Measurements of the forward-backward asymmetry in neutral-current Drell-Yan di-lepton production have primarily been used for determinations of the weak mixing angle $theta_W$. We observe that, unlike the case of Run-I of the Large Hadron Collider (LHC Run-I), for the first time at the LHC Run-II the reconstructed forward-backward asymmetry has the capability of placing useful constraints on the determination of the parton distribution functions (PDFs). By examining the statistical and the PDF uncertainties on the reconstructed forward-backward asymmetry, we investigate its potential for disentangling the flavour content of quark and antiquark PDFs. Access to the valence/sea $u$-quark and to the sea up-type antiquark PDFs, in particular, may be gained by the appropriate use of selection cuts in the rapidity of the emerging lepton pair in regions both near the $Z$-boson peak and away from it, in a manner complementary, though more indirect, to the case of the charged-current asymmetry. We study the extension of these results for the planned high-luminosity (HL) LHC.
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