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 $M_t=180\mathrm{}$ GeV and consider all possible values of $tan\beta$. We also analyze the possibility that the top and/or the bottom Yukawa couplings result from an intermediate quasifixed point (QFP) of the equations. We show that the quark mixings of the third family do not have a QFP behavior (in contrast with the masses, the renormalization of all the mixings is linear), and we evaluate the low energy value of $V_{\mathrm{ub}}$ which corresponds to $V_{\mathrm{ub}}\left(M_X\right)=0\mathrm{}$. Then we focus on the renormalization-group corrections to (i) typical relations obtained in models with flavor symmetries at the unification scale and (ii) a superstring-motivated pattern of quark mass matrices. We show that in most of the models the numerical prediction for $V_{\mathrm{ub}}$ can be corrected in both directions (by varying $tan\beta$) due to top or bottom radiative corrections.