Decays of the heavy top and new insights on $$\epsilon _K$$ ϵ K in a one-VLQ minimal solution to the CKM unitarity problem

Abstract

Abstract We propose a minimal extension of the Standard Model where an up-type vector-like quark, denoted T, is introduced and provides a simple solution to the CKM unitarity problem. We adopt the Botella-Chau parametrization in order to extract the $$4\times 3$$ 4 × 3 quark mixing matrix which contains the three angles of the $$3\times 3$$ 3 × 3 CKM matrix plus three new angles denoted $$\theta _{14}$$ θ 14 , $$\theta _{24}$$ θ 24 , $$\theta _{34}$$ θ 34 . It is assumed that the mixing of T with standard quarks is dominated by $$\theta _{14}$$ θ 14 . Imposing a recently derived, and much more restrictive, upper-bound on the New Physics contributions to $$\epsilon _{K}$$ ϵ K , we find, in the limit of exact $$\theta _{14}$$ θ 14 dominance where the other extra angles vanish, that $$\epsilon _{K}^{\text {NP}}$$ ϵ K NP is too large. However, if one relaxes the exact $$\theta _{14}$$ θ 14 dominance limit, there exists a parameter region, where one may obtain $$\epsilon _{K}^{\text {NP}}$$ ϵ K NP in agreement with experiment while maintaining the novel pattern of T decays with the heavy quark decaying predominantly to the light quarks d and u. We also find a reduction in the decay rate of $$K_L\rightarrow \pi ^0 \nu {\overline{\nu }}$$ K L → π 0 ν ν ¯ .