Using Drell-Yan $A_{FB}$ to constrain PDFs

We show that measurements of the forward-backward charge asymmetry ($A_{FB}(M,y)$) of Drell-Yan dilepton events produced at hadron colliders provide a new powerful tool to constrain Parton Distribution Functions (PDFs). PDF uncertainties are the dominant source of systematic error in precision measurements at hadron colliders (e.g. $\chi^2$ values of fits to extract $\sin^2\theta_{eff}^{lept}(M_Z)$ from $A_{FB}(M,y)$ with different PDF replicas can be used to place additional constraints on PDFs.In turn, using these constrained PDFs significantly reduces the PDF errors in precision measurements of electroweak parameters. The measurement of the on-shell $\sin^2\theta_{W}=1-M_W^2/M_Z^2$ is equivalent to an indirect measurement of the W mass. The errors in this indirect measurement of the W mass are competitive with direct measurements. For example, with 200 fb$^{-1}$ at 13 TeV, the expected error in the indirect measurement of the W mass is $\pm$9 MeV.