Lattice calculation of the $\pi^0$, $\eta$ and $\eta^{\prime}$ transition form factors and the hadronic light-by-light contribution to the muon $g-2$
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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2023
- DOI:
- arXiv:
- arXiv:2305.04570
- Bibcode:
- 2023arXiv230504570G
- Keywords:
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- High Energy Physics - Lattice;
- High Energy Physics - Phenomenology
- E-Print:
- 29 pages, 16 figures. Typos corrected. Add figure 6