Scale dependence of quark mass matrices in models with flavor symmetries
  Numerical correlations between fermion masses and mixings could indicate the presence of a flavor symmetry at high energies. In general, the search for these correlations using low-energy data requires an estimate of leading-log radiative corrections. We present a complete analysis of the evolution between the electroweak and the grand unification scales of quark mass parameters in minimal supersymmetric models. We take $M_t=180$ GeV and consider all possible values of $\tan \beta$. We also analize the possibility that the {\it top} and/or the {\it bottom} Yukawa couplings result from an intermediate quasifixed point (QFP) of the equations. We show that the quark mixings of the third family do {\it not} have a QFP behaviour (in contrast to the masses, the renormalization of all the mixings is linear), and we evaluate the low-energy value of $V_{ub}$ which corresponds to $V_{ub}(M_X)=0$. Then we focus on the renormalization-group corrections to {\it (i)} typical relations obtained in models with flavor symmetries at the unification scale and {\it (ii)} a superstring-motivated pattern of quark mass matrices. We show that in most of the models the numerical prediction for $V_{ub}$ can be {\it corrected} in both directions (by varying $\tan\beta$) due to {\it top} or {\it bottom} radiative corrections. 
J. A. Aguilar-Saavedra, M. Masip