transition Form Factor in Lattice QCD
The disconnected quark-loop contribution to the pion transition form factor has the same sign as the connected contribution, at roughly 1% of its size, as calculated on one N_f=2+1 clover ensemble.
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Field-theoretical approach to neutral pion contribution to muon $g-2$
The neutral pion contribution to muon g-2 should contain only the on-shell pole term, with no principal-value part, because off-shell pions are not well-defined states in QCD.
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