  The large cross sections for gauge boson production at the Fermilab Tevatron
and the CERN Large Hadron Collider (LHC) might give a chance to determine the
electroweak parameters with high precision. We calculated two different
forward-backward charge asymmetries (A^CS_FB and A^j_FB) of lepton pairs in
events with a large transverse momentum jet p p (pbar) -> Z, gamma* + j -> e-
e+ j at next-to-leading order (NLO), O(alpha_s) corrections, making use of the
Monte Carlo programs MCFM and ALPGEN. These observables could provide a new
determination of the weak mixing angle sin^2 theta^lept_eff (M_Z^2) with a
statistical precision for each lepton flavour of 10^{-3} (7 x 10^{-3}) at LHC
(Tevatron). If b jets are identified, a new asymmetry with respect to the b
quark (A^b_FB) can also be measured with a statistical precision of 2 x 10^{-3}
(4 x 10^{-2}) at LHC (Tevatron). Finally, we comment on the dependence of our
results on various sources of uncertainties and compare, in the case of A^b_FB,
the exact result with an approximation that might be more suitable when
performing a realistic experimental analysis.
