Bounds on quark mass matrices elements due to measured properties of the mixing matrix and present values of the quark masses

摘要

We obtain constraints on possible structures of mass matrices in the quarksector by using as experimental restrictions the determined values of the quarkmasses at the $M_Z$ energy scale, the magnitudes of the quark mixing matrixelements $V_{\rm ud}$, $V_{\rm us}$, $V_{\rm cd}$, and $V_{\rm cs}$, and theJarlskog invariant $J(V)$. Different cases of specific mass matrices areexamined in detail. The quality of the fits for the Fritzsch and Stech typemass matrices is about the same with $\chi^2/{\rm dof}=4.23/3=1.41$ and$\chi^2/{\rm dof}=9.10/4=2.28$, respectively. The fit for a simplegeneralization (one extra parameter) of the Fritzsch type matrices, in thephysical basis, is much better with $\chi^2/{\rm dof}=1.89/4=0.47$. Forcomparison we also include the results using the quark masses at the 2 GeVenergy scale. The fits obtained at this energy scale are similar to that at$M_Z$ energy scale, implying that our results are unaffected by the evolutionof the quark masses from 2 to 91 GeV.