  In this paper, some subtleties in the measurement of the transverse
polarization of the produced hadrons on symmetric colliders -- such as the
Large Hadron Collider when conducting the $pp$ collisions -- are revealed. It
can be proved that the transverse polarization of the produced particles with
opposite pseudorapidity takes exactly opposite values if the normal vector of
the production plane is defined in a convention-dependent way, regardless of
whether parity is conserved or not in the production process. The analysis
shows that, due to the symmetry of the initial state, the $\Lambda_b$
transverse polarization measured by the CMS collaboration in Phys. Rev. D 97,
072010 (2018) should be exactly equal to zero. A modified measurement of the
$\Lambda_b$ polarization for CMS and ATLAS is proposed, the result of which can
be compared to the LHCb measurement.
