  We consider two polarization asymmetries in the process of top-antitop
production at LHC. We show that the theoretical predictions for these two
quantities, at the strong and electroweak partonic one-loop level, are free of
QCD and QED effects. At this perturbative level we derive two sum rules, that
relate measurable quantities of top-antitop production to genuinely weak
inputs. This would allow to perform two independent tests of the candidate
theoretical model, with a precision that will be fixed by the future
experimental accuracies of the different polarization measurements. A tentative
quantitative illustration of this statement for a specific MSSM scenario is
enclosed, and a generalization to include two other future realistic
measurements is also proposed.
