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

Abstract 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 π 0 , 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: $$ {a}_{\mu}^{\pi^0-\textrm{pole}}=\left(61.9\pm {0.6}_{-1.5}^{+2.4}\right)\times {10}^{-11} $$ a μ π 0 − pole = 61.9 ± 0.6 − 1.5 + 2.4 × 10 − 11 , $$ {a}_{\mu}^{\eta -\textrm{pole}}=\left(15.2\pm {0.5}_{-0.8}^{+1.1}\right)\times {10}^{-11} $$ a μ η − pole = 15.2 ± 0.5 − 0.8 + 1.1 × 10 − 11 and $$ {a}_{\mu}^{\eta^{\prime }-\textrm{pole}}=\left(14.2\pm {0.7}_{-0.9}^{+1.4}\right)\times {10}^{-11} $$ a μ η ′ − pole = 14.2 ± 0.7 − 0.9 + 1.4 × 10 − 11 , for a total of $$ {a}_{\mu}^{\pi^0+\eta +{\eta}^{\prime }-\textrm{pole}}=\left(91.3\pm {1.0}_{-1.9}^{+3.0}\right)\times {10}^{-11} $$ a μ π 0 + η + η ′ − pole = 91.3 ± 1.0 − 1.9 + 3.0 × 10 − 11 , where the first and second errors are the statistical and systematic uncertainties, respectively.