HEP
In the literature: open
What determines the hierarchy of quark and lepton masses?
In plain words
The top quark is about 340000 times heavier than the electron, and quark mixing is small while neutrino mixing is large. No theory predicts these numbers.
Precise statement
The SM Yukawa couplings span $y_e \sim 3e-6$ to $y_t \sim 1$, CKM angles are small ($\theta_C \sim 0.23$, |V_ub| ~ 4e-3) while PMNS angles are large ($\theta_{12} \sim 34\,\mathrm{deg}$, $\theta_{23} \sim 45\,\mathrm{deg}$). An answer is a mechanism (Froggatt-Nielsen charges, modular or discrete flavor symmetries, extra-dimensional localization, partial compositeness) that predicts these values with fewer parameters than it explains.
What would settle it
A model with fewer free parameters than observables whose extra predictions (mixing sum rules, flavor-violating rates, new states) are confirmed.