Yukawa enhancement of $Z$-mediated New Physics in $\Delta S=2$ and $\Delta B=2$ Processes

Abstract

We discuss Yukawa-enhanced contributions from $Z$-mediated new physics to down-type quark $\Delta F=2$ processes in the framework of the standard model gauge-invariant effective theory (SMEFT). Besides the renormalization group (RG) mixing of the $Z$-mediating ${\psi }^2{H}^{2}D$ operators into $\Delta F=2$ operators, we include at the electroweak scale one-loop (NLO) matching corrections consistently, necessary for the removal of the matching scale dependence. We point out that the right-handed $Z$-mediated interactions generate through Yukawa RG mixing $\Delta F=2$ left-right operators, which are further enhanced through QCD RG effects and chirally enhanced hadronic matrix elements. We investigate the impact of these new effects on the known correlations between $\Delta F=2$ and $\Delta F=1$ transitions in the SMEFT framework and point out qualitative differences to previous parameterizations of $Z$-mediated new physics that arise for the left-handed case. We illustrate how specific models fit into our model-independent framework by using four models with vector-like quarks. We carry out model-independent analyses of scenarios with purely left-handed and purely right-handed new-physics $Z$ couplings for each of the three sectors $s\to d$, $b\to s$ and $b\to d$. Specifically we discuss the correlations between ${\epsilon }^{\prime }/\epsilon$, ${\epsilon }_K$, $K_L\to {\mu }^{+}{\mu }^{-}$ $K^{+}\to {\pi }^{+}\nu \bar{\nu }$ and $K_L\to {\pi }^0\nu \bar{\nu }$ in the Kaon sector, and ${\varphi }_s$, $B_s\to {\mu }^{+}{\mu }^{-}$ and $B\to K^{(\ast )}({\mu }^{+}{\mu }^{-},\nu \bar{\nu })$ in the $b\to s$ sector and $B_d\to {\mu }^{+}{\mu }^{-}$ in the $b\to d$ sector.

Comments: 40 pages, 11 figures; v2: 2nd plot in figure 2 and references added, comparison with v2 of 1612.08839, conclusion unchanged; v3: improvements on text and presentation, matches published version