We propose a new observable for the measurement of the forward–backward asymmetry
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Abstract in Drell–Yan lepton production. At hadron colliders, the$$(A_{FB})$$ distribution is sensitive to both the electroweak (EW) fundamental parameter$$A_{FB}$$ , the weak mixing angle, and the parton distribution functions (PDFs). Hence, the determination of$$\sin ^{2} \theta _{W}$$ and the updating of PDFs by directly using the same$$\sin ^{2} \theta _{W}$$ 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$$A_{FB}$$ on$$A_{FB}$$ is dominated by its average value around the$$\sin ^{2} \theta _{W}$$ Z pole region, while the shape (or gradient) of the spectrum is insensitive to$$A_{FB}$$ 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$$\sin ^{2} \theta _{W}$$ when updating the PDFs using the same$$\sin ^{2} \theta _{W}$$ data.$$A_{FB}$$