Improved π⁰, η, η′ transition form factors in resonance chiral theory and their \( {a}_{\mu}^{\textrm{HLbL}} \) contribution

Working with Resonance Chiral Theory, within the two resonance multiplets saturation scheme, we satisfy leading (and some subleading) chiral and asymptotic QCD constraints and accurately fit simultaneously the π⁰, η, η′ transition form factors, for single and double virtuality. In the latter case, we supplement the few available measurements with lattice data to ensure a faithful description. Mainly due to the new results for the doubly virtual case, we improve over existing descriptions for the η and η′. Our evaluation of the corresponding pole contributions to the hadronic light-by-light piece of the muon g − 2 read: $a_{\mu }^{{\pi }^0-\text{pole}}=\left(61.9\pm {0.6}_{-1.5}^{+2.4}\right)\times {10}^{-11}$ \( {a}_{\mu}^{\pi^0-\textrm{pole}}=\left(61.9\pm {0.6}_{-1.5}^{+2.4}\right)\times {10}^{-11} \) , $a_{\mu }^{\eta -\text{pole}}=\left(15.2\pm {0.5}_{-0.8}^{+1.1}\right)\times {10}^{-11}$ \( {a}_{\mu}^{\eta -\textrm{pole}}=\left(15.2\pm {0.5}_{-0.8}^{+1.1}\right)\times {10}^{-11} \) and $a_{\mu }^{{\eta }^{\prime }-\text{pole}}=\left(14.2\pm {0.7}_{-0.9}^{+1.4}\right)\times {10}^{-11}$ \( {a}_{\mu}^{\eta^{\prime }-\textrm{pole}}=\left(14.2\pm {0.7}_{-0.9}^{+1.4}\right)\times {10}^{-11} \) , for a total of $a_{\mu }^{{\pi }^0+\eta +{\eta }^{\prime }-\text{pole}}=\left(91.3\pm {1.0}_{-1.9}^{+3.0}\right)\times {10}^{-11}$ \( {a}_{\mu}^{\pi^0+\eta +{\eta}^{\prime }-\textrm{pole}}=\left(91.3\pm {1.0}_{-1.9}^{+3.0}\right)\times {10}^{-11} \) , where the first and second errors are the statistical and systematic uncertainties, respectively.