  Pairs of top and antitop quarks are produced at the LHC to a large extent in
association with a hard jet. We investigate the charge asymmetry in top pair +
jet production in quantum chromodynamics (QCD) and with additional massive
color-octet vector bosons. The total charge asymmetry at the LHC is suppressed
by the large charge-symmetric background from gluon-gluon fusion. We show to
what extent the asymmetry can be enhanced by suitable phase space cuts and, in
particular, elaborate on the kinematics of the hard jet in the top pair + jet
final state. We demonstrate that in QCD, the asymmetry amounts to -1.5% for
central jets without an excessive reduction of the cross section. By applying
additional kinematical cuts, the asymmetry can be enhanced to -4%, but at the
cost of a strong reduction of the cross section. Massive color-octet states can
generate sizeable effects in top pair + jet production, both on the charge
asymmetry and on the cross section. The charge asymmetry probes both vector and
axial-vector couplings to quarks. We show that massive color octets can
generate asymmetries up to +-10% for moderate and up to +-30% for strong
kinematical cuts to be used in experimental analyses at the LHC. Jet kinematics
can be used to obtain further information about the nature of the couplings and
thereby to discriminate between different models.
