theory top propagator in Eq.(\[toppropagator\]) which differs from the one for a stable particle. Likewise, the interference effects described by the absorptive electroweak matching conditions for the operators ${\cal O}_{V,{\mbox{\scriptsize\boldmath $p$}}}$ and ${\cal O}_{A,{\mbox{\scriptsize\boldmath $p$}}}$ would not have to be taken into account if the top quarks were stable particles. UV divergences of the same kind have already been observed and described before in the NNLL relativistic corrections to the S-wave zero-distance Green function if the unstable propagator in Eq.(\[toppropagator\]) is used [@hmst1; @HoangTeubnerdist; @HoangTeubner]. For the P-wave zero-distance Green function, which is generated by $t\bar t$ production through an axial-vector current from the Z-exchange and that contributes only at NNLL order, a similar UV divergence arises already at leading order in the non-relativistic expansion. Like for the case of the time dilatation corrections these divergences originate from the modified high energy behavior of the unstable top propagator. We believe it is evident that these divergences do not represent a deficiency of the effective theory, because the concept of separating resonant and non-resonant fluctuations appears to be the only practical way to make systematic predictions involving unstable particles. Thus these UV divergences should be handled with the renormalization techniques known 