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In the models with vector like quark doublets, the mass matrices of up anddown type quarks are related. Precise diagonalization for the mass matricesbecame an obstacle in the numerical studies. In this work we propose adiagonalization method at first. As its application, in the standard model withone vector like quark doublet we present quark mass spectrum, Feynman rules forthe calculation of $B\to X_s\gamma$. We find that i) under the constraints ofthe CKM matrix measurements, the mass parameters in the bilinear term areconstrained to a small value by the small deviation from unitarity; ii)compared with the fourth generation extension of the standard model, there isan enhancement to $B\to X_s\gamma$ process in the contribution of vector likequark, resulting a non-decoupling effect in such models.

General scan in flavor parameter space in the models with vector quark doublets and an enhancement in $B\to X_s\gamma$ process