  We study the polarization of particles in relativistic heavy-ion collisions
at very high energy along the beam direction within a relativistic hydrodynamic
framework. We show that this component of the polarization decreases much
slower with center-of-mass energy compared to the transverse component, even in
the ideal longitudinal boost-invariant scenario with non-fluctuating initial
state, and that it can be measured by taking advantage of its quadrupole
structure in the transverse momentum plane. In the ideal longitudinal
boost-invariant scenario, the polarization is proportional to the gradient of
temperature at the hadronization and its measurement can provide important
information about the cooling rate of the Quark Gluon Plasma around the
critical temperature.
