Beyond oblique contributions: $\Delta$r and W-mass in models with scalar leptoquarks

We study the dominant non-universal contributions to muon decay for the five scalar leptoquarks (LQs) allowed by the Standard Model gauge symmetries. By using a common computational framework, we isolate the new-Physics (NP) one-loop corrections over the observable $\Delta r$ and explore the connection with the $W$ boson mass. We highlight the role of non-universal terms considering, for the $SU(2)$ doublet and triplet LQs, a completely degenerate scenario, thus cancelling/moderating the effects of the oblique parameters S,T and U . We determine simple formulas that exhibit the leading non-universal behaviour generated by the introduction of extra Yukawa terms, and confront them against a present tension in $M_W$ and the projected FCC-ee accuracy.