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We propose a minimal extension of the Standard Model where an up-typevector-like quark, denoted $T$, is introduced and provides a simple solution tothe CKM unitarity problem. We adopt the Botella-Chau parametrization in orderto extract the $4\times 3$ quark mixing matrix which contains the three anglesof the $3\times 3$ CKM matrix plus three new angles denoted $\theta_{14}$,$\theta_{24}$, $\theta_{34}$. It is assumed that the mixing of $T$ withstandard quarks is dominated by $\theta_{14}$. Imposing a recently derived, andmuch more restrictive, upper-bound on the New Physics contributions to$\epsilon_{K}$, we find, in the limit of exact $\theta_{14}$ dominance wherethe other extra angles vanish, that $\epsilon_{K}^{\text{NP}}$ is too large.However, if one relaxes the exact $\theta_{14}$ dominance limit, there exists aparameter region, where one may obtain $\epsilon_{K}^{\text{NP}}$ in agreementwith experiment while maintaining the novel pattern of $T$ decays with theheavy quark decaying predominantly to the light quarks $d$ and $u$. We alsofind a reduction in the decay rate of $K_L\rightarrow \pi^o \nu\bar{\nu}$.

Decays of the Heavy Top and New Insights on $\epsilon_K$ in a one-VLQ Minimal Solution to the CKM Unitarity Problem