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Review on top forward-backward asymmetry

The top forward-backward asymmetry (FBA) observed at the Tevatron has been a hot issue in particle physics for the last few years. In this talk, I describe two different approaches for the top FBA at the Tevatron, one in effective field theory (EFT) approach and the other in explicit model for $Z'$. Within the first approach, I identify a class of models which can accommodate the top FBA when new physics scale is very heavy. Axigluon or $t$-channel scalar exchanges with flavor dependent couplings can do the job. In the second approach, I show that the chiral couplings of $Z'$ necessarily invites multi Higgs doublets with $Z'$ couplings. Otherwise the top quark becomes massless, which is completely unphysical. Newly introduced multi Higgs doublets also contribute to the top FBA, $σ_{tt}$ and the charge asymmetry at the LHC, and there are parameter regions which are compatible with all the observations related with the top quarks.