The electro-weak couplings of the top and bottom quarks -- global fit and future prospects

We evaluate the implications of LHC and LEP/SLC measurements for the electro-weak couplings of the top and bottom quarks. We derive global bounds on the Wilson coefficients of ten two-fermion operators in an effective field theory description. The combination of hadron collider data with $Z$-pole measurements is found to yield tight limits on the operator coefficients that modify the left-handed couplings of the bottom and top quark to the $Z$ boson. We also present projections for the high-luminosity phase of the LHC and for future electron-positron colliders. The bounds on the operator coefficients are expected to improve substantially during the remaining LHC programme, by factors of $1$ to $5$ if systematic uncertainties are scaled as statistical ones. The operation of an $e^+e^-$ collider at a center-of-mass energy above the top-quark pair production threshold is expected to further improve the bounds by one to two orders of magnitude. The combination of measurements in $pp$ and $e^+e^-$ collisions allows for a percent-level determination of the top-quark Yukawa coupling, that is robust in a global fit.