Yukawa enhancement of $Z$-mediated New Physics in $ΔS = 2$ and $ΔB = 2$ Processes

Abstract

We discuss Yukawa-enhanced contributions from $Z$-mediated new physics to down-type quark $ΔF=2$ processes in the framework of the standard model gauge-invariant effective theory (SMEFT). Besides the renormalization group (RG) mixing of the $Z$-mediating $ψ^2 H^2 D$ operators into $ΔF = 2$ 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 $ΔF=2$ 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 $ΔF=2$ and $ΔF=1$ 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 $\varepsilon'/\varepsilon$, $\varepsilon_K$, $K_L\to μ^+μ^-$ $K^+\to π^+ν\barν$ and $K_L\toπ^0ν\barν$ in the Kaon sector, and $ϕ_s$, $B_s\toμ^+μ^-$ and $B\to K^{(*)} (μ^+μ^-, ν\barν)$ in the $b\to s$ sector and $B_d\toμ^+μ^-$ in the $b\to d$ sector.