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In this paper, some subtleties in the measurement of the transversepolarization of the produced hadrons on symmetric colliders -- such as theLarge Hadron Collider when conducting the $pp$ collisions -- are revealed. Itcan be proved that the transverse polarization of the produced particles withopposite pseudorapidity takes exactly opposite values if the normal vector ofthe production plane is defined in a convention-dependent way, regardless ofwhether parity is conserved or not in the production process. The analysisshows 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 canbe compared to the LHCb measurement.

How to measure the transverse polarization of the produced hadrons in a symmetric collider?