Patterns of Flavour Violation in Models with Vector-Like Quarks

Abstract

We study the patterns of flavour violation in renormalisable extensions of the Standard Model (SM) that contain vector-like quarks (VLQs) in a single complex representation of either the SM gauge group $G_{SM}$ or $G_{SM}^{\prime }=G_{SM}\times U(1{)}_{L_{\mu }-L_{\tau }}$. We first decouple VLQs in the $M=(1-10)$ TeV range and then at the electroweak scale also $Z,Z^{\prime }$ gauge bosons and additional scalars to study the resulting phenomenology that depends on the relative size of $Z$- and $Z^{\prime }$-induced flavour-changing neutral currents, as well as the size of $\Delta F=2$ contributions including the effects of renormalisation group Yukawa evolution from $M$ to the electroweak scale that turn out to be very important for models with right-handed currents through the generation of left-right operators. In addition to rare decays like $P\to \ell \bar{\ell }$, $P\to P^{\prime }\ell \bar{\ell }$, $P\to P^{\prime }\nu \bar{\nu }$ with $P=K,B_s,B_d$ and $\Delta F=2$ observables we analyze the ratio ${\epsilon }^{\prime }/\epsilon$ which appears in the SM to be significantly below the data. We study patterns and correlations between these observables which taken together should in the future allow for differentiating between VLQ models. In particular the patterns in models with left-handed and right-handed currents are markedly different from each other. Among the highlights are large $Z$-mediated new physics effects in Kaon observables in some of the models and significant effects in $B_{s,d}$-observables. ${\epsilon }^{\prime }/\epsilon$ can easily be made consistent with the data, implying then uniquely the suppression of $K_L\to {\pi }^0\nu \bar{\nu }$. Significant enhancements of $Br(K^{+}\to {\pi }^{+}\nu \bar{\nu })$ are still possible. We point out that the combination of $\Delta F=2$ and $\Delta F=1$ observables in a given meson system generally allows to determine the masses of VLQs independently of the size of VLQ couplings.

50 + 24 pages, 12 figures; v3: added top-Yukawa RG evolution, details on VLQ matching on G_SM^(')-EFT, one figure, references; revised numerics; some changes in conclusions

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