$A_{FB}$ in the SMEFT: precision Z physics at the LHC

We study the forward-backward asymmetry $A_{FB}$ in $pp\to {\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ at the Z peak within the Standard Model Effective Field Theory (SMEFT). We find that this observable provides per mille level constraints on the vertex corrections of the Z boson to quarks,which close a flat direction in the electroweak precision SMEFT fit. Moreover, we show that current $A_{FB}$ data is precise enough so that its inclusion in the fit improves significantly LEP bounds even in simple New Physics setups. This demonstrates that the LHC can compete with and complement LEP when it comes to precision measurements of the Z boson properties