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

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 ¯ .

Vector-like Quarks

“…at the level of 2 to 3 standard deviations [39][40][41][42]. One may wonder whether or not this two to three sigma deviation should be taken as a serious hint for physics beyond the SM.…”

“…It is possible to account for these deviations with simple extensions of the Standard Model with vector-like quarks. This possibility was analysed in detail in [39][40][41][42].…”

Do the Small Numbers in the Quark Mixing arise from New Physics?

“…In the case studied here, this crucial EWPM quantity now receives a new contribution, which was absent, in leading order, in the realistic s 14 -dominance case presented in [23].…”

“…These upper-bounds for |V 24 | and |V 34 | are well within the allowed regions presented in [24], where the parameter regions of a general model with a heavy-top are scanned while imposing the experimental constraints coming from K 0 − K 0 and B 0 d,s − B 0 d,s . Nonetheless, as it was pointed out in [23], the NP contributions to ε K are currently much more constrained, roughly 10% of the standard model contribution which is very near to the experimental bound. Therefore, when introducing a VLQ, one should be very careful as not to exceed this bound.…”

“…In Appendix B, we provide more detail. An extensive analyses of the NP contributions to these phenomena was done in [23][24][25], where, in the context of an up-VLQ, a solution to the CKM unitarity problem was proposed with ∆ ≈ 0.04.…”