  We adopt a Markov Chain Monte Carlo method to examine various new physics
models which can generate the forward-backward asymmetry in top quark pair
production observed at the Tevatron by the CDF Collaboration. We study the
following new physics models: (1) exotic gluon $G^\prime$, (2) extra $Z^\prime$
boson with flavor-conserving interaction, (3) extra $Z^\prime$ with
flavor-violating $u$-$t$-$Z^\prime$ interaction, (4) extra $W^\prime$ with
flavor-violating $d$-$t$-$W^\prime$ interaction, and (5) extra scalars $S$ and
$S^\pm$ with flavor-violating $u$-$t$-$S$ and $d$-$t$-$S^\pm$ interactions.
After combining the forward-backward asymmetry with the measurement of the top
pair production cross section and the $t\bar{t}$ invariant mass distribution at
the Tevatron, we find that an axial vector exotic gluon $G^\prime$ of mass
about $1 {\rm TeV}$ or $2 {\rm TeV}$ or a $W^\prime$ of mass about $2 {\rm
TeV}$ offer an improvement over the Standard Model. The other models considered
do not fit the data significantly better than the Standard Model. We also
emphasize a few points which have been long ignored in the literature for new
physics searches: (1) heavy resonance width effects, (2) renormalization scale
dependence, and (3) NLO corrections to the $t\bar{t}$ invariant mass spectrum.
We argue that these three effects are crucial to test or exclude new physics
effects in the top quark pair asymmetry.
