2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/214620New results at four-loop order in perturbative QCD for the first two Taylor coefficients of the heavy quark vacuum polarization function are presented. They can be used to perform a precise determination of the charm- and bottom-quark mass. Implications for the value of the quark masses are briefly discussed.8 pages, 13 figures; final version accepted for publication in the journalHigh Energy Physics - Phenomenologytext