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