We employ a mathematical framework based on rational approximants in order to calculate the pseudoscalar-pole piece of the hadronic light-by-light contribution to the anomalous magnetic moment of the muon, $a_{\mu }^{\mathrm{HLbL};P}$. The method is systematic and data based, profiting from over 13 different collaborations, and able to ascribe, for the first time, a systematic uncertainty which provides for the model independence. As a result, we obtain $a_{\mu }^{\mathrm{HLbL};P}=94.3(5.3)\times {10}^{-11}$, whose uncertainty is well below the one foreseen at future experiments measuring the $(g_{\mu }-2)$.

• Received 26 January 2017

DOI:https://doi.org/10.1103/PhysRevD.95.054026