  The measured forward-backward asymmetry in top pair events at the Fermilab
Tevatron collider deviates significantly from the standard model expectation.
Several models have been proposed to describe the observed asymmetry which
grows with the rapidity difference of the top pairs and also with the
$t\bar{t}$ invariant mass. The presence of a heavy charged gauge boson $W'$
with the coupling $W'-t-d$ (left-handed, right-handed, and a mixture of left
and right-handed couplings) could generate the desired top forward-backward
asymmetry keeping the top pair cross section consistent with the standard model
prediction. Such $W'$-boson makes contribution to the electric dipole moment of
the neutron through contribution to the $d$-quark electric dipole moment,
recently measured charge asymmetry ($A_{C}$) by the LHC experiments, and the
total cross section of top pair at the LHC and Tevatron. We show that the upper
bounds on neutron and top electric dipole moments disfavour any $W'$ with a
mass below 240 GeV which could explain the Tevatron forward-backward asymmetry.
It is shown that the charge asymmetry provides an allowed region in the
parameters space with no overlap with the allowed region where the asymmetry
could be described.
