Constraining anomalous $W tb$ and related SMEFT couplings using low-energy and electroweak precision observables

We investigate constraints on couplings of Standard Model effective field theory (SMEFT) operators contributing to $Wtb$ effective vertex at tree level. We study the one-loop level impact of these couplings on the low-energy flavour changing charged and neutral current processes and on the electroweak precision observables. We use the available data on these relevant processes to constrain the associated SMEFT/$Wtb$ couplings. Solving the renormalisation group equations, we connect the SMEFT couplings at different scales and use the bounds at low energy to obtain the relevant bounds at the large scale $\Lambda$. Our findings indicate significantly improved constraints on the couplings compared to existing constraints on $Wtb$ couplings by ATLAS and CMS. Additionally, we predict branching ratios for various top-FCNC processes, which exceed SM expectations by several orders of magnitude but remain within the reach of future colliders. These SMEFT couplings, or anomalous couplings of the effective $Wtb$ vertex, can further constrain different UV-complete and simplified models that generate such interactions at the tree or loop level.