To visualize what kind of departure from the standard model we need to explain the Tevatron data, see the plot borrowed from this paper The plot shows a model independent fit to the Tevatron top results. The axes are the forward and backward production cross sections of top pairs with the high invariant mass, m_ttbar > 450 GeV. One can see that the cross sections has to be modified by some 10-20 percent, and that the best fit point corresponds to the backward cross section being smaller than the standard model one. This is possible if new physics contribution to the top pair production interferes destructively with that of QCD.
To modify the cross section one can introduce one or more particles beyond the standard model that mess up into the top production. The successful models have to satisfy 2 basic requirements:
- the new particle should not be too heavy and should couple strongly enough to both the 1st generation quarks and to the top quarks. Otherwise the effect would not show up on top of the QCD top pair production.
- the new particle should couple chirally, that is to say, with a different strength to left- and right-handed quarks. Otherwise it would not generate a forward-backward asymmetry.
- s-channel mediators,
- t-channel mediators,
- new particles decaying to tops
In the s-channel models the asymmetry is due to a resonance which can be produced in a q-qbar collision and decays to a pair of top quarks. An example of such a resonance is a Kaluza-Klein excitation of the gluon in Randall-Sundrum-type models, or more generally an axigluon in models where the standard model SU(3) color group is extended. This class is somewhat disfavored by experiment. Since the differential top production cross section measured at the Tevatron agrees very well with the standard model, the resonance has to be either very heavy or very wide. Furthermore, since the resonance has to couple strongly to the 1st generation quarks, it is constrained by the negative results from the LHC resonance and contact interaction searches in the dijet final state.
In the t-channel models the asymmetry is generated by an exchange of an off-shell particle that has a cubic vertex with one 1st generation and one top quark. There are many possibilities for the mediator: it could be a gauge boson or a scalar; electrically charged or neutral; a color triplet, sextet, sexist, octet, and so on. Some of these models survive all experimental constraints, although there is always some tension with the measured differential top production cross section. Another problem with this class is philosophical: the new particle has to have a large flavor violating coupling to the 1st and the 3rd generation, whereas similar couplings to the 1st and 2nd or to the 2nd and 3rd generations appear to be severely constrained by experiment. If any of these models corresponds to reality then some unexpected flavor structure is being revealed.
As for the last class mentioned above, I'm aware of only one model of that kind where a new color triplet scalar decays to a top quark plus a light invisible fermion. Sounds much like stop → top + neutralino, although the required couplings do not fit SUSY. As the new particle production cannot of course interfere with the QCD top production, this possibility is somewhat disfavored by the top cross section measurements. On the other hand, such a new particle can be very well disguised, especially when its mass is close to the top mass, and is currently poorly constrained by new physics searches.
So which model is true? If we're lucky the answer may already be in the 2010 LHC data; however very few top analyses has gone public so far. Otherwise we'll have to wait till the summer conferences. If the LHC continues at this pace we may have 1 inverse femtobarn to play with by that time.