Quantum coherence, top transverse polarisation and the Tevatron asymmetry $A_{FB}^\ell$

We revisit the relation between the asymmetries $A_{FB}$ and $A_{FB}^\ell$ in $t \bar t$ production at the Tevatron, using as new physics benchmark a colour octet. We find that $A_{FB}^\ell$ receives large contributions from the interference between $\lambda = \pm 1/2$ top helicity states, which has been ignored in some of the previous literature on the subject. The omission of these contributions results in a severe underestimation of the asymmetry, around $1/2$ and $1/50$ of the true value for right-handed and left-handed top couplings to the octet, respectively. Interference effects are closely related to a $\mathcal{O}(1)$ transverse top polarisation, as yet not considered in this context.