$\tau$ data-driven evaluation of Euclidean windows for the hadronic vacuum polarization

We compute for the first time the $\tau$ data-driven Euclidean windows for the hadronic vacuum polarization contribution to the muon $g-2$. We show that $\tau$-based results agree with the available lattice window evaluations and with the full result. On the intermediate window, where all lattice evaluations are rather precise and agree, $\tau$-based results are compatible with them. This is particularly interesting, given that the disagreement of the $e^+e^-$ data-driven result with the lattice values in this window is the main cause for their discrepancy, affecting the interpretation of the $a_\mu$ measurement in terms of possible new physics.
Comment: 15 pages, 4 figures, 4 tables. Accepted for publication in PLB