  We consider the Z polarization asymmetry
A_Z=(sigma(Z_R)-sigma(Z_L))/(sigma(Z_R)+sigma(Z_L)) in the process of
associated bZ production at the LHC. We show that in the Standard Model (SM)
this quantity is essentially given by its Born approximation, remaining almost
unaffected by QCD scales and parton distribution functions variations as well
as by electroweak corrections. The theoretical quantity that appears in A_Z is
the same that provides the LEP1 Z -> b bbar forward-backward asymmetry, the
only measured observable still in some contradiction with the SM prediction. In
this sense, A_Z would provide the possibility of an independent verification of
the possible SM discrepancy, which could reach, if consistency with LEP1
measurements is imposed, values of the relative ten percent size.
