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

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