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The current 3$\sigma$ discrepancy between experiment and Standard Modelpredictions for $\pi^0 \to e^+e^-$ is reconsidered using the Pad\'e Theory forbivariate functions, the Canterbury approximants. This method provides amodel-independent data-driven approximation to the decay as soon asexperimental data for the doubly virtual $\pi^0$ transition form factor areavailable. It also implements the correct QCD constraints of the form factorboth at low- and high-energies. We reassess the Standard Model resultincluding, for the first time, a systematic error. Our result, BR$(\pi^0 \toe^+e^-)=6.23(5)\times 10^{-8}$, still represents a discrepancy larger than$2\sigma$, unsurmountable with our present knowledge of the Standard Model, andwould claim New Physics if the experimental result is confirmed by a newmeasurement. Our method also provides the adequate tool to extract the doublyvirtual form factor from experimental data in a straightforward manner. Thismeasurement would further shrink our error and establish once and for all theNew Physics nature of the discrepancy. In addition, we remark the challengethis discrepancy poses in the evaluation of the hadronic light-by-lightscattering contribution to the $(g-2)_{\mu}$, specially confronted with theforeseen accuracy of the forthcoming $(g-2)_{\mu}$ experiments.

Phenomenology of bivariate approximants: the pi0 to e+e- case and its impact on the electron and muon g-2