Insisting on the role of experimental data: the pseudoscalar-pole piece to the $(g_\mu-2)$ and the $|V_{ub}|$ from $B \to \pi \ell \nu_{\ell}$ differential branching ratio

Abstract

We employ a mathematical framework based on rational approximants in order to calculate meson form factors. The method profits from unitary, is systematic and data based, and is able to ascribe a systematic uncertainty which provides for the desired model independence. Two examples are discussed: the transition form factor entering the pseudoscalar-pole piece of the hadronic light-by-light contribution to the anomalous magnetic moment of the muon, and the $B \to \pi$ form factor participating the $B\to\pi\ell\nu_{\ell}$ differential branching ratios which allows to determine the $|V_{ub}|$ CKM parameter.