  We study the cross section \sigma and Forward-Backward asymmetry A_{FB} in
the process pp \to \gamma^*,Z \to \ell^+\ell^- (with \ell=e,\mu) for
determinations of Parton Distribution Functions (PDFs) of the proton. We show
that, once mapped in the invariant mass of the di-lepton final state,
M({\ell\ell}), both observables, \sigma and A_{FB}, display a statistical error
which is presently competitive with that assigned to the existing PDF sets and
which will rapidly become smaller than the latter as the luminosity being
accumulated at Run-II of the LHC grows. This statement is applicable to both
on-peak and off-peak M({\ell\ell}) regions, both (just) below and above it,
thereby offering a means of constraining the quark PDFs over a sizeable (x,Q^2)
range.
