Reduction of the electroweak correlation in the PDF updating by using the forward–backward asymmetry of Drell–Yan process

Abstract We propose a new observable for the measurement of the forward–backward asymmetry $$(A_{FB})$$ ( A FB ) in Drell–Yan lepton production. At hadron colliders, the $$A_{FB}$$ A FB distribution is sensitive to both the electroweak (EW) fundamental parameter $$\sin ^{2} \theta _{W}$$ sin 2 θ W , the weak mixing angle, and the parton distribution functions (PDFs). Hence, the determination of $$\sin ^{2} \theta _{W}$$ sin 2 θ W and the updating of PDFs by directly using the same $$A_{FB}$$ A FB spectrum are strongly correlated. This correlation would introduce large bias or uncertainty into both precise measurements of EW and PDF sectors. In this article, we show that the sensitivity of $$A_{FB}$$ A FB on $$\sin ^{2} \theta _{W}$$ sin 2 θ W is dominated by its average value around the Z pole region, while the shape (or gradient) of the $$A_{FB}$$ A FB spectrum is insensitive to $$\sin ^{2} \theta _{W}$$ sin 2 θ W and contains important information on the PDF modeling. Accordingly, a new observable related to the gradient of the spectrum is introduced, and demonstrated to be able to significantly reduce the potential bias on the determination of $$\sin ^{2} \theta _{W}$$ sin 2 θ W when updating the PDFs using the same $$A_{FB}$$ A FB data.