Improved ${\pi }^0,\eta ,{\eta }^{\prime }$ transition form factors in resonance chiral theory and their $a_{\mu }^{\mathrm{HLbL}}$ 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 ${\pi }^0,\eta ,{\eta }^{\prime }$ 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 $\eta$ and ${\eta }^{\prime }$. Our evaluation of the corresponding pole contributions to the hadronic light-by-light piece of the muon $g-2$ read: $a_{\mu }^{{\pi }^0\text{-}\mathrm{pole}}=\left(61.9\pm 0.6_{-1.5}^{+2.4}\right)\times 10^{-11}$, $a_{\mu }^{\eta \text{-}\mathrm{pole}}=\left(15.2\pm 0.5_{-0.8}^{+1.1}\right)\times 10^{-11}$ and $a_{\mu }^{{\eta }^{\prime }\text{-}\mathrm{pole}}=\left(14.2\pm 0.7_{-0.9}^{+1.4}\right)\times 10^{-11}$, for a total of $a_{\mu }^{{\pi }^0+\eta +{\eta }^{\prime }\text{-}\mathrm{pole}}=\left(91.3\pm 1.0_{-1.9}^{+3.0}\right)\times 10^{-11}$, where the first and second errors are the statistical and systematic uncertainties, respectively.

Comments: 49 pages, 8 figures. The correlations between the pseudo-data points from Lattice QCD were considered and the Global Analysis was changed accordingly in this version. Furthermore, the high energy behavior was analyzed in the whole spectrum of asymmetries between the single virtual and the double virtual case