Oblique corrections from vectorlike singlet and doublet quarks

We derive general formulas for the oblique-correction parameters $S$, $T$, and $U$ in an extension of the standard model with an arbitrary number of vectorlike singlet and vectorlike doublet quarks, or with mirror quarks, which mix with the standard quarks of the same electric charge. We analyze numerically the oblique corrections caused by some simple structures of exotic quarks, paying special attention to the decoupling properties.